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value_iteration.py
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/
value_iteration.py
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# Value iteration agent
# Model-based learning which requires mdp.
#
# ---
# @author Yiren Lu
# @email luyiren [at] seas [dot] upenn [dot] edu
#
# MIT License
import math
import numpy as np
def value_iteration(P_a, rewards, gamma, error=0.01, deterministic=True):
"""
static value iteration function. Perhaps the most useful function in this repo
inputs:
P_a NxNxN_ACTIONS transition probabilities matrix -
P_a[s0, s1, a] is the transition prob of
landing at state s1 when taking action
a at state s0
rewards Nx1 matrix - rewards for all the states
gamma float - RL discount
error float - threshold for a stop
deterministic bool - to return deterministic policy or stochastic policy
returns:
values Nx1 matrix - estimated values
policy Nx1 (NxN_ACTIONS if non-det) matrix - policy
"""
N_STATES, _, N_ACTIONS = np.shape(P_a)
values = np.zeros([N_STATES])
# estimate values
while True:
values_tmp = values.copy()
for s in range(N_STATES):
v_s = []
values[s] = max([sum([P_a[s, s1, a]*(rewards[s] + gamma*values_tmp[s1]) for s1 in range(N_STATES)]) for a in range(N_ACTIONS)])
if max([abs(values[s] - values_tmp[s]) for s in range(N_STATES)]) < error:
break
if deterministic:
# generate deterministic policy
policy = np.zeros([N_STATES])
for s in range(N_STATES):
policy[s] = np.argmax([sum([P_a[s, s1, a]*(rewards[s]+gamma*values[s1])
for s1 in range(N_STATES)])
for a in range(N_ACTIONS)])
return values, policy
else:
# generate stochastic policy
policy = np.zeros([N_STATES, N_ACTIONS])
for s in range(N_STATES):
v_s = np.array([sum([P_a[s, s1, a]*(rewards[s] + gamma*values[s1]) for s1 in range(N_STATES)]) for a in range(N_ACTIONS)])
policy[s,:] = np.transpose(v_s/np.sum(v_s))
return values, policy
class ValueIterationAgent(object):
def __init__(self, mdp, gamma, iterations=100):
"""
The constructor builds a value model from mdp using dynamic programming
inputs:
mdp markov decision process that is required by value iteration agent definition:
https://github.com/stormmax/reinforcement_learning/blob/master/envs/mdp.py
gamma discount factor
"""
self.mdp = mdp
self.gamma = gamma
states = mdp.get_states()
# init values
self.values = {}
for s in states:
if mdp.is_terminal(s):
self.values[s] = mdp.get_reward(s)
else:
self.values[s] = 0
# estimate values
for i in range(iterations):
values_tmp = self.values.copy()
for s in states:
if mdp.is_terminal(s):
continue
actions = mdp.get_actions(s)
v_s = []
for a in actions:
P_s1sa = mdp.get_transition_states_and_probs(s, a)
R_sas1 = [mdp.get_reward(s1) for s1 in [p[0] for p in P_s1sa]]
v_s.append(sum([P_s1sa[s1_id][1] * (mdp.get_reward(s) + gamma *
values_tmp[P_s1sa[s1_id][0]]) for s1_id in range(len(P_s1sa))]))
# V(s) = max_{a} \sum_{s'} P(s'| s, a) (R(s,a,s') + \gamma V(s'))
self.values[s] = max(v_s)
def get_values(self):
"""
returns
a dictionary {<state, value>}
"""
return self.values
def get_q_values(self, state, action):
"""
returns qvalue of (state, action)
"""
return sum([P_s1_s_a * (self.mdp.get_reward_sas(s, a, s1) + self.gamma * self.values[s1])
for s1, P_s1_s_a in self.mdp.get_transition_states_and_probs(state, action)])
def eval_policy_dist(self, policy, iterations=100):
"""
evaluate a policy distribution
returns
a map {<state, value>}
"""
values = {}
states = self.mdp.get_states()
for s in states:
if self.mdp.is_terminal(s):
values[s] = self.mdp.get_reward(s)
else:
values[s] = 0
for i in range(iterations):
values_tmp = values.copy()
for s in states:
if self.mdp.is_terminal(s):
continue
actions = self.mdp.get_actions(s)
# v(s) = \sum_{a\in A} \pi(a|s) (R(s,a,s') + \gamma \sum_{s'\in S}
# P(s'| s, a) v(s'))
values[s] = sum([policy[s][i][1] * (self.mdp.get_reward(s) + self.gamma * sum([s1_p * values_tmp[s1]
for s1, s1_p in self.mdp.get_transition_states_and_probs(s, actions[i])]))
for i in range(len(actions))])
return values
def get_optimal_policy(self):
"""
returns
a dictionary {<state, action>}
"""
states = self.mdp.get_states()
policy = {}
for s in states:
policy[s] = [(self.get_action(s), 1)]
return policy
def get_action_dist(self, state):
"""
args
state current state
returns
a list of {<action, prob>} pairs representing the action distribution on state
"""
actions = self.mdp.get_actions(state)
# \sum_{s'} P(s'|s,a)*(R(s,a,s') + \gamma v(s'))
v_a = [sum([s1_p * (self.mdp.get_reward_sas(state, a, s1) + self.gamma * self.values[s1])
for s1, s1_p in self.mdp.get_transition_states_and_probs(state, a)])
for a in actions]
# I exponentiated the v_s^a's to make them positive
v_a = [math.exp(v) for v in v_a]
return [(actions[i], v_a[i] / sum(v_a)) for i in range(len(actions))]
def get_action(self, state):
"""
args
state current state
returns
an action to take given the state
"""
actions = self.mdp.get_actions(state)
v_s = []
for a in actions:
P_s1sa = self.mdp.get_transition_states_and_probs(state, a)
R_sas1 = [self.mdp.get_reward(s1) for s1 in [p[0] for p in P_s1sa]]
v_s.append(sum([P_s1sa[s1_id][1] *
(self.mdp.get_reward(state) +
self.gamma *
self.values[P_s1sa[s1_id][0]]) for s1_id in range(len(P_s1sa))]))
a_id = v_s.index(max(v_s))
return actions[a_id]