1_evolution_strategy.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/akimotolab/CMAES_Tutorial/blob/main/1_evolution_strategy.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "collapsed": true,
        "id": "uiv6Kc5jNWCR"
      },
      "outputs": [],
      "source": [
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "collapsed": true,
        "id": "BJce3DvvNWCU"
      },
      "outputs": [],
      "source": [
        "from __future__ import division          # use // for integer division\n",
        "from __future__ import absolute_import   # use from . import\n",
        "from __future__ import print_function    # use print(\"...\") instead of print \"...\"\n",
        "from __future__ import unicode_literals  # all the strings are unicode"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yUSjN14cNWCU"
      },
      "source": [
        "#Evolution Strategyによる非制約連続最適化"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pFTHT8SxNWCV"
      },
      "source": [
        "Evolution Strategy (ES) は，進化計算と呼ばれる\"生物の進化に着想を得た\"最適化アルゴリズムの一種である．現在，Covariance Matrix Adaptation Evolution Strategy (CMA-ES) と呼ばれるESの一種が，最も優れたアルゴリズムの一つとして広く用いられている．\n",
        "\n",
        "ここでは，Step-Size Adaptive ESと呼ばれるシンプルなアルゴリズムを例にとり，ESの動作原理を理解する．"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VDJJXqAkNWCW"
      },
      "source": [
        "## ステップサイズの更新を行わないES"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "ここでは，ESのほとんどの機能を取り除いた骨格だけの場合に，どのような振る舞いをするのかを確認する．その上で，この先のノートブックにおいて，現在CMA-ESに実装されている各コンポーネントの役割を一つずつ確認していく．\n",
        "\n",
        "以下では，次の手続きを繰り返すだけのランダムサーチを実装している．\n",
        "\n",
        "1. 平均ベクトル$m$，ステップサイズ$\\sigma$を初期化\n",
        "2. 正規分布$\\mathcal{N}(m, \\sigma^2 I)$に従って，$\\lambda$個の独立な解 $x_i = m + \\sigma \\mathcal{N}(0, I)$ (for $i = 1,\\dots, \\lambda$) を生成\n",
        "3. それぞれの解の目的関数値 $f(x_i)$ を（並列に）評価\n",
        "4. 目的関数の昇順に解をソート．$x_{i:\\lambda}$ を $i$番目に目的関数値の小さな解とする．\n",
        "5. 平均ベクトルを以下のように更新\n",
        "$$\n",
        "m \\leftarrow m + \\sum_{i=1}^{\\lambda} w_{i} (x_{i:\\lambda} - m) = \\sum_{i=1}^{\\lambda} w_{i} x_{i:\\lambda}\n",
        "$$\n",
        "6. ステップ2に戻る\n",
        "\n",
        "ここで，$w_1 \\leq \\dots \\leq w_\\lambda$ は解のランキング毎に与えられる重みであり，以下では簡単のため$\\mu = \\lfloor \\lambda / 4 \\rfloor$とし（上位解の選択数），$w_1 = \\dots = w_\\mu = 1/\\mu$，$w_{\\mu+1} = \\dots = w_{\\lambda} = 0$ とする．最新のCMA-ESでは重みに傾斜をつけているが，大幅に探索性能が変わるわけでは無いため，簡単のためこのような重みを利用する．\n",
        "\n",
        "以上のように，このアルゴリズムは，複数の解を正規分布から生成し，上位$\\mu$個の解の平均値を次の正規分布の平均ベクトルとする，ということを繰り返すだけのランダムサーチである．"
      ],
      "metadata": {
        "id": "dfGJZbSWXRXS"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "collapsed": true,
        "id": "FlHnRpZfNWCW"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "oGEqnstENWCW"
      },
      "outputs": [],
      "source": [
        "class ES(object):\n",
        "    \"\"\"ステップサイズの更新を行わない Evolution Strategy\"\"\"\n",
        "    \n",
        "    def __init__(self, func, init_mean, init_sigma, nsample):\n",
        "        \"\"\"コンストラクタ\n",
        "        \n",
        "        Parameters\n",
        "        ----------\n",
        "        func : callable\n",
        "            目的関数 (最小化)\n",
        "        init_mean : ndarray (1D)\n",
        "            初期平均ベクトル\n",
        "        init_sigma : float\n",
        "            初期ステップサイズ\n",
        "        nsample : int\n",
        "            サンプル数\n",
        "        \"\"\"\n",
        "        self.func = func\n",
        "        self.mean = init_mean\n",
        "        self.sigma = init_sigma\n",
        "        self.N = self.mean.shape[0]                     # 探索空間の次元数\n",
        "        self.arx = np.zeros((nsample, self.N)) * np.nan # 候補解\n",
        "        self.arf = np.zeros(nsample) * np.nan           # 候補解の評価値\n",
        "        \n",
        "        self.weights = np.zeros(nsample)\n",
        "        self.weights[:nsample//4] = 1.0 / (nsample//4)  # 重み．総和が1\n",
        "    \n",
        "    def sample(self):\n",
        "        \"\"\"候補解を生成する．\"\"\"\n",
        "        self.arx = self.mean + self.sigma * np.random.normal(size=self.arx.shape)\n",
        "    \n",
        "    def evaluate(self):\n",
        "        \"\"\"候補解を評価する．\"\"\"\n",
        "        for i in range(self.arf.shape[0]):\n",
        "            self.arf[i] = self.func(self.arx[i])\n",
        "        \n",
        "    def update_mean(self):\n",
        "        \"\"\"平均ベクトルを更新する．\"\"\"\n",
        "        idx = np.argsort(self.arf)  # idx[i]は評価値がi番目に良い解のインデックス\n",
        "        self.mean += np.dot(self.weights, (self.arx[idx] - self.mean))\n",
        "        "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "id": "9Hu11uYKNWCX"
      },
      "outputs": [],
      "source": [
        "def sphere(x):\n",
        "    \"\"\"ベクトルのノルムを返す関数．最適解は(0,...,0)\"\"\"\n",
        "    return np.linalg.norm(x)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "30c2aoJYNWCY"
      },
      "source": [
        "####ESを用いてSphere関数を最適化する．"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "id": "g0s0jZ7YNWCY"
      },
      "outputs": [],
      "source": [
        "es = ES(func=sphere,            \n",
        "        init_mean=np.ones(10),  \n",
        "        init_sigma=0.001,        \n",
        "        nsample=10)             \n",
        "\n",
        "maxiter = 5000\n",
        "fbest = np.zeros(maxiter) * np.nan\n",
        "fmean = np.zeros(maxiter) * np.nan\n",
        "sigmaN = np.zeros(maxiter) * np.nan\n",
        "for i in range(fbest.shape[0]):\n",
        "    es.sample()\n",
        "    es.evaluate()\n",
        "    es.update_mean()\n",
        "    fbest[i] = es.arf.min()\n",
        "    fmean[i] = sphere(es.mean)\n",
        "    sigmaN[i] = es.sigma * es.N"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u_p14zT0NWCZ"
      },
      "source": [
        "####結果をプロットする．"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "mXo6QYjTNWCZ",
        "outputId": "15e0730f-ff25-4722-a707-260feb003852"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x10d980c90>"
            ]
          },
          "execution_count": 7,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
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pqihVLLeMR6BUpdLilCS25NYgPx9iXHGurFT50K+7i2j7p82JWNRsmkhtDrBz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\nTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x103bb7490>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.semilogy(fbest, '-r', label='f(best)')\n",
        "plt.semilogy(fmean, '-b', label='f(mean)')\n",
        "plt.semilogy(sigmaN, '--g', label='sigma*N')\n",
        "plt.xlabel('no. of iterations', fontsize='large')\n",
        "plt.grid()\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lgpBBvg3NWCa"
      },
      "source": [
        "##考察"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9YvbdF8ANWCa"
      },
      "source": [
        "* init_mean や init_sigma を変えて実験してみよう (適宜maxiterを変更すること)\n",
        "* 振る舞いを三つの状況(序盤の遅い探索，中盤の速い探索，終盤の停滞)に分けて，それぞれmeanとsigmaがどのような関係にあるのか考えよう\n",
        "* 中盤の速い探索が続くように，ステップサイズの更新を実装しよう．"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xzHpTduqNWCa"
      },
      "outputs": [],
      "source": [
        "es = ES(func=sphere,            \n",
        "        init_mean=np.ones(10),  \n",
        "        init_sigma=0.001,        \n",
        "        nsample=10)             \n",
        "\n",
        "maxiter = 100\n",
        "fbest = np.zeros(maxiter) * np.nan\n",
        "fmean = np.zeros(maxiter) * np.nan\n",
        "sigmaN = np.zeros(maxiter) * np.nan\n",
        "for i in range(fbest.shape[0]):\n",
        "    es.sample()\n",
        "    es.evaluate()\n",
        "    es.update_mean()\n",
        "    # ステップサイズを更新\n",
        "    old_sigma = es.sigma\n",
        "    \n",
        "    es.sigma = sphere(es.mean) / es.N\n",
        "    # ここまで\n",
        "    fbest[i] = es.arf.min()\n",
        "    fmean[i] = sphere(es.mean)\n",
        "    sigmaN[i] = es.sigma * es.N"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": true,
        "id": "qGBigtMhNWCa"
      },
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    },
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "gpuClass": "standard"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}