Proximal_policy_optimization_ITA.ipynb

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        "# Proximal policy optimization (PPO)\n",
        "\n",
        "Mario Fiorino\n",
        "\n",
        "$\\;$\n",
        "\n",
        "Gli algoritmi basati su tecniche di *Policy Gradient* sono un'area di ricerca molto attiva, con numerosi sviluppi negli ultimi anni. Tra questi Proximal Policy Optimization (PPO) risulta attualmente (anno 2025) tra i più usati per scopi applicativi. A riguardo OpenAI scrive:\n",
        "\n",
        "*Proximal Policy Optimization (PPO), which perform comparably or better than state-of-the-art approaches while being much simpler to implement and tune. PPO has become the default reinforcement learning algorithm at OpenAI because of its ease of use and good performance.*\n",
        "https://openai.com/index/openai-baselines-ppo/\n",
        "\n",
        "$\\;$\n",
        "\n",
        "Avviso ai naviganti:\n",
        "\n",
        "Per una comprensione dei concetti in questo notebook, si raccomanda ai lettori di prendere visione dei precedenti notebook dedicati alla tematica del Policy Gradient.\n",
        "Può essere utile ricordare che i metodi definiti *Policy Gradient* sono algoritmi che utilizzano approssimatori parametrizzati, ovvero modelli matematici, per rappresentare le funzioni per la policy. I parametri di tali modelli vengono aggiornati iterativamente attraverso il metodo *Gradient ascent*, con l'obiettivo di massimizzare il *Return*."
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        "#### Ref.\n",
        "\n",
        "PPO: [J. Schulman et al., \"Proximal Policy Optimization Algorithms.\" arXiv preprint arXiv:1707.06347, 2017.](https://arxiv.org/abs/1707.06347.pdf)\n",
        "\n",
        "TRPO: [Schulman, John, et al. \"Trust region policy optimization.\" International conference on machine learning. 2015.](http://proceedings.mlr.press/v37/schulman15.pdf)\n",
        "\n",
        "Spinning Up - OpenAI :\n",
        "\n",
        "https://spinningup.openai.com/en/latest/algorithms/trpo.html\n",
        "\n",
        "https://spinningup.openai.com/en/latest/algorithms/ppo.html\n",
        "\n",
        "Foundations of Reinforcement Learning: https://wensun.github.io/CS6789.html\n",
        "\n",
        "Berkeley slide di Joshua Achiam:\n",
        "https://rail.eecs.berkeley.edu/deeprlcourse-fa17/f17docs/lecture_13_advanced_pg.pdf\n",
        "\n",
        "Foundations of Deep Reinforcement Learning: Theory and Practice in Python di Laura Graesser, Wah Loon Keng"
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        "### Alcune premesse\n",
        "\n",
        "**Notazioni**\n",
        "$\\;$\n",
        "\n",
        "$P \\{X = x\\}$ : probabilità che una variabile aleatoria $X$ assuma uno specifico valore (detto campione) $x$.  \n",
        "\n",
        "$\\;$\n",
        "\n",
        "$X \\sim p$: la variabile aleatoria $X$ è distribuita secondo la distribuzione di probabilità  $p$. In altre parole, un campione di $X$ viene estratto da una distribuzione con funzione di probabilità $p$.\n",
        "\n",
        "$\\;$\n",
        "\n",
        "$\\mathbb{E}[X]$: valore atteso o expectation di una variabile aleatoria \\(X\\), cioè  $ \\mathbb{E}[X] = \\sum_x p(x)x $\n",
        "\n",
        "In pratica l'expectation, non è altro che un numero che rappresenta la media dei possibili valori che una variabile aleatoria può assumere, ciascuno ponderato in base alla probabilità di uscita. Ad esempio il valore atteso di una sola estrazione tra 3 premi rispettivamente di $\\{5, 20, 50 \\}$ euro, con pari probabilità di uscita $(1/3)$, è di $ 25 $ euro. Se la probabilità di $5$ euro è $1/2$ e gli altri due di $1/4$ ; allora il valore atteso è:\n",
        "$E(X) = (5 \\times \\frac{1}{2}) + (20 \\times \\frac{1}{4}) + (50 \\times \\frac{1}{4}) = 20$ euro\n",
        "\n",
        "$\\;$\n",
        "\n",
        "$\\arg\\max_a f(a) ≡$ valore di $a$ per cui $f(a)$ raggiunge il suo massimo.\n",
        "\n",
        "$\\;$\n",
        "\n",
        "$\\pi (a | s)$ definisce la probabilità di selezionare il valore $a$, dato come noto $s$.\n",
        "$\\;$"
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        "**Markov State Distributions**\n",
        "\n",
        "Una *Markov Chain*, o processo di Markov, è un modello che descrive una sequenza di possibili eventi, dove la probabilità di ogni evento dipende esclusivamente dallo stato del sistema all'istante precedente.\n",
        "\n",
        "Le *Markov State Distributions* descrivono la probabilità di trovare il sistema in un determinato stato in un dato momento.\n",
        "\n",
        "Consideriamo un processo di Markov; una sequenza di $n$ variabili aleatorie $ [ X_0, X_1, ... , X_n ] $ , dove lo spazio degli esiti per ogni  $X_i$ è definito come $S = \\{1, 2, 3, \\dots,r\\} $\n",
        "\n",
        "Supponiamo di conoscere la distribuzione di probabilità iniziale $X_0$. Più precisamente, definiamo il vettore riga $d_{X_0}$ come  \n",
        "\n",
        "$d_{X_0} = [P(X_0=1), \\quad P(X_0=2), \\quad \\dots \\quad , P(X_0=r)] $\n",
        "\n",
        "Come possiamo ricavare la distribuzione di probabilità di $X_1, X_2, \\dots$? Possiamo utilizzare la legge della probabilità totale.\n",
        "\n",
        "Più precisamente, per ogni campione $ j \\in S$ :  \n",
        "\n",
        "$P(X_1 = j) = \\sum_{k=1}^{r} P(X_1 = j \\mid X_0 = k) P(X_0 = k) = \\sum_{k=1}^{r} T_{kj} P(X_0 = k)$\n",
        "\n",
        "dove $T$ è la matrice di transizione degli stati o anche detta *transition probabilities*.\n",
        "\n",
        "In formula sintetica si riduce al prodotto riga colonna tra vettore e matrice:\n",
        "\n",
        "$d_{X_1} = d_{X_0} \\; T$\n",
        "\n",
        "Più in generale, ad un certo istante $n$, per ricavare il vettore\n",
        "\n",
        "$d_{X_n} = [P(X_n=1), \\quad P(X_n=2), \\quad \\dots \\quad , P(X_n=r)] $\n",
        "\n",
        "abbiamo:\n",
        "\n",
        "$d_{X_n} = d_{X_0} \\; T^{n} $\n",
        "\n",
        "$\\;$\n",
        "\n",
        "Esempio\n",
        "\n",
        "Consideriamo un sistema che può trovarsi in uno dei due possibili stati, $ S = \\{0,1\\} $. In particolare, supponiamo che la matrice di transizione sia data da  \n",
        "\n",
        "$T = \\begin{bmatrix} \\frac{1}{2} & \\frac{1}{2} \\\\ \\frac{1}{3} & \\frac{2}{3} \\end{bmatrix}.$\n",
        "\n",
        "Le righe indicizzano lo stato corrente, le colonne indicizzano gli stati futuri. Ad esempio, per $T_{[1,0]} = \\frac{1}{3}$ stiamo dicendo che partiamo dallo stato $1$ per cambiare nello stato $0$, e che questa transizione ha probabilità $\\frac{1}{3}$. Per $T_{[1,1]} = \\frac{2}{3}$ stiamo dicendo che la probabilità di restare nello stato $1$ e pari a $\\frac{2}{3}$.\n",
        "\n",
        "Supponiamo inoltre che il sistema si trovi nello stato $0$ al tempo $n = 0$; come ricavare la probabilità che il sistema sia nello stato $1$ al tempo $n=3$ ?\n",
        "\n",
        "Noi sappiamo che lo stato del sistema iniziale è $X_0 = 0$, quindi la distribuzione di probabilità iniziale $X_0$:\n",
        "\n",
        "$ d_{X_0} = [P(X_0 = 0) , \\quad P(X_0 = 1)] = [1 , \\quad 0]$\n",
        "\n",
        "Applicanso la formula:\n",
        "  \n",
        "\n",
        "$d_{X_3} = d_{X_0} \\; T^3 = [1 \\quad 0] \\begin{bmatrix} \\frac{1}{2} & \\frac{1}{2} \\\\ \\frac{1}{3} & \\frac{2}{3} \\end{bmatrix}^3 = \\left[ \\frac{29}{72} \\quad \\frac{43}{72} \\right]$\n",
        "\n",
        "Di conseguenza, la probabilità che il sistema si trovi nello stato $1$ al tempo $n=3$ è $\\frac{43}{72}$. (Mentre nello stato $0$ è $\\frac{29}{72}$)\n",
        "\n",
        "Ref.\n",
        "\n",
        "https://www.probabilitycourse.com/chapter11/11_2_3_probability_distributions.php"
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        "**Discounted future state distribution**\n",
        "\n",
        "Introduciamo la definizione di *discounted future state distribution* (o *discounted state distribution*)  per una data policy $\\pi$, cioè:\n",
        "\n",
        "$∀s \\in S$,\n",
        "\n",
        "$d^{\\pi}(s) = (1 - \\gamma) \\sum_{k=0}^{\\infty}  \\;\n",
        " \\gamma^k \\; P(s_k = s| \\pi) \\;$\n",
        "\n",
        "Sia $S$ l'insieme di tutti gli stati campionabili del sistema.\n",
        "\n",
        "Sia $\\gamma \\in (0,1)$ il fattore di discount, allora la serie geometrica $\\sum_{k=0}^{\\infty}  \\gamma^k$ converge a $\\frac{1}{(1 - \\gamma)}$, e il fattore $(1 - \\gamma)$ è da considerarsi un fattore di normalizzazione.\n",
        "\n",
        "Sia $P(s_k = s| \\pi)$ la probabilità di trovarsi (o ritrovarsi) in un certo stato $s$, al tempo $k$, seguendo una certa la policy $𝜋$.\n",
        "\n",
        "In sostanza, la distribuzione $d^{\\pi}(s)$ tiene conto del fatto che un certo stato $s$ possa essere visitato più volte in istanti di tempo differenti, seguendo una determinata policy $\\pi$.\n",
        "Con questa definizione, agli stati prossimi a quello di partenza, con $k=0$, viene dato un peso maggiore.\n",
        "\n",
        "Questa definizione rientra nell'ambito del *discounted weighting of states* ; vedi il lavoro di tesi di dottorato di Bacon 2018: https://pierrelucbacon.com/bacon2018thesis.pdf\n",
        "\n",
        "Note:\n",
        "\n",
        "1.\n",
        "\n",
        "Perchè introduciamo il fattore di discount $\\gamma$ nella ditribuzione degli stati?  In un processo decisionale di Markov con orizzonte infinito, il numero di volte in cui uno stato può essere visitato puo crescere indefinitamente. Introducendo il fattore $\\gamma$ ci assicuriamo che la somma totale rimanga finita, con un valore $\\le 1$. Per tanto il fattore discount, può essere pensato come una forma di \"terminazione del episodio su scenari ad orizzonte infinito\".\n",
        "\n",
        "Maggiori info: https://ai.stackexchange.com/questions/27172/why-do-we-discount-the-state-distribution\n",
        "\n",
        "2.\n",
        "\n",
        "Come ricaviamo una distribuzione del genere dato che è implicitamente definita dalle dinamiche ambientali e dalla policy. Semplicemente eseguendo un *roll-out* secondo la policy $\\pi$ per un tempo sufficientemente lungo, si otterrà un campionamento degli stati dalla distribuzione  $d^{\\pi}$.\n",
        "\n",
        "$\\;$"
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        "## Problema: come gestire efficacemente l’update dei parametri della policy ?\n",
        "\n",
        "Ovvero, come trovare lo *step-size* di aggiornamento massimo possibile (utilizzando i dati disponibili) senza compromettere le prestazioni ?  \n",
        "\n",
        "Nei metodi policy gradient, l' update dei parametri $θ$ che caratterizzano la policy segue l'equazione:\n",
        "\n",
        "$∆θ = α∇_θ J(π_θ)$\n",
        "\n",
        "Va evidenziato che lo spazio delle policy e lo spazio dei parametri non sempre presentano una corrispondenza biunivoca, nel senso che una stessa distanza tra parametri non implica una distanza equivalente tra le rispettive policy; in ternimi matematici si dice che il *mapping è non-isometrico*.\n",
        "\n",
        "Mi spiego: si considerino due coppie di parametri, denotate con $(\\theta_1, \\theta_2)$ e $(\\theta_2, \\theta_3)$, e si assuma che esse presentino la medesima distanza (ad esempio una distanza euclidea) nello spazio dei parametri, ovvero $D_{\\theta}(\\theta_1, \\theta_2) = D_{\\theta}(\\theta_2, \\theta_3)$. Tuttavia, le policy corrispondenti, mappate rispettivamente come $(\\pi_{\\theta_1}, \\pi_{\\theta_2})$ e $(\\pi_{\\theta_2}, \\pi_{\\theta_3})$, potrebbero non rispettare la stessa relazione di distanza quando si considera le loro performance, misurata ad esempio attraverso il *Return* ottenuto.\n",
        "\n",
        "In simboli:\n",
        "$D_{\\theta}(\\theta_1, \\theta_2) = D_{\\theta}(\\theta_2, \\theta_3) \\not\\Leftrightarrow D_R(π_{θ_1}, π_{θ_2}) = D_R(π_{θ_2}, π_{θ_3})$\n",
        "\n",
        "In altre parole, variazioni anche minime nei parametri possono indurre differenze significative nelle prestazioni della policy. Ciò implica che un aggiornamento non adeguatamente controllato può portare a un deterioramento della performance (*performance collapse*)\n",
        "\n",
        "Definiamo una metrica, o volendo una distanza nello spazio delle policy, che valuti la differenza di performance tra due policy.\n",
        "\n",
        "**Relative policy performance identity**:\n",
        "\n",
        "$ J(\\pi') - J(\\pi) =  \\mathbb{E}_{\\tau \\sim {\\pi'}} \\bigg[ \\sum_{t=0} ^T \\gamma^t \\; A^{\\pi}(s_t, a_t) \\bigg]$\n",
        "\n",
        "per ogni policy $π$, e $π'$.\n",
        "\n",
        "Si osservi che questa metrica mette in relazione le prestazione di $π'$ con la funzione Advantage di $π$\n",
        "\n",
        "Supponiamo ora di avere una policy $ \\pi $, e che, a seguito di un aggiornamento dei parametri $ \\theta $, la sua successiva iterazione sia rappresentata da $\\pi'$. Con questa assunzione è possibile osservare alcune proprietà di interessanti. In tal caso infatti,La *relative policy performance identity*, $J(\\pi') - J(\\pi)$, funge da metrica per quantificare i miglioramenti apportati a una pocily. Un valore positivo di tale differenza indica che la nuova policy, $\\pi'$, produce prestazioni migliori della policy precedente, $\\pi$. Durante un processo di training, l'obiettivo ideale consiste nel selezionare una nuova politica, $\\pi'$, che consente di massimizzare tale differenza ad ogni step di aggiornamento dei paramentri. Di conseguenza, massimizzare l'*objective function* $J(\\pi')$ equivale a massimizzare questa identità, ovvero:\n",
        "\n",
        "$\\max\\limits_{\\pi'} \\bigg( J(\\pi') - J(\\pi) \\bigg) $\n",
        "\n",
        "\n",
        "**Idea di fondo**\n",
        "\n",
        "Impostare il problema della ricerca di una policy ottimale in modo tale da massimizza tale identità, implica che ogni iterazione della policy debba garantire un miglioramento non negativo (monotono), ovvero, $J(\\pi) - J(\\pi') \\geq 0$; poiché, nel caso peggiore, si può semplicemente porre $\\pi = \\pi'$ (ed ottenere un miglioramento pari a $0$).  Questo consente di evitare crolli di performance durante l'addestramento (*performance collapse*).\n",
        "\n",
        "Un limite di questa formulazione è la necessità di traiettorie campionate dalla nuova policy $ \\pi'$ (vedi: Expectation : ${\\tau \\sim {\\pi'}}$), le quali non sono disponibili prima dell'aggiornamento."
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        "Che fare?\n",
        "\n",
        "Si consideri:\n",
        "\n",
        "- la *relative policy performance identity*:\n",
        " $J(\\pi_0) - J(\\pi) = \\mathbb{E}_{\\tau \\sim {\\pi'}} \\bigg[ \\sum_{t=0} ^∞ \\gamma^t \\; A^{\\pi}(s_t, a_t) \\bigg] $\n",
        "\n",
        "- la distribuzione di probabilità degli stati per una data policy $\\pi$;  ad esempio nelle premesse, abbiamo definito la  *discounted future state distribution* per una certa policy $\\pi$, ed indicata con $d^{\\pi}(\\cdot)$\n",
        "\n",
        "\n",
        "Sfruttando:\n",
        "\n",
        "- la proprietà di linearità dell'expectation (cioè: $E[a_1 X_1 + a_2 X_2  + ... + a_n X_n ]=a_1 E[X_1]+ a_2 E[X_2] + ... +  a_n E[X_n]$); invece di esprimere l'expectation sull'intera traiettoria, possiamo riscrivere l'expectation come una somma su singoli step temporali\n",
        "\n",
        "- per $\\gamma \\in (0,1)$ , la serie geometria è convergente $\\sum_{t=0}^{\\infty} \\gamma^t = \\frac{1}{1-\\gamma}$,\n",
        "\n",
        "possiamo scrivere:\n",
        "\n",
        "$\\mathbb{E}_{\\tau \\sim \\pi'} \\left[ \\sum_{t=0}^{\\infty} \\gamma^t A^{\\pi} (s_t, a_t) \\right] = \\frac{1}{1 - \\gamma} \\mathbb{E}_{s \\sim d^{\\pi'},{\\;a \\sim \\pi'(\\cdot | s)}}  \\left[  A^{\\pi}(s, a) \\right] $\n",
        "\n",
        "per maggior chiarezza, espandendo l'expectation:\n",
        "\n",
        "$\\mathbb{E}_{\\tau \\sim \\pi'} \\left[ \\sum_{t=0}^{\\infty} \\gamma^t A^{\\pi} (s_t, a_t) \\right] =  \\frac{1}{1 - \\gamma} \\sum_{s} d^{\\pi'}(s) \\sum_{a} \\pi'(a | s) A^{\\pi}(s, a) $\n",
        "\n",
        "Esiste una limitazione che impedisce l'impiego di questa espressione come funzione obiettivo, cioè per ottmizzare i parametri della \"nuova\" policy $\\pi'$. Per effettuare un aggiornamento, essa richiede che le traiettorie siano campionate dalla \"nuova\" politica da ricavare. Chiaramente, questa risulta non disponibile fino a dopo che l'aggiornamento sia stato completato...\n",
        "\n",
        "Proviamo a risolvere la cosa usando le informazione disponibili, ovvero la \"vecchia\" policy $\\pi$.\n",
        "\n",
        "Riscriviamo l'identità relativa della performance, sfruttando il *weighted importance sampling* (in pratica: un metodo utilizzato per ricavare uno stimatore, nel nostro caso il valore atteso, di una distribuzione, generando campioni da una distribuzione diversa, ma nota), ovvero:\n",
        "\n",
        "$ \\frac{1}{1 - \\gamma} \\mathbb{E}_{s_t \\sim d^{\\pi'},{\\;a_t \\sim \\pi'}}  \\left[  A^{\\pi}(s, a) \\right] = \\frac{1}{1 - \\gamma} \\mathbb{E}_{s \\sim d^{\\pi'},{\\;a \\sim \\pi}}  \\left[ \\frac{\\pi'(a|s)}{\\pi(a|s)} A^{\\pi}(s, a) \\right] $\n",
        "\n",
        "Questa formula pesa i valori della funzione Advance, generati utilizzando la distribuzione $\\pi$,  mediante il rapporto delle probabilità di azione tra le due policy successive, $\\pi$ e $\\pi'$.  \n",
        "\n",
        "L' unico problema rimane $s \\sim d^{\\pi'}$.\n",
        "\n",
        "Se attuiamo una approssimazione del tipo $d^{\\pi'} \\approx d^{\\pi}$, assmuniamo che policy successive $\\pi$ e $\\pi'$ siano relativamente vicine; si noti ciò può essere misurato usando la divergenza KL. Quanto devono essere vicine affinche la cosa funzioni è una bella domanda che vederemo dopo.\n",
        "Al momento tale approssimazione ci permette di scrivere:\n",
        "\n",
        "$ J(\\pi') - J(\\pi)  ≈ \\frac{1}{1 - \\gamma} \\mathbb{E}_{s \\sim d^{\\pi},{\\;a \\sim \\pi}}  \\left[ \\frac{\\pi'(a|s)}{\\pi(a|s)} A^{\\pi}(s, a) \\right] = \\mathbb{E}_{\\tau \\sim \\pi} \\left[ \\sum_{t=0}^{\\infty} \\gamma^t \\frac{\\pi'(a_t|s_t)}{\\pi(a_t|s_t)} A^{\\pi}(s_t, a_t) \\right] $\n",
        "\n",
        "e definire il **surrogate objective**, detto anche *surrogate advantage* :\n",
        "\n",
        "$ J^{CPI} (\\pi, \\pi') = \\mathbb{E}_{\\tau \\sim \\pi} \\left[ \\sum_{t=0}^{\\infty} \\gamma^t \\frac{\\pi'(a_t|s_t)}{\\pi(a_t|s_t)} A^{\\pi}(s_t, a_t) \\right]$\n",
        "\n",
        "Dove CPI sta per *conservative policy iteration*.\n",
        "\n",
        "Si noti, $J^{CPI} (\\pi, \\pi')$ è qualcosa su cui possiamo lavorare per ottmizzare i parametri $\\theta$ della nuova policy $\\pi'$; usando infomazioni campionate dalla \"vecchia\" policy $π$.\n",
        "\n",
        "Si noti anche, a differenza dell'importance sampling classico, il \"peso\" usato, cioè : $ \\frac{\\pi'(a|s)}{\\pi(a|s)}$, dipende solo dal time-step corrente, e non dall'intera storia precedente (in pratica non c'è una produttoria che accumula i vari time step - vedi importance sampling ratio). Questo permette di evitare che tale \"peso\" produca valori estremamente grandi o piccoli, complessi da gestire.\n",
        "\n",
        "Appendice.\n",
        "\n",
        "Al fine di una maggior chiarezza, espandendo expectation sulle traiettorie $\\tau = (s_0, a_0, s_1, a_1, \\dots)$, otteniamo:\n",
        "\n",
        "$ J^{CPI} (\\pi, \\pi') = \\sum_{\\tau}  P(\\tau | \\pi) \\sum_{t=0}^{\\infty} \\gamma^t \\frac{\\pi'(a_t | s_t)}{\\pi(a_t | s_t)} A^{\\pi}(s_t, a_t)  $\n",
        "\n",
        "dove $P(\\tau | \\pi)$ è la probabilità che una certa traiettoria $\\tau$ si campionata da $\\pi$; che può essere ulteriorimente fattorizzata come: $P(\\tau \\mid \\pi) = \\rho_0 (s_0) \\prod_{t=0}^{\\infty} Pr(s_{t+1} \\mid s_t, a_t) \\pi(a_t \\mid s_t)$\n",
        "\n",
        "In cui $s_0$ viene campionato randomly dalla *start-state distribution*, indicata con $\\rho_0$.\n",
        "\n",
        "$\\;$"
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        "Adesso, l'idea di base è usare il *surrogate objective* come funzione obiettivo al fine di ottimizzare i parametri attraverso l'algoritmo di gradient ascent, garantendo al contempo una gestione stabile dell'update (i.e. un miglioramento monotono delle prestazioni) durante la fase di training.\n",
        "\n",
        "C'è una proprietà interessante di cui gode il *surrogate objective* e che supporta la nostra idea di base, ovvero che il suo gradiente, valutando l'espressione in $θ = θ_{old}$,  è uguale al gradiente della policy:\n",
        "\n",
        "$\\nabla_\\theta J^{CPI} (\\theta_{old},\\theta) = \\nabla_\\theta J(\\pi_\\theta)$\n",
        "\n",
        "Inoltre, il *surrogate objective* puo pensarsi come un'approssimazione lineare di $J(\\pi') - J(\\pi)$, poiché le loro derivate di primo ordine coincidono.\n",
        "\n",
        "Torniamo un momento alla questione lasciata in sospeso, quanto devono essere vicine policy  $π$  e  $π′$ (o l'approssimazione  $d^{π'}≈d^π$) , affiche la *surrogate objective* sia un approssimazione accetabile.\n",
        "\n",
        "Per avere una misura di questa vicinanza introduciamo il **relative policy performance bound**\n",
        "\n",
        "$| ( J(\\pi') - J(\\pi) ) - J^{CPI} (\\pi, \\pi')  | \\; \\leq \\;  C \\; \\; \\sqrt{ \\mathbb{E}_{s \\sim d^\\pi} \\bigg[ D_{KL} (\\pi'|| \\pi )[s] \\bigg] } $\n",
        "\n",
        "Dove $D_{KL}(\\pi' || \\pi)[s]$: è la *Kullback-Leibler (KL) divergence* tra le policy $\\pi'$ e $\\pi$ nello state $s$. In formula:\n",
        "\n",
        "$D_{KL}(\\pi' || \\pi)[s] = \\sum_{a} \\pi'(a|s) \\log \\frac{\\pi'(a|s)}{\\pi(a|s)}$\n",
        "\n",
        "con sommatoria su tutte le possibili azioni $a$ in un certo stato $s$.\n",
        "\n",
        "$C$ è una costante che deve essere opportunamente determinata\n",
        "\n",
        "Riscirvendola in modo da esplicitare le sue caratteristiche:\n",
        "\n",
        "$ J^{CPI} (\\pi, \\pi') - C \\sqrt{\\mathbb{E}_{s \\sim d^\\pi} \\left[ D_{KL}(\\pi' || \\pi)[s] \\right]} \\leq J(\\pi') - J(\\pi)  \\leq  J^{CPI} (\\pi, \\pi') + C \\sqrt{\\mathbb{E}_{s \\sim d^\\pi} \\left[ D_{KL}(\\pi' || \\pi)[s] \\right]} $\n",
        "\n",
        "In pratica il *relative policy performance bound* afferma che la differenza di performance tra una nuova policy $\\pi'$ e la vecchia policy $\\pi$ è limitata (*bounded*) da un termine che dipende dalla divergenza KL tra le due policy.\n",
        "\n",
        "A fine di accettare una modifica alla policy, la stima  $J^{CPI} (\\pi, \\pi')$  di $J(\\pi') - J(\\pi)$,  deve essere contenuta nell'errore: $C \\sqrt{\\mathbb{E}_{s \\sim d^\\pi} \\left[ D_{KL}(\\pi' || \\pi)[s] \\right]}$\n",
        "\n",
        "Se inseriamo questi vincoli (*error bound*) nel nostro problema di ottimizzazione, possiamo garantire un miglioramento monotono della policy; in simboli:\n",
        "\n",
        "$\\underset{\\pi'}{\\operatorname{arg max}} \\bigg( J^{CPI} (\\pi, \\pi') - C \\sqrt{ \\mathbb{E}_{s \\sim d^\\pi}  D_{KL}(\\pi' || \\pi)[s]} \\bigg) \\Rightarrow J(\\pi') - J(\\pi) \\geq 0$\n",
        "\n",
        "E' fondamentale notare è che un miglioramento monotono **non garantisce la convergenza a una politicy ottimale**\n",
        "\n",
        "L'ottimizzazione della politica può comunque rimanere bloccata in un massimo locale in cui ogni iterazione della politica non produce alcun miglioramento, in pratica $J(\\pi') - J(\\pi) = 0$.\n",
        "\n",
        "Garantire la convergenza rimane un problema aperto complesso."
      ],
      "metadata": {
        "id": "4TdjZD2M-q00"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Come formulare questa condizione di vincolo nella nostra procedura di ottimizzazione?\n",
        "\n",
        "Una possibile strategia consiste nel limitare in modo diretto l'expectation della divergenza di KL:\n",
        "\n",
        "$\\mathbb{E}_{s \\sim d^\\pi} D_{KL}(\\pi' || \\pi)[s] \\leq δ$\n",
        "\n",
        "Il parametro $δ$ limita l'ampiezza della divergenza di KL, restringendo così la distanza con cui una nuova policy rispetto alla policy precedente. Questo intervallo è denominato **Trust Region**, e la disuguaglianza prima scritta è nota come **vincolo di trust region**.\n",
        "\n",
        "Si osservi che $δ$  è un iperparametro che deve essere opportunamente regolato.\n",
        "\n",
        "$\\;$"
      ],
      "metadata": {
        "id": "7FYHZFQ638Lf"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Concludendo**\n",
        "\n",
        "$\\theta_{k+1} = \\arg \\max_\\limits{\\theta} \\; \\mathbb{E}_{\\tau \\sim \\pi_{\\theta_{k}}} \\left[ \\sum_{t=0}^{\\infty} \\gamma^t \\frac{\\pi_{\\theta}(a_t|s_t)}{\\pi_{\\theta_{k}}(a_t|s_t)} A^{\\pi_{\\theta_{k}}}(s_t, a_t) \\right] $\n",
        "\n",
        "${subject\\;to\\; the\\; constraints \\;:\\;}  \\mathbb{E}_{s \\sim \\pi_{\\theta_k}} \\bigg[{ D_{KL}\\left(\\pi_{\\theta}(\\cdot|s) || \\pi_{\\theta_k} (\\cdot|s) \\right)} \\bigg] \\leq δ$\n",
        "\n",
        "La formula sopra è detta : **Trust Region Policy Optimization(TRPO) update**.\n",
        "\n",
        "Lo scopo è trovare i valori di $θ$ che massimizzano la funzione obiettivo $J^{CPI} (\\pi_{\\theta_{k}},\\pi_{\\theta})$, ma considerando solo i valori di $θ$ che soddisfano la condizione di vincolo di trust region.\n",
        "\n",
        "Finché le modifiche alla policy rimangono all'interno della trust region, è possibile evitare un deterioramento delle prestazioni (*performance collapse*)\n",
        "\n",
        "Si noti:\n",
        "\n",
        "1.\n",
        "\n",
        "$\\mathbb{E}_{s \\sim \\pi_{\\theta_k}} \\left[ D_{KL}\\left(\\pi_{\\theta}(\\cdot|s) || \\pi_{\\theta_k} (\\cdot|s) \\right) \\right]$ rappresenta la divergenza KL media tra le politiche $\\pi_{\\theta}$ e $\\pi_{\\theta_k}$, ponderata sulla distribuzione degli stati visitati dalla vecchia policy $\\pi_{\\theta_k}$.\n",
        "\n",
        "2.\n",
        "\n",
        "L'idea fondamentale risiede nell'utilizzo di $J^{CPI} (\\pi_{\\theta_{k}},\\pi_{\\theta})$ come un'approssimazione di $J(\\pi_{\\theta}) - J(\\pi_{\\theta_{k}})$, campionando dati dalla policy disponibile $\\pi_{\\theta_k}$. L' introduzione di tale approssimazione comporta inevitabilmente l'insorgere di un errore. Tuttavia, è possibile definire un limite per tale errore: trasformando questo limite in un vincolo nell'ambito del problema di ottimizzazione."
      ],
      "metadata": {
        "id": "hnIZ777h0p1H"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Proximal Policy Optimization, algoritmo\n",
        "\n",
        "Diversi algoritmi sono stati proposti per risolvere il problema di ottimizzazione con vincoli di trust region. Tra questi:  *Natural Policy Gradient (NPG)* , il *Trust Region Policy Optimization (TRPO)*  e il *Constrained Policy Optimization (CPO)*, *Proximal Policy Optimization (PPO)*.\n",
        "\n",
        "PPO rappresenta un approccio di facile implementazione, con un costo computazionale basso, e privo della necessità di selezionare il parametro $\\delta$.\n",
        "\n",
        "Per queste ragioni, non solo è divenuto uno degli algoritmi di riferimento per la risoluzione di problemi di ottimizzazione vincolata trust region, ma anche uno dei metodi più diffusi nell'ambito dei policy gradient\n",
        "\n",
        "Esistono due principali varianti dell'algoritmo PPO:\n",
        "\n",
        "1.\n",
        "\n",
        "La variante **PPO-KL-Penalty** converte la *constraint* sulla KL-divergence: $\\mathbb{E}_t [ D_{KL} (\\pi_{\\theta} (a_t | s_t) || \\pi_{\\theta_{\\text{k}}} (a_t | s_t))] \\leq \\delta $, in una penalizzazione ( che scoraggia la nuova policy dallo discostarsi troppo da quella vecchia ${\\pi_{\\theta_{\\text{k}}}}$) adattiva, che viene sottratta al *importance-weighted advantage*:\n",
        "\n",
        "$ \\arg \\max_\\limits{\\theta} \\; \\mathbb{E}_t \\left[ \\frac{\\pi_{\\theta} (a_t | s_t)}{\\pi_{\\theta_{\\text{k}}} (a_t | s_t)} A^{\\pi_{\\theta_{\\text{k}}}} (a_t , s_t) - \\beta \\; D_{KL}\\left(\\pi_{\\theta}(a_t | s_t) || \\pi_{\\theta_{\\text{k}}} (a_t | s_t) \\right) \\right] $\n",
        "\n",
        "dove $\\beta$ è il coefficiente che controlla le dimensione della penalizzazione sulla KL-divergence. Il suo valore viene automaticamente calibrato nel corso dell'addestramento usando metodi euristici (*heuristic-based update rule*), non derivanti cioè da da principi teorico-matematici. Per maggiori info applicative vedi il paper: J. Schulman et al., \"Proximal Policy Optimization Algorithms\"\n",
        "\n",
        "2.\n",
        "\n",
        "La variante **PPO-Clip**, invece, non include alcun termine di KL-divergence nella funzione obiettivo, ma sostituisce il vincolo sulla KL-divergence con una tecnica detta di clipping:\n",
        "\n",
        "$ \\arg \\max_\\limits{\\theta} \\; \\mathbb{E}_t \\bigg[ \\min\\left( \\frac{\\pi_{\\theta}(a|s)}{\\pi_{\\theta_k}(a|s)} A^{\\pi_{\\theta_k}}(s,a), \\ \\text{clip}\\left(\\frac{\\pi_{\\theta}(a|s)}{\\pi_{\\theta_k}(a|s)}, 1 - \\epsilon, 1+\\epsilon \\right) A^{\\pi_{\\theta_k}}(s,a) \\right)  \\bigg] $\n",
        "\n",
        "$\\epsilon$ è un iperparametro che deve essere messo a punto, e può essere ridotto progressivamente durante l'addestramento.\n",
        "\n",
        "Il primo termine all'interno dell'operatore $\\min(\\cdot)$ corrisponde semplicemente all' *surrogate objective* $J^{CPI}$ . Il secondo termine, $\\text{clip} (...)$, vincola il valore di $J^{CPI}$ all'intervallo $[(1 - \\epsilon) A^{\\pi_{\\theta_k}}(s,a), (1 + \\epsilon) A^{\\pi_{\\theta_k}}(s,a)]$.  \n",
        "\n",
        "In pratica, se il rapporto $\\frac{\\pi_{\\theta}(a|s)}{\\pi_{\\theta_k}(a|s)}$ assume valori al di fuori dell'intervallo $[1 - \\epsilon, 1 + \\epsilon]$, l'operatore di clipping $\\text{clip}(\\cdot)$ fornirà in uscita $(1 - \\epsilon) A^{\\pi_{\\theta_k}}(s,a)$ nel caso di valori inferiori al limite inferiore $1 - \\epsilon$, mentre restituirà $(1 + \\epsilon) A^{\\pi_{\\theta_k}}(s,a)$ nel caso di valori superiori al limite superiore.\n",
        "\n",
        "Quando $\\frac{\\pi_{\\theta}(a|s)}{\\pi_{\\theta_k}(a|s)}$ appartiene all'intervallo $[1 - \\epsilon, 1 + \\epsilon]$, entrambi i termini all'interno dell'operatore $\\min(\\cdot)$ assumono lo stesso valore.\n",
        "\n",
        "Con questa metodologia non vi è alcun incentivo a effettuare aggiornamenti di policy eccessivamente ampi.  \n",
        "\n",
        "In genere, massimizzare l'obiettivo surrogato $J^{\\text{CPI}}$ senza alcun vincolo potrebbe favorire aggiornamenti significativi nei parametri $𝜃$ della policy durante il processo di apprendimento. Ciò avviene poiché uno dei meccanismi attraverso cui è possibile massimizzare la funzione obiettivo consiste nell'apportare ampie variazioni a $\\frac{\\pi_{\\theta}(a|s)}{\\pi_{\\theta_k}(a|s)}$. Per andare più a fondo nella questione suggerisco la lettura del *7.2 Proximal Policy Optimization (PPO)* - PDF 205, del testo *Foundations of Deep Reinforcement Learning: Theory and Practice in Python di Laura Graesser, Wah Loon Keng*\n",
        "\n",
        "Infine, si osserva che i metodi PPO sono applicabili ad entrambi gli algoritmi di policy gradient studiati, REINFORCE e Actor-Critic. Appartiene alla classe degli algoritmi on-policy, e può essere applicato ad ambienti con spazi delle azioni sia discreti che continui.\n"
      ],
      "metadata": {
        "id": "Ozcwx2P7Cw1h"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mmdiMmn_CIc4"
      },
      "source": [
        "# Coding : Actor-Critic PPO-clip  --> Solving Pendulum"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Moduli"
      ],
      "metadata": {
        "id": "XQj2WQc9MSyR"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "omuf8cyFCIdK"
      },
      "outputs": [],
      "source": [
        "import warnings\n",
        "warnings.filterwarnings('ignore')\n",
        "\n",
        "import sys\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import random\n",
        "from collections import deque\n",
        "from typing import Deque, Dict, List, Tuple\n",
        "\n",
        "import gym\n",
        "\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "import torch.optim as optim\n",
        "from torch.distributions import Normal\n",
        "\n",
        "from IPython.display import clear_output\n",
        "\n",
        "#Codice ispirato:\n",
        "# https://github.com/MrSyee/pg-is-all-you-need/blob/master/02.PPO.ipynb"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ccq68l2lCIdY"
      },
      "source": [
        " [Codice](https://github.com/openai/gym/blob/master/gym/envs/classic_control/pendulum.py) di Pendulum-v1, dal  repository di OpenAI."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Premesse tecniche"
      ],
      "metadata": {
        "id": "sVpmTicoA6BU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Come funziona il Clipping ?\n",
        "\n",
        "epsilon = 3.7\n",
        "epsilon = torch.tensor(epsilon)\n",
        "\n",
        "for ratio in [-10, -3, 0, 4.65 ,4.75, 10]:\n",
        "   ratio = torch.tensor(ratio)\n",
        "   clipped_surr_loss = ( torch.clamp(ratio, 1.0 - epsilon, 1.0 + epsilon) )\n",
        "   print(clipped_surr_loss)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Z8-MkAMG-pwM",
        "outputId": "cfa11190-23e9-4ecd-be2a-be56f4736c58"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor(-2.7000)\n",
            "tensor(-2.7000)\n",
            "tensor(0.)\n",
            "tensor(4.6500)\n",
            "tensor(4.7000)\n",
            "tensor(4.7000)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        " # in GAE\n",
        " #  use of \"deque / appendleft()\"\n",
        "\n",
        "returns = deque()\n",
        "for i in range(1,5):\n",
        "  returns.appendleft(i)\n",
        "\n",
        "print(list(returns))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PxHPnRYWAddX",
        "outputId": "84d7d52e-4a70-4d94-f0a1-ad406e3bd4e9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[4, 3, 2, 1]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# mini-batch\n",
        "\n",
        "buffer_size = 100\n",
        "mini_batch_size = 7\n",
        "\n",
        "imb = np.random.choice(buffer_size, mini_batch_size)\n",
        "print(imb)\n",
        "print(\"\")\n",
        "\n",
        "values = torch.randn(buffer_size)\n",
        "print(values[imb])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TW3WOTuWsHy-",
        "outputId": "aaa8ba33-c2b8-4678-97ff-04d0ae08ec37"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[62  0 38 96  5 62  1]\n",
            "\n",
            "tensor([ 1.8233, -1.0158,  0.4469,  1.1398,  0.1003,  1.8233, -0.2942])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PQoj-wPQCIdN"
      },
      "source": [
        "## Network\n",
        "\n",
        "Questo codice definisce due modelli di rete neurale separati, uno per l'Actor, altro per il Critic.\n",
        "\n",
        "La rete Actor è responsabile della selezione del valore dell' azione dato in input uno stato. Esattamente produce in uscita la media (`mu`) e la deviazione standard logaritmica (`log_std`) della distribuzione (gaussiana) di probabilità dell'azione.\n",
        "\n",
        "La rete Critic ricevuto lo stato in input, restituisce uno scalare che rappresenta il valore della *value fuction* dello stato.\n",
        "\n",
        "Si ricordi:\n",
        "\n",
        "L'ambiente Pendulum ha solo una singola azione con un intervallo compreso tra -2 e 2. Per garantire che l'azione rientri in tale intervallo, l'Actor restituisce un valore medio  ottenuto da una moltiplicazione per 2 di tanh. Si ricorda che tanh normalizza l'output tra -1 e 1.\n",
        "\n",
        "Si noti infine che solo i pesi e i bias degli ultimi livelli vengono inizializzati con una distribuzione uniforme.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "6Lrlnw7xCIdP",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b8b041ca-8b1d-4046-beba-2f72f44cbcaf"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.11/dist-packages/ipykernel/ipkernel.py:283: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.\n",
            "  and should_run_async(code)\n"
          ]
        }
      ],
      "source": [
        "def init_layer_uniform(layer: nn.Linear, init_w: float = 3e-3) -> nn.Linear:\n",
        "    \"\"\"Init uniform parameters on the single layer.\"\"\"\n",
        "    layer.weight.data.uniform_(-init_w, init_w)\n",
        "    layer.bias.data.uniform_(-init_w, init_w)\n",
        "\n",
        "    return layer\n",
        "\n",
        "class Actor(nn.Module):\n",
        "    def __init__(\n",
        "        self,\n",
        "        in_dim: int,\n",
        "        out_dim: int,\n",
        "        log_std_min: int = -20,\n",
        "        log_std_max: int = 0,\n",
        "    ):\n",
        "        \"\"\"Initialize.\"\"\"\n",
        "        super(Actor, self).__init__()\n",
        "\n",
        "        self.log_std_min = log_std_min\n",
        "        self.log_std_max = log_std_max\n",
        "        self.hidden = nn.Linear(in_dim, 32)\n",
        "\n",
        "        self.mu_layer = nn.Linear(32, out_dim)\n",
        "        self.mu_layer = init_layer_uniform(self.mu_layer)\n",
        "\n",
        "        self.log_std_layer = nn.Linear(32, out_dim)\n",
        "        self.log_std_layer = init_layer_uniform(self.log_std_layer)\n",
        "\n",
        "    def forward(self, state: torch.Tensor) -> torch.Tensor:\n",
        "        \"\"\"Forward method implementation.\"\"\"\n",
        "        x = F.relu(self.hidden(state))\n",
        "\n",
        "        #torch.tanh activation -> values ​​between -1 and 1\n",
        "        mu = torch.tanh(self.mu_layer(x))* 2\n",
        "\n",
        "        log_std = torch.tanh(self.log_std_layer(x))\n",
        "\n",
        "        log_std = self.log_std_min + 0.5 * (self.log_std_max - self.log_std_min) * (log_std + 1)\n",
        "        # Rescale this the value [-1,1] of log_std to the range [log_std_min, log_std_max]\n",
        "        # why [-20, 0] ?\n",
        "        # Since neural networks can output unbounded values, we constrain log_std to be within [-20, 0]\n",
        "        # These values define the minimum and maximum possible standard deviation (std) for the action distribution.\n",
        "        # std = e^−20 ≈ 2.06×10^−9 --> This ensures that std never becomes too small\n",
        "        # std = e^0   = 1 --> This ensures that std never becomes too large. Note e^1.5 ≈ 4.5\n",
        "        # Answer :   Ensures that std never becomes exactly zero and avoids excessive randomness.\n",
        "\n",
        "        std = torch.exp(log_std)\n",
        "\n",
        "        dist = Normal(mu, std)\n",
        "        action = dist.sample()\n",
        "\n",
        "        return action, dist\n",
        "\n",
        "\n",
        "class Critic(nn.Module):\n",
        "    def __init__(self, in_dim: int):\n",
        "        \"\"\"Initialize.\"\"\"\n",
        "        super(Critic, self).__init__()\n",
        "\n",
        "        self.hidden = nn.Linear(in_dim, 64)\n",
        "        self.out = nn.Linear(64, 1)\n",
        "        self.out = init_layer_uniform(self.out)\n",
        "\n",
        "    def forward(self, state: torch.Tensor) -> torch.Tensor:\n",
        "        \"\"\"Forward method implementation.\"\"\"\n",
        "        x = F.relu(self.hidden(state))\n",
        "        value = self.out(x)\n",
        "\n",
        "        return value"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1GAL8L3eCIdQ"
      },
      "source": [
        "## GAE\n",
        "\n",
        "Per la stima della funzione Advantage, è usato il metodo del Generalized Advantage Estimation (GAE).\n",
        "\n",
        "Questo approccio mira a ridurre la varianza dello stimatore, mantenendo al contempo il bias introdotto il più contenuto possibile.\n",
        "\n",
        "Sia\n",
        "\n",
        "$δ_t = r_t + γ  V^π (s_{t+1}) - V^π (s_{t})$\n",
        "\n",
        "$A^{GAE, \\; \\pi} _t  = \\sum _{l=0} ^∞ {(γ \\; λ)^l \\; δ_{t+l} }$\n",
        "\n",
        "con $\\lambda \\in (0, 1)$ e  $\\gamma \\in [0, 1)$\n",
        "\n",
        "Maggiori info: [Schulman J. et al (2015). High-dimensional continuous control using generalized advantage estimation.](https://arxiv.org/pdf/1506.02438)\n",
        "\n",
        "Si ricordi che, per l'apprendimento della value function (output del Critic), l’approccio più semplice consiste nel risolvere un problema di regressione, trovando i valori dei parametri $\\mathbf{w}$ che minizzano l'espressione :\n",
        "\n",
        "$ \\sum_{t=1}^T \\left\\| V^{\\pi} _{target}(s_{t})  - \\hat{V}^\\pi(s_{t};\\mathbf{w})  \\right\\|^2$\n",
        "\n",
        "nello specifico:\n",
        "\n",
        "GAE optimization:\n",
        "\n",
        " $V^{\\pi} _{target} (s_t) ≈ A^{GAE \\; \\pi} _t (s_{t};\\mathbf{w})  + \\hat{V^\\pi} (s_{t};\\mathbf{w})$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "KlVLru_SCIdQ"
      },
      "outputs": [],
      "source": [
        "def compute_gae(\n",
        "    next_value: float,\n",
        "    rewards: list,\n",
        "    masks: list,\n",
        "    values: list,\n",
        "    gamma: float,\n",
        "    tau: float\n",
        ") -> List:\n",
        "    \"\"\"Compute gae.\"\"\"\n",
        "    values = values + [next_value]\n",
        "    gae = 0\n",
        "    returns: Deque[float] = deque()\n",
        "\n",
        "    for step in reversed(range(len(rewards))):\n",
        "        delta = (rewards[step] + gamma * values[step + 1] * masks[step] - values[step])\n",
        "        gae = delta + gamma * tau * masks[step] * gae\n",
        "        returns.appendleft(gae + values[step])\n",
        "        # returns.appendleft(...) : returns list in the correct order while iterating in reverse\n",
        "        # (gae + values[step]) : we need the target values for training the critic.\n",
        "\n",
        "    return list(returns)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Test gae\n",
        "next_value = 0.0\n",
        "rewards = [1.0, 0.5, 1.0, 1.0, 0.02]\n",
        "masks =   [1, 1, 1, 1, 1]\n",
        "values =  [0.2, 1, 5, 1, 0.4]\n",
        "gamma = 0.99\n",
        "tau = 0.95\n",
        "\n",
        "returns = compute_gae(next_value, rewards, masks, values, gamma, tau)\n",
        "print(returns)\n"
      ],
      "metadata": {
        "id": "nYBo-BQrGAub",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f2423c21-7461-4e0a-9d7d-1ab8dd57e3e5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[3.5448788966588767, 2.6532470990525003, 2.026312705, 1.0386099999999998, 0.020000000000000018]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MTqnZj3VCIdR"
      },
      "source": [
        "## PPO Agent\n",
        "Summary PPOAgent class.\n",
        "\n",
        "| Method           | Note                                                 |\n",
        "|---               |---                                                   |\n",
        "|select_action     | select an action from the input state.               |\n",
        "|step              | take an action and return the response of the env.   |\n",
        "|update_model      | update the model by gradient descent.                |\n",
        "|train             | train the agent during num_frames.                   |\n",
        "|evaluate_agent_performance              | test the agent.                          |\n",
        "|_plot             | plot the training progresses.                        |\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Mini-batch generator\n",
        "\n",
        "L' algoritmo aggiorna il modello più volte (esattamente `epoch`volte), utilizzando strutture di memoria basate su liste (`List[torch.Tensor]`), la cui dimensione è determinata dal parametro `rollout_len`.\n",
        "\n",
        "In pratica, per l'update,  la funzione `ppo_iter` estrae campioni (*mini-batch experience data*) da queste liste, fungendo da generatore di dati.\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "xREqZtpkUb3_"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "id": "7h73qp21CIdS"
      },
      "outputs": [],
      "source": [
        "def ppo_iter(\n",
        "    epoch: int,\n",
        "    mini_batch_size: int,\n",
        "    states: torch.Tensor,\n",
        "    actions: torch.Tensor,\n",
        "    values: torch.Tensor,\n",
        "    log_probs: torch.Tensor,\n",
        "    returns: torch.Tensor,\n",
        "    advantages: torch.Tensor,\n",
        "):\n",
        "    \"\"\"Yield mini-batches.\"\"\"\n",
        "    buffer_size = states.size(0) # = rollout_len\n",
        "    for _ in range(epoch):\n",
        "            rand_ids = np.random.choice(buffer_size, mini_batch_size)\n",
        "            yield states[rand_ids, :], actions[rand_ids], values[rand_ids], log_probs[rand_ids], returns[rand_ids], advantages[rand_ids]"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#The dataset contains buffer_size samples.\n",
        "# We divide it into smaller groups of mini_batch_size samples each.\n",
        "#  The mini_batch produced, usally will be different from each other, due to:\n",
        "#    rand_ids = np.random.choice(buffer_size, mini_batch_size)\n",
        "\n",
        "# Define input\n",
        "buffer_size = 6\n",
        "state_dim = 4  # Assume states have 4 features\n",
        "action_dim = 3  # Assume actions have 3 possible choices\n",
        "\n",
        "# Create random tensors\n",
        "states = torch.randn(buffer_size, state_dim)\n",
        "actions = torch.randint(0, action_dim, (buffer_size,))\n",
        "values = torch.randn(buffer_size)\n",
        "log_probs = torch.randn(buffer_size)\n",
        "returns = torch.randn(buffer_size)\n",
        "advantages = torch.randn(buffer_size)\n",
        "# Print the generated tensors\n",
        "print(\"States:\\n\", states)\n",
        "print(\"\\nActions:\\n\", actions)\n",
        "print(\"\\nValues:\\n\", values)\n",
        "print(\"\\nLog Probs:\\n\", log_probs)\n",
        "print(\"\\nReturns:\\n\", returns)\n",
        "print(\"\\nAdvantages:\\n\", advantages)\n",
        "print(\"\\n\")\n",
        "\n",
        "# Hyperparameters\n",
        "epochs = 2           # Number of times to loop over data\n",
        "mini_batch_size = 3  # Number of elements in mini-batch\n",
        "\n",
        "#print(ppo_iter(epochs, mini_batch_size, states, actions, values, log_probs, returns, advantages)) # <generator object ppo_iter at 0x7eda404b7df0>\n",
        "\n",
        "# Testing\n",
        "c = 0\n",
        "for mini_batch in ppo_iter(epochs, mini_batch_size, states, actions, values, log_probs, returns, advantages):\n",
        "    c+=1\n",
        "    print(\"Mini-batch:\", c)\n",
        "    for data in mini_batch:\n",
        "        print(data)\n",
        "    print(\"-\" * 40,\"\\n\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fui7V_BwVWUo",
        "outputId": "57301e8b-d7fc-4840-b900-13722b4fcab9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "States:\n",
            " tensor([[ 1.0789,  0.2666, -0.6753,  0.3825],\n",
            "        [ 0.9448, -0.0754,  0.6641, -0.1140],\n",
            "        [ 0.0560,  0.7851,  1.9089,  0.1962],\n",
            "        [-0.4523,  0.1661, -0.1562,  0.8245],\n",
            "        [-1.5028, -0.7979, -0.0726, -0.7814],\n",
            "        [ 0.1081,  0.0803, -0.3265, -0.1117]])\n",
            "\n",
            "Actions:\n",
            " tensor([0, 2, 0, 2, 0, 2])\n",
            "\n",
            "Values:\n",
            " tensor([-0.0441,  1.2948,  0.1950, -0.3552,  2.0536,  0.2982])\n",
            "\n",
            "Log Probs:\n",
            " tensor([ 0.5328, -0.2248,  0.5454, -0.4114, -0.5961,  0.9094])\n",
            "\n",
            "Returns:\n",
            " tensor([ 2.1009, -1.5110,  0.1362,  1.4254,  0.6449, -1.2025])\n",
            "\n",
            "Advantages:\n",
            " tensor([-1.1808,  1.9435,  0.7037,  1.3710,  0.8751, -0.1698])\n",
            "\n",
            "\n",
            "Mini-batch: 1\n",
            "tensor([[ 0.1081,  0.0803, -0.3265, -0.1117],\n",
            "        [ 0.0560,  0.7851,  1.9089,  0.1962],\n",
            "        [ 0.9448, -0.0754,  0.6641, -0.1140]])\n",
            "tensor([2, 0, 2])\n",
            "tensor([0.2982, 0.1950, 1.2948])\n",
            "tensor([ 0.9094,  0.5454, -0.2248])\n",
            "tensor([-1.2025,  0.1362, -1.5110])\n",
            "tensor([-0.1698,  0.7037,  1.9435])\n",
            "---------------------------------------- \n",
            "\n",
            "Mini-batch: 2\n",
            "tensor([[ 1.0789,  0.2666, -0.6753,  0.3825],\n",
            "        [ 1.0789,  0.2666, -0.6753,  0.3825],\n",
            "        [ 0.9448, -0.0754,  0.6641, -0.1140]])\n",
            "tensor([0, 0, 2])\n",
            "tensor([-0.0441, -0.0441,  1.2948])\n",
            "tensor([ 0.5328,  0.5328, -0.2248])\n",
            "tensor([ 2.1009,  2.1009, -1.5110])\n",
            "tensor([-1.1808, -1.1808,  1.9435])\n",
            "---------------------------------------- \n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### PPOAgent class"
      ],
      "metadata": {
        "id": "1Rih_KEnVTav"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {
        "id": "CigGVegvCIdT"
      },
      "outputs": [],
      "source": [
        "class PPOAgent:\n",
        "    \"\"\"PPO Agent.\n",
        "    Attributes:\n",
        "        env (gym.Env): Gym env for training\n",
        "        gamma (float): discount factor\n",
        "        tau (float): lambda of generalized advantage estimation (GAE)\n",
        "        batch_size (int): Number of elements in mini-batch for update\n",
        "        epsilon (float): amount of clipping surrogate objective\n",
        "        epoch (int): the number of update\n",
        "        rollout_len (int): the number of rollout\n",
        "        entropy_weight (float): rate of weighting entropy into the loss function\n",
        "        actor (nn.Module): target actor model to select actions\n",
        "        critic (nn.Module): critic model to predict state values\n",
        "        transition (list): temporory storage for the recent transition\n",
        "        device (torch.device): cpu / gpu\n",
        "        total_step (int): total step numbers\n",
        "        is_test (bool): flag to show the current mode (train / test)\n",
        "    \"\"\"\n",
        "\n",
        "    def __init__(\n",
        "        self,\n",
        "        env: gym.Env,\n",
        "        batch_size: int,\n",
        "        gamma: float,\n",
        "        tau: float,\n",
        "        epsilon: float,\n",
        "        epoch: int,\n",
        "        rollout_len: int,\n",
        "        entropy_weight: float,  # Trailing commas makes it easy to add more arguments later, if necessary ...\n",
        "    ):\n",
        "        \"\"\"Initialize.\"\"\"\n",
        "        self.env = env\n",
        "        self.gamma = gamma\n",
        "        self.tau = tau\n",
        "        self.b_size = batch_size\n",
        "        self.epsilon = epsilon\n",
        "        self.epoch = epoch\n",
        "        self.rollout_len = rollout_len\n",
        "        self.entropy_weight = entropy_weight\n",
        "\n",
        "        # device: cpu / gpu\n",
        "        self.device = torch.device(\n",
        "            \"cuda\" if torch.cuda.is_available() else \"cpu\"\n",
        "        )\n",
        "        print(self.device)\n",
        "\n",
        "        # setting the networks\n",
        "        obs_dim = env.observation_space.shape[0]\n",
        "        action_dim = env.action_space.shape[0]\n",
        "        self.actor = Actor(obs_dim, action_dim).to(self.device)\n",
        "        self.critic = Critic(obs_dim).to(self.device)\n",
        "\n",
        "        # optimizer\n",
        "        self.actor_optimizer = optim.Adam(self.actor.parameters(), lr=0.001)\n",
        "        self.critic_optimizer = optim.Adam(self.critic.parameters(), lr=0.005)\n",
        "\n",
        "        # set memory for the training -> see: ppo_iter generator\n",
        "        self.states: List[torch.Tensor] = []\n",
        "        self.actions: List[torch.Tensor] = []\n",
        "        self.rewards: List[torch.Tensor] = []\n",
        "        self.values: List[torch.Tensor] = []\n",
        "        self.masks: List[torch.Tensor] = []\n",
        "        self.log_probs: List[torch.Tensor] = []\n",
        "\n",
        "        # total steps count\n",
        "        self.total_step = 0\n",
        "\n",
        "        # mode: train / test\n",
        "        self.is_test = False\n",
        "\n",
        "    def select_action(self, state: np.ndarray) -> np.ndarray:\n",
        "        \"\"\"Select an action from the input state.\"\"\"\n",
        "        state = torch.FloatTensor(state).to(self.device)\n",
        "        action, dist = self.actor(state)\n",
        "        selected_action = dist.mean if self.is_test else action\n",
        "\n",
        "        if not self.is_test:\n",
        "            value = self.critic(state)\n",
        "            self.states.append(state)                # All these \".append()\"\" will serve as dataset for mini-batch experience data\n",
        "            self.actions.append(selected_action)\n",
        "            self.values.append(value)\n",
        "            self.log_probs.append(dist.log_prob(selected_action))\n",
        "\n",
        "        # \"selected_action.cpu().detach().numpy()[0]\" somthieng like that : [0.02601556]\n",
        "        return selected_action.cpu().detach().numpy()[0]\n",
        "\n",
        "    def step(self, action: np.ndarray) -> Tuple[np.ndarray, np.float64, bool]:\n",
        "        \"\"\"Take an action and return the response of the env.\"\"\"\n",
        "\n",
        "        if self.is_test:\n",
        "            next_state, reward, done, _ = self.env.step(action.reshape(1))\n",
        "            return next_state, reward, done\n",
        "\n",
        "        next_state, reward, done, _ = self.env.step(action)\n",
        "        next_state = np.reshape(next_state, (1, -1)).astype(np.float64)\n",
        "        reward = np.reshape(reward, (1, -1)).astype(np.float64)\n",
        "        done = np.reshape(done, (1, -1))\n",
        "\n",
        "        if not self.is_test:\n",
        "            self.rewards.append(torch.FloatTensor(reward).to(self.device))\n",
        "            self.masks.append(torch.FloatTensor(1 - done).to(self.device))\n",
        "\n",
        "        return next_state, reward, done\n",
        "\n",
        "    def update_model(self, next_state: np.ndarray) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:\n",
        "        \"\"\"Update the model by gradient descent.\"\"\"\n",
        "        device = self.device  # for shortening the following lines\n",
        "\n",
        "        next_state = torch.FloatTensor(next_state).to(device)\n",
        "        next_value = self.critic(next_state)\n",
        "\n",
        "        returns = compute_gae(\n",
        "            next_value,\n",
        "            self.rewards,\n",
        "            self.masks,\n",
        "            self.values,\n",
        "            self.gamma,\n",
        "            self.tau,\n",
        "        )\n",
        "\n",
        "        # Processing memory for training\n",
        "        states = torch.cat(self.states).view(-1, 3)\n",
        "        actions = torch.cat(self.actions)\n",
        "        returns = torch.cat(returns).detach()\n",
        "        values = torch.cat(self.values).detach()\n",
        "        log_probs = torch.cat(self.log_probs).detach()\n",
        "        advantages = returns - values\n",
        "\n",
        "        actor_losses, critic_losses = [], []\n",
        "\n",
        "        for state, action, old_value, old_log_prob, return_, adv in ppo_iter(\n",
        "            epoch=self.epoch,\n",
        "            mini_batch_size=self.b_size,\n",
        "            states=states,\n",
        "            actions=actions,\n",
        "            values=values,\n",
        "            log_probs=log_probs,\n",
        "            returns=returns,\n",
        "            advantages=advantages, # Trailing commas in function calls does not affect execution and ignored by the interpreter.\n",
        "        ):\n",
        "            # calculate ratios\n",
        "            _, dist = self.actor(state)\n",
        "            #Note\n",
        "            # state torch.Size([64, 3])\n",
        "            # dist torch.Size([64, 1])\n",
        "            # action torch.Size([64, 1])\n",
        "            # old_log_prob torch.Size([64, 1])\n",
        "            log_prob = dist.log_prob(action)\n",
        "            ratio = (log_prob - old_log_prob).exp() # Quotient of powers property: a^m / a^n = a^(m-n)\n",
        "            # Note: (log_prob).exp() is a way to convert back from log probabilities to regular probabilities\n",
        "\n",
        "            # actor_loss\n",
        "            surr_loss = ratio * adv\n",
        "            #Clipping\n",
        "            clipped_surr_loss = (torch.clamp(ratio, 1.0 - self.epsilon, 1.0 + self.epsilon) * adv)\n",
        "\n",
        "            # Entropy regularization\n",
        "            entropy = dist.entropy().mean()\n",
        "\n",
        "            actor_loss = ( -torch.min(surr_loss, clipped_surr_loss).mean() - entropy * self.entropy_weight)\n",
        "            # \"( -torch.min(surr_loss, clipped_surr_loss)\" is somthing like this : torch.Size([64, 1])  ->  tensor([[17.0310],...[17.3662]])\n",
        "            # \"( -torch.min(surr_loss, clipped_surr_loss).mean()\" :  tensor(13.0414)\n",
        "\n",
        "            # critic_loss\n",
        "            value = self.critic(state)\n",
        "            #Alternative: clipped_value = old_value + (value - old_value).clamp(-0.5, 0.5)\n",
        "            critic_loss = (return_ - value).pow(2).mean()\n",
        "            # \"(return_ - value).pow(2) \" is somthing like this : torch.Size([64, 1])  ->  tensor([[1.4190], ..., [0.2553]])\n",
        "            # \"(return_ - value).pow(2).mean()\"  :  tensor(1.1228)\n",
        "\n",
        "            # train critic\n",
        "            self.critic_optimizer.zero_grad()\n",
        "            critic_loss.backward(retain_graph=True)\n",
        "            self.critic_optimizer.step()\n",
        "\n",
        "            # train actor\n",
        "            self.actor_optimizer.zero_grad()\n",
        "            actor_loss.backward()\n",
        "            self.actor_optimizer.step()\n",
        "\n",
        "            actor_losses.append(actor_loss.item())\n",
        "            critic_losses.append(critic_loss.item())\n",
        "\n",
        "        self.states, self.actions, self.rewards = [], [], []\n",
        "        self.values, self.masks, self.log_probs = [], [], []\n",
        "\n",
        "        actor_loss = sum(actor_losses) / len(actor_losses)\n",
        "        critic_loss = sum(critic_losses) / len(critic_losses)\n",
        "\n",
        "        return actor_loss, critic_loss\n",
        "\n",
        "    def train(self, num_frames: int, plotting_interval: int = 5_000):\n",
        "        \"\"\"Train the agent.\"\"\"\n",
        "        self.is_test = False\n",
        "\n",
        "        state = self.env.reset()\n",
        "        state = np.expand_dims(state, axis=0)\n",
        "\n",
        "        actor_losses, critic_losses = [], []   # for plotting\n",
        "        scores = []                            # for plotting\n",
        "        score = 0\n",
        "\n",
        "        while self.total_step <= num_frames + 1:\n",
        "            for _ in range(self.rollout_len):\n",
        "                self.total_step += 1\n",
        "                # The data that will then be used by the ppo_iter generator\n",
        "                #  are stored thanks to the following two instructions\n",
        "                action = self.select_action(state)\n",
        "                next_state, reward, done = self.step(action)\n",
        "\n",
        "                state = next_state\n",
        "                score += reward[0][0]\n",
        "\n",
        "                # if episode ends\n",
        "                if done[0][0]:\n",
        "                    state = env.reset()\n",
        "                    state = np.expand_dims(state, axis=0)\n",
        "                    scores.append(score)\n",
        "                    score = 0\n",
        "\n",
        "                # Plot\n",
        "                if self.total_step % plotting_interval == 0:\n",
        "                    self._plot(self.total_step, scores, actor_losses, critic_losses)\n",
        "                    self.entropy_weight = self.entropy_weight * 0.5   # decay of entropy_weight\n",
        "\n",
        "\n",
        "            #Update the model\n",
        "            actor_loss, critic_loss = self.update_model(next_state)\n",
        "            actor_losses.append(actor_loss)\n",
        "            critic_losses.append(critic_loss)\n",
        "\n",
        "        # termination\n",
        "        self.env.close()\n",
        "\n",
        "    def evaluate_agent_performance(self,num_episodes=1_000, baseline_reward=-150):\n",
        "\n",
        "        #Baseline_reward:\n",
        "        #https://github.com/openai/gym/wiki/Leaderboard\n",
        "\n",
        "        better_scores_count = 0\n",
        "\n",
        "        self.is_test = True\n",
        "        state = self.env.reset(seed=99) # for the experimentation a \"seed\" different from the training\n",
        "\n",
        "        # Run episodes\n",
        "        for k in range(num_episodes):\n",
        "\n",
        "          done = False\n",
        "          score = 0\n",
        "\n",
        "          while not done:\n",
        "            action = self.select_action(state)\n",
        "            next_state, reward, done = self.step(action)\n",
        "\n",
        "            state = next_state\n",
        "            score += reward\n",
        "\n",
        "          state = env.reset()\n",
        "          if score > baseline_reward:\n",
        "             better_scores_count += 1\n",
        "\n",
        "        # Compute the percentage\n",
        "        success_percentage = (better_scores_count / num_episodes) * 100\n",
        "\n",
        "        print(\"A better score than the\", baseline_reward, \" was taken in \", round(success_percentage,2), \"% of times\" )\n",
        "\n",
        "        self.env.close()\n",
        "        return None\n",
        "\n",
        "    def _plot(\n",
        "        self,\n",
        "        frame_idx: int,\n",
        "        scores: List[float],\n",
        "        actor_losses: List[float],\n",
        "        critic_losses: List[float],\n",
        "    ):\n",
        "        \"\"\"Plot the training progresses.\"\"\"\n",
        "\n",
        "        def subplot(loc: int, title: str, values: List[float]):\n",
        "            plt.subplot(loc)\n",
        "            plt.title(title)\n",
        "            plt.plot(values)\n",
        "\n",
        "        subplot_params = [\n",
        "            (131, f\"frame {frame_idx}. score: {np.mean(scores[-10:])}\", scores),\n",
        "            (132, \"actor_loss\", actor_losses),\n",
        "            (133, \"critic_loss\", critic_losses),\n",
        "        ]\n",
        "\n",
        "        clear_output(True)\n",
        "        plt.figure(figsize=(30, 5))\n",
        "        for loc, title, values in subplot_params:\n",
        "            subplot(loc, title, values)\n",
        "        plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tO5y8t8vCIdb"
      },
      "source": [
        "## Initialize"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {
        "id": "BeOmsOdyCIdc",
        "outputId": "d2c6533e-af2e-443b-a882-a1844204e82f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "cuda\n"
          ]
        }
      ],
      "source": [
        "# environment\n",
        "env = gym.make(\"Pendulum-v1\", render_mode=\"rgb_array\")\n",
        "\n",
        "# Set random seed\n",
        "def seed_torch(seed):\n",
        "    torch.manual_seed(seed)\n",
        "    if torch.backends.cudnn.enabled:\n",
        "        torch.backends.cudnn.benchmark = False\n",
        "        torch.backends.cudnn.deterministic = True\n",
        "\n",
        "seed = 777\n",
        "random.seed(seed)\n",
        "np.random.seed(seed)\n",
        "seed_torch(seed)\n",
        "\n",
        "# parameters\n",
        "num_frames = 100_000\n",
        "\n",
        "agent = PPOAgent(\n",
        "    env,\n",
        "    gamma = 0.9,\n",
        "    tau = 0.8,\n",
        "    batch_size = 64,          # Number of elements in mini-batch for update\n",
        "    epsilon = 0.3,\n",
        "    epoch = int((200*8)/2),   # Number of update per rollout-dataset\n",
        "    rollout_len = 200*8,\n",
        "    entropy_weight = 0.8      # this value will decay during the training\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jdoPtPOJCIdd"
      },
      "source": [
        "## Train"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "agent.train(num_frames)  # time : 13 minute"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 196
        },
        "id": "xRkoRGidt60h",
        "outputId": "f0cc14a0-486b-4002-cf43-6d24bd0757ee"
      },
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 3000x500 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "agent.entropy_weight"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Mas68noEuDz2",
        "outputId": "7b9bdded-4291-4c6f-8edc-179283d15321"
      },
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "7.62939453125e-07"
            ]
          },
          "metadata": {},
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Test"
      ],
      "metadata": {
        "id": "uhvEkUo38dFx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "agent.evaluate_agent_performance(num_episodes=1_000,baseline_reward=-150)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FJbp3Hw8wUfg",
        "outputId": "b42ee6ee-6b60-42f6-f722-17f683e3334b"
      },
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "A better score than the -150  was taken in  61.3 % of times\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    },
    "colab": {
      "provenance": [],
      "collapsed_sections": [
        "fIkEW1THDa8T",
        "WmkayDBmIrgE",
        "XQj2WQc9MSyR",
        "sVpmTicoA6BU",
        "PQoj-wPQCIdN",
        "1GAL8L3eCIdQ"
      ],
      "gpuType": "T4"
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}