notebooks/RL_multi_step.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import jax.numpy as jnp\n",
    "import jax"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "始める前に表記について説明します。今回は次の表記を使っていきます。\n",
    "* $(\\pi Q)(x):=\\sum_{a \\in \\mathbf{A}} \\pi(a \\mid x) Q(x, a)$\n",
    "* $(\\mathcal{P} V)(x, a):=\\sum_{y \\in \\mathbf{X}} \\mathcal{P}(y \\mid x, a) V(y)$\n",
    "\n",
    "また、$\\pi_Q \\in G(Q)$をQについての貪欲方策とし、$\\mathcal{T}^{\\pi}Q :=r + \\gamma\\mathcal{P}^\\pi Q$、$\\mathcal{T}Q :=r + \\gamma\\mathcal{P}^{\\pi_Q} Q$とします。\n",
    "他のNotationは[論文](https://arxiv.org/abs/2103.00107)と雰囲気に任せます。"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
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   "source": [
    "# マルチステップ強化学習\n",
    "\n",
    "参考\n",
    "* [Revisiting Peng's Q(λ) for Modern Reinforcement Learning](https://arxiv.org/abs/2103.00107)\n",
    "\n",
    "強化学習の基本は``推定``と``制御``にあります。\n",
    "RLアルゴリズムは「推定と制御で何ステップ分の情報を使うか？」で一般化することができます。\n",
    "今回は一般的なアルゴリズムをいくつか確認していきましょう。\n",
    "\n",
    "まず、一番基本であるValue Iterationアルゴリズムを確認します。\n",
    "\n",
    "--- \n",
    "\n",
    "**Value Iteration (VI)**\n",
    "\n",
    "* 推定: $Q_{k+1} := r + \\mathcal{P}^{\\pi_k} Q_k$\n",
    "* 制御: $\\pi_{k+1} := \\pi_{Q_{k+1}}$\n",
    "* ベルマン作用素: $\\mathcal{T}^\\pi Q := r + \\gamma \\mathcal{P}^\\pi Q$\n",
    "\n",
    "これは「1ステップの貪欲方策」と「1ステップの推定」をしていると考えることができます。\n",
    "\n",
    "---\n",
    "\n",
    "マルチステップのアルゴリズムを見ていきましょう。\n",
    "まずは推定についてマルチステップなアルゴリズムを見ていきます。\n",
    "\n",
    "## マルチステップ推定\n",
    "\n",
    "### On-policyのアルゴリズム\n",
    "\n",
    "---\n",
    "**Modified Policy Iteration (MPI)** \n",
    "* 参考文献: [Modified Policy Iteration Algorithms for Discounted Markov Decision Problems](https://www.jstor.org/stable/2630487)\n",
    "\n",
    "MPIは価値反復法の一般化です。$n$-ステップ推定をします。$n=1$ならVIと同じです。\n",
    "\n",
    "* 推定: $Q_{k+1} := \\left(\\mathcal{T}^{\\pi_{k}}\\right)^n Q_k = r + \\mathcal{P}^{\\pi_k} \\left(r + \\mathcal{P}^{\\pi_k} + \\left(\\dots + \\left(r + \\mathcal{P}^{\\pi_k} Q_k\\right)\\right)\\right)$\n",
    "* 制御: $\\pi_{k+1} := \\pi_{Q_{k+1}}$\n",
    "* ベルマン作用素: $\\mathcal{T}_n^\\pi := \\left(\\mathcal{T}^{\\pi}\\right)^n Q$\n",
    "\n",
    "---\n",
    "\n",
    "---\n",
    "**$\\lambda$-Policy Iteration ($\\lambda$-PI)**\n",
    "* 参考文献: [Temporal Differences-Based Policy Iteration and Applications in Neuro-Dynamic Programming](https://web.mit.edu/dimitrib/www/Tempdif.pdf)\n",
    "\n",
    "$\\lambda$-PIはMPIの一般化です。$[1 \\dots \\infty]$-ステップ推定を$\\lambda$で重み付けして混ぜます。\n",
    "* 推定: $Q_{k+1} := (1 - \\lambda)\\sum^\\infty_{n=1}\\lambda^{n-1}\\mathcal{T}^{\\pi_k}_n Q_k$\n",
    "* 制御: $\\pi_{k+1} := \\pi_{Q_{k+1}}$\n",
    "* ベルマン作用素: $\\mathcal{T}^\\pi_\\lambda := (1 - \\lambda)\\sum^\\infty_{n=1}\\lambda^{n-1}\\mathcal{T}^{\\pi}_n Q = Q + (I - \\gamma \\lambda \\mathcal{P}^\\pi)^{-1} (\\mathcal{T}^\\pi Q - Q)$\n",
    "\n",
    "---\n",
    "\n",
    "先にOn-policyのアルゴリズムをPythonで確認してみましょう。\n",
    "まずMDPを作ります。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
     ]
    }
   ],
   "source": [
    "from typing import Optional, NamedTuple\n",
    "\n",
    "def create_rew_P(S: int, A: int):\n",
    "    \"\"\" テーブルMDP (報酬関数, 遷移確率) を作成します\n",
    "\n",
    "    Args:\n",
    "        S (int): 状態空間のサイズ\n",
    "        A (int): 行動空間のサイズ\n",
    "\n",
    "    Returns:\n",
    "        rew (float): 報酬関数\n",
    "        P (float): 遷移確率\n",
    "    \"\"\"\n",
    "    rew = np.random.rand(S, A)  # ランダムな報酬関数。実験のために0~1に正規化します。\n",
    "    rew = rew / np.abs(rew).max()\n",
    "\n",
    "    # ランダムな遷移確率を作ります\n",
    "    P = np.random.rand(S, A, S)\n",
    "    P = P / np.sum(P, axis=-1, keepdims=True)  # 正規化して確率にします\n",
    "    assert P.shape == (S, A, S)\n",
    "    np.testing.assert_almost_equal(P.sum(axis=-1), 1)\n",
    "\n",
    "    return jnp.array(rew), jnp.array(P)\n",
    "\n",
    "class MDP(NamedTuple):\n",
    "    S_array: np.array  # 状態空間\n",
    "    A_array: np.array  # 行動空間\n",
    "    gamma: float  # 割引率\n",
    "    horizon: int  # ホライゾン\n",
    "    rew: float  # 報酬関数\n",
    "    P: float  # 遷移確率\n",
    "    optimal_Q: Optional[np.ndarray] = None  # 最適Q値\n",
    "    optimal_Q_idx: Optional[np.ndarray] = None  # 後でplot用に使います\n",
    "\n",
    "    @property\n",
    "    def S(self) -> int:  # 状態空間のサイズ\n",
    "        return len(self.S_array)\n",
    "\n",
    "    @property\n",
    "    def A(self) -> int:  # 行動空間のサイズ\n",
    "        return len(self.A_array)\n",
    "\n",
    "\n",
    "S = 10\n",
    "A = 2\n",
    "S_array = np.arange(S)\n",
    "A_array = np.arange(A)\n",
    "gamma = 0.99\n",
    "horizon = int(1 / (1 - gamma))\n",
    "\n",
    "# テーブルMDPを作ります\n",
    "t_rew, t_P = create_rew_P(S, A)\n",
    "table_MDP = MDP(S_array, A_array, gamma, horizon, t_rew, t_P)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "実験の前に、いくつか便利な関数を導入します。\n",
    "\n",
    "1. ``compute_greedy_policy``: Q関数 ($S \\times A \\to \\mathcal{R}$) の貪欲方策を返します\n",
    "2. ``compute_optimal_Q``: MDPの最適Q関数 $q_* : S \\times A \\to \\mathcal{R}$ を返します。\n",
    "3. ``compute_policy_Q``: 方策 $\\pi$ のQ関数 $q_\\pi : S \\times A \\to \\mathcal{R}$ を返します。\n",
    "4. ``compute_optimality_gap``: 方策 $\\pi$ と最適解との差 $\\|q_* - q_{\\pi}\\|_\\infty$ を返します。この値が小さいほど、$\\pi$ はほぼ全ての状態行動対で最適な方策になっています。\n",
    "5. ``compute_Ppi``: 方策$\\pi$の元での遷移行列$\\mathcal{P}^{\\pi}$を返します。[これ](http://proceedings.mlr.press/v28/pirotta13.pdf)の２ページ目を参考にしてください"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from functools import partial\n",
    "\n",
    "\n",
    "# >>>> 1 >>>>\n",
    "@jax.jit\n",
    "def compute_greedy_policy(Q: np.ndarray):\n",
    "    greedy_policy = jnp.zeros_like(Q)\n",
    "    S, A = Q.shape\n",
    "    greedy_policy = greedy_policy.at[jnp.arange(S), Q.argmax(axis=1)].set(1)\n",
    "    assert greedy_policy.shape == (S, A)\n",
    "    return greedy_policy\n",
    "# <<<< 1 <<<<\n",
    "\n",
    "\n",
    "# >>>> 2 >>>>\n",
    "@partial(jax.jit, static_argnames=(\"S\", \"A\"))\n",
    "def _compute_optimal_Q(mdp: MDP, S: int, A: int):\n",
    "\n",
    "    def backup(optimal_Q):\n",
    "        greedy_policy = compute_greedy_policy(optimal_Q)\n",
    "        max_Q = (greedy_policy * optimal_Q).sum(axis=1)\n",
    "        next_v = mdp.P @ max_Q\n",
    "        assert next_v.shape == (S, A)\n",
    "        return mdp.rew + mdp.gamma * next_v\n",
    "    \n",
    "    optimal_Q = jnp.zeros((S, A))\n",
    "    body_fn = lambda i, Q: backup(Q)\n",
    "    return jax.lax.fori_loop(0, mdp.horizon + 1000, body_fn, optimal_Q)\n",
    "\n",
    "compute_optimal_Q = lambda mdp: _compute_optimal_Q(mdp, mdp.S, mdp.A)\n",
    "# <<<< 2 <<<<\n",
    "\n",
    "\n",
    "# >>>> 3 >>>>\n",
    "def compute_policy_Q(mdp: MDP, policy: np.ndarray):\n",
    "    S, A = policy.shape\n",
    "\n",
    "    def backup(policy_Q):\n",
    "        max_Q = (policy * policy_Q).sum(axis=1)\n",
    "        next_v = mdp.P @ max_Q\n",
    "        assert next_v.shape == (S, A)\n",
    "        return mdp.rew + mdp.gamma * next_v\n",
    "    \n",
    "    policy_Q = jnp.zeros((S, A))\n",
    "    body_fn = lambda i, Q: backup(Q)\n",
    "    return jax.lax.fori_loop(0, mdp.horizon + 1000, body_fn, policy_Q)\n",
    "# <<<< 3 <<<<\n",
    "\n",
    "# >>>> 4 >>>>\n",
    "@jax.jit\n",
    "def compute_optimality_gap(mdp: MDP, policy: np.ndarray):\n",
    "    policy_Q = compute_policy_Q(mdp, policy)\n",
    "    optimality_gap = jnp.abs(mdp.optimal_Q - policy_Q).max()\n",
    "    return optimality_gap\n",
    "# <<<< 4 <<<<\n",
    "\n",
    "\n",
    "# >>>> 5 >>>>\n",
    "@jax.jit\n",
    "def compute_Ppi(mdp: MDP, policy: np.ndarray):\n",
    "    P = mdp.P.reshape(S*A, S)\n",
    "    PI = jnp.zeros((S, S, A))\n",
    "    for s in range(S):\n",
    "        PI = PI.at[s, s].set(policy[s])\n",
    "    PI = PI.reshape(S, S*A)\n",
    "    Ppi = P @ PI\n",
    "    assert Ppi.shape == (S*A, S*A)\n",
    "    return Ppi\n",
    "# <<<< 5 <<<<\n",
    "\n",
    "table_MDP = table_MDP._replace(optimal_Q=compute_optimal_Q(table_MDP))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## On-policyアルゴリズムの実験\n",
    "\n",
    "さっそくOn-policyアルゴリズムの実験をしてみます。\n",
    "それぞれIterationの回数で比較していますが、これはあんまりフェアではありません。MPIの$n$が大きくなるほど計算量が増えるためであり、また、そもそも$\\lambda$-PIの解析回は無限和を使っています。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fbf58087910>"
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     "execution_count": 7,
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     "output_type": "execute_result"
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",
      "text/plain": [
       "<Figure size 1600x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@partial(jax.jit, static_argnames=(\"n_step\"))\n",
    "def n_step_evaluate(mdp: MDP, Q: np.ndarray, policy: np.ndarray, n_step: int):\n",
    "    # n-step 推定をします\n",
    "    S, A = Q.shape\n",
    "    for i in range(n_step):\n",
    "        Q_pi = np.sum(policy * Q, axis=1).reshape(1, 1, S)\n",
    "        next_v = np.sum(mdp.P * Q_pi, axis=-1)\n",
    "        assert next_v.shape == (S, A)\n",
    "        Q = mdp.rew + mdp.gamma * next_v\n",
    "        assert Q.shape == (S, A)\n",
    "    return Q\n",
    "\n",
    "\n",
    "@partial(jax.jit)\n",
    "def lambda_evaluate(mdp: MDP, Q: np.ndarray, policy: np.ndarray, lam: float):\n",
    "    # lambda-PIの推定ステップをします\n",
    "    S, A = Q.shape\n",
    "    TQ = n_step_evaluate(mdp, Q, policy, 1)\n",
    "    Ppi = compute_Ppi(mdp, policy)\n",
    "    return Q + (jnp.linalg.inv(jnp.eye(S*A) - gamma * lam * Ppi) @ (TQ - Q).reshape(S*A)).reshape(S, A)\n",
    "\n",
    "\n",
    "\n",
    "def do_table_value_iteration(mdp: MDP, n_step: int, lam: float, iteration: int):\n",
    "    optimality_gaps = []\n",
    "    Q_gaps = []\n",
    "    \n",
    "    # >>>> Do value iteration >>>>\n",
    "    Q_table = np.zeros((mdp.S, mdp.A))\n",
    "    for i in range(iteration):\n",
    "        greedy_policy = compute_greedy_policy(Q_table)\n",
    "        if lam is None:\n",
    "            Q_table = n_step_evaluate(mdp, Q_table, greedy_policy, n_step)\n",
    "        elif n_step is None:\n",
    "            Q_table = lambda_evaluate(mdp, Q_table, greedy_policy, lam)\n",
    "        optimality_gaps.append(compute_optimality_gap(mdp, greedy_policy))\n",
    "        Q_gaps.append(np.abs(Q_table - mdp.optimal_Q).max())\n",
    "    # <<<< Do value iteration <<<<\n",
    "\n",
    "    return optimality_gaps, Q_gaps\n",
    "\n",
    "VI_opt, VI_q = do_table_value_iteration(table_MDP, 1, None, 100)\n",
    "MPI_opt, MPI_q = do_table_value_iteration(table_MDP, 10, None, 100)\n",
    "lam01_opt, lam01_q = do_table_value_iteration(table_MDP, None, 0.1, 100)\n",
    "lam099_opt, lam099_q = do_table_value_iteration(table_MDP, None, 0.99, 100)\n",
    "\n",
    "\n",
    "plt.figure(figsize=(16, 4))\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(VI_opt, label=\"Value Iteration\")\n",
    "plt.plot(MPI_opt, label=\"Modified Policy Iteration (n=10)\")\n",
    "plt.plot(lam01_opt, label=r\"$\\lambda$-PI ($\\lambda=0.1$)\")\n",
    "plt.plot(lam099_opt, label=r\"$\\lambda$-PI ($\\lambda=0.99$)\")\n",
    "plt.xlabel(\"Iteration\")\n",
    "plt.ylabel(r\"$\\|q^* - q_{\\pi_k}\\|_\\infty$\")\n",
    "plt.title(\"Optimality Gap\")\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.plot(VI_q, label=\"Value Iteration\")\n",
    "plt.plot(MPI_q, label=\"Modified Policy Iteration (n=10)\")\n",
    "plt.plot(lam01_q, label=r\"$\\lambda$-PI ($\\lambda=0.1$)\")\n",
    "plt.plot(lam099_q, label=r\"$\\lambda$-PI ($\\lambda=0.99$)\")\n",
    "plt.xlabel(\"Iteration\")\n",
    "plt.ylabel(r\"$\\|q^* - q_{k}\\|_\\infty$\")\n",
    "plt.title(\"Learned Q vs Optimal Q\")\n",
    "# <<<< Plot results <<<<\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.legend()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Off-policyのアルゴリズム\n",
    "\n",
    "On-policyのアルゴリズムでは推定で$r + \\mathcal{P}^{\\pi_k}(r + \\dots)$が登場していました。\n",
    "しかし、これはいつでもできるわけではありません。Off-policyでは別の方策で代替します。\n",
    "\n",
    "### Traceによる補正をしないアルゴリズム\n",
    "\n",
    "On-policyのアルゴリズムをそのままOff-policyにするとBehavior方策とTarget方策間の差異による問題が発生します。\n",
    "これを補正するために、Trajectoryの計算中に補正用の係数 (trace) をかけることがあります。\n",
    "一方で、方策の補正が面倒くさいのでしないアルゴリズムも存在しています。先にそっちを見てみましょう。\n",
    "\n",
    "---\n",
    "**Uncorrected $n$-step Return** \n",
    "* 参考文献: [Rainbow: Combining Improvements in Deep Reinforcement Learning](https://arxiv.org/abs/1710.02298)\n",
    "* 参考文献: [Recurrent experience replay in distributed reinforcement learning](https://www.deepmind.com/publications/recurrent-experience-replay-in-distributed-reinforcement-learning)\n",
    "\n",
    "MPIはOn-policyな更新でした。これはOff-policyアルゴリズムでは使うのが難しいので、RainbowやR2D2では次のOff-policy版を使っています。\n",
    "\n",
    "* 推定: $Q_{k+1} := \\left(\\mathcal{T}^{\\mu_k}\\right)^{n-1} \\mathcal{T}^{\\pi_k}Q_k = r + \\mathcal{P}^{\\mu_k} \\left(r + \\mathcal{P}^{\\mu_k} + \\left(\\dots + \\left(r + \\mathcal{P}^{\\pi_k} Q_k\\right)\\right)\\right)$\n",
    "* 制御: $\\pi_{k+1} := \\pi_{Q_{k+1}}$\n",
    "* ベルマン作用素: $\\mathcal{N}_n^{\\mu, \\pi} := \\left(\\mathcal{T}^{\\mu}\\right)^{n-1} \\mathcal{T}^\\pi Q$\n",
    "\n",
    "---\n",
    "\n",
    "---\n",
    "**Peng's $Q(\\lambda)$ (PQL)** \n",
    "* 参考文献: [Incremental multi-step Q-learning](https://link.springer.com/article/10.1007/BF00114731)\n",
    "\n",
    "PQLは$\\lambda$-PIのOff-policyバージョンです。\n",
    "\n",
    "* 推定: $Q_{k+1} := (1 - \\lambda)\\sum^\\infty_{n=1}\\lambda^{n-1}\\mathcal{N}^{\\mu_k, \\pi_k}_n Q_k$\n",
    "* 制御: $\\pi_{k+1} := \\pi_{Q_{k+1}}$\n",
    "* ベルマン作用素: $\\mathcal{N}^{\\mu, \\pi}_\\lambda := (1 - \\lambda)\\sum^\\infty_{n=1}\\lambda^{n-1}\\mathcal{N}^{\\mu, \\pi}_n Q$\n",
    "\n",
    "---\n",
    "\n",
    "最後に、補正を含めた一般的なアルゴリズムを確認してみます。\n",
    "\n",
    "---\n",
    "\n",
    "**General Retrace**\n",
    "\n",
    "* 参考文献: [Revisiting Peng's Q(λ) for Modern Reinforcement Learning](https://arxiv.org/abs/2103.00107)\n",
    "\n",
    "General RetraceはPQLに補正項を追加したものです。\n",
    "補正項を導入するために、次の遷移カーネルを導入します：\n",
    "\n",
    "$$\\left(\\mathcal{P}^{c \\mu} Q\\right)(x, a):=\\sum_{(y, b) \\in \\mathbf{X} \\times \\mathbf{A}} \\mathcal{P}(y \\mid x, a) c(y, b) \\mu(b \\mid y) Q(y, b)$$\n",
    "\n",
    "これを使ってGeneral Retraceは次で推定と制御をします。\n",
    "\n",
    "* 推定: $Q_{k+1} := \\mathcal{R}_{\\lambda}^{c_k \\mu_k, \\pi_k} Q_k$\n",
    "* 制御: $\\pi_{k+1} := \\pi_{Q_{k+1}}$\n",
    "* ベルマン作用素: $\\mathcal{R}_{\\lambda}^{c \\mu, \\pi} Q:=Q+\\left(\\mathcal{I}-\\gamma \\lambda \\mathcal{P}^{c \\mu}\\right)^{-1}\\left(\\mathcal{T}^{\\pi} Q-Q\\right) .\n",
    "$\n",
    "\n",
    "ここで、$Q_k$は\n",
    "$$\n",
    "Q_{k}\\left(x_{0}, a_{0}\\right)+\\sum_{t=0}^{\\infty}\\left(\\prod_{u=1}^{t} c\\left(x_{u}, a_{u}\\right)\\right) \\gamma^{t} \\lambda^{t} \\delta_{t}\n",
    "$$\n",
    "の形で書き直せます。$\\delta_t$はTD誤差です。これはつまり、Off-policyなTD誤差を$\\prod_{u=1}^{t} c\\left(x_{u}, a_{u}\\right)$ で補正しているとみなせます。この補正項$\\prod_{u=1}^{t} c\\left(x_{u}, a_{u}\\right)$がtraceと呼ばれます。\n",
    "\n",
    "$c_k$の設計次第で様々なアルゴリズムが復元されます。$\\rho_k = \\pi_k / \\mu_k$, $\\widetilde{\\rho}_k = (1 - \\alpha) + \\alpha \\pi_{Q_k}$として、下の表を参考にしてください (参考文献のTable 2と同じですが、論文では$\\lambda$と$1-\\lambda$が逆になってます)。\n",
    "\n",
    "| Algorithm     | $c_{k}$                                       | $\\pi_{k}$                                 |\n",
    "|----------------------|-----------------------------------------------|-------------------------------------------|\n",
    "| $\\alpha$-TRACE | $\\min \\left\\{1, \\widetilde{\\rho}_{k}\\right\\}$ | $(1-\\alpha) \\pi_{Q_{k}}+\\alpha \\mu_{k}$   |\n",
    "| C-TRACE              | $\\min \\left\\{1, \\widetilde{\\rho}_{k}\\right\\}$ | $(1-\\alpha) \\pi_{Q_{k}}+\\alpha \\mu_{k}$   |\n",
    "| HQL                  | 1                                             | $\\pi_{Q_{k}}$                             |\n",
    "| RETRACE              | $\\min \\left\\{1, \\rho_{k}\\right\\}$             | $\\mathrm{ANY}$                            |\n",
    "| TBL                  | $\\pi_{k}$                                     | $\\mathrm{ANY}$                            |\n",
    "| $\\mathrm{WQL}$       | $\\min \\left\\{1, \\rho_{k}\\right\\}$             | $\\pi_{Q_{k}}$                             |\n",
    "| PQL                  | 1                                             | $(1-\\lambda) \\pi_{Q_{k}}+\\lambda \\mu_{k}$ |\n",
    "\n",
    "\n",
    "---"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Off-policyアルゴリズムの実験\n",
    "\n",
    "Off-policyアルゴリズムの実験をしてみましょう。\n",
    "様々な$c_k$や$\\pi_k$でGeneral Retraceの挙動を観察してみます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fbfaef563d0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@partial(jax.jit)\n",
    "def lambda_evaluate(mdp: MDP, Q: np.ndarray, policy: np.ndarray, c_k: np.ndarray, behavior_policy: np.ndarray, lam: float):\n",
    "    # lambda-PIの推定ステップをします\n",
    "    S, A = Q.shape\n",
    "    TQ = n_step_evaluate(mdp, Q, policy, 1)\n",
    "    Ppi = compute_Ppi(mdp, c_k * behavior_policy)\n",
    "    return Q + (jnp.linalg.inv(jnp.eye(S*A) - gamma * (1-lam) * Ppi) @ (TQ - Q).reshape(S*A)).reshape(S, A)\n",
    "\n",
    "\n",
    "def do_table_value_iteration(mdp: MDP, lam: float, c_type: str, iteration: int):\n",
    "    optimality_gaps = []\n",
    "    Q_gaps = []\n",
    "    \n",
    "    # Initialize Q\n",
    "    Q_table = np.zeros((mdp.S, mdp.A))\n",
    "\n",
    "    # Behavior policy\n",
    "    behavior_policy = np.ones_like(Q_table)  # 一様分布です\n",
    "    behavior_policy = behavior_policy / behavior_policy.sum(axis=1, keepdims=True)\n",
    "\n",
    "    # >>>> Do value iteration >>>>\n",
    "    for i in range(iteration):\n",
    "        greedy_policy = compute_greedy_policy(Q_table)\n",
    "\n",
    "        # c_kを計算し、pi_kも計算します\n",
    "        if c_type == \"TBL\":\n",
    "            c_k = greedy_policy\n",
    "            policy = greedy_policy\n",
    "\n",
    "        elif c_type == \"PQL\":\n",
    "            c_k = 1\n",
    "            policy = (1-lam) * greedy_policy + lam * behavior_policy\n",
    "\n",
    "        elif c_type == \"Retrace\":\n",
    "            c_k = np.minimum(1, greedy_policy / behavior_policy)\n",
    "            policy = greedy_policy\n",
    "\n",
    "        Q_table = lambda_evaluate(mdp, Q_table, policy, c_k, behavior_policy, lam)\n",
    "        optimality_gaps.append(compute_optimality_gap(mdp, policy))\n",
    "        Q_gaps.append(np.abs(Q_table - mdp.optimal_Q).max())\n",
    "    # <<<< Do value iteration <<<<\n",
    "    return Q_gaps\n",
    "\n",
    "lam = 0.9\n",
    "iteration = 1000\n",
    "res_TBL = do_table_value_iteration(table_MDP, lam, \"TBL\", iteration)\n",
    "res_PQL_09 = do_table_value_iteration(table_MDP, lam, \"PQL\", iteration)\n",
    "res_Retrace = do_table_value_iteration(table_MDP, lam, \"Retrace\", iteration)\n",
    "res_PQL_01 = do_table_value_iteration(table_MDP, 0.1, \"PQL\", iteration)\n",
    "res_PQL_001 = do_table_value_iteration(table_MDP, 0.01, \"PQL\", iteration)\n",
    "\n",
    "plt.plot(res_TBL, label=r\"TBL ($\\lambda = 0.9$)\")\n",
    "plt.plot(res_Retrace, label=r\"Retrace ($\\lambda = 0.9$)\")\n",
    "plt.plot(res_PQL_001, label=r\"PQL ($\\lambda = 0.01$)\")\n",
    "plt.plot(res_PQL_01, label=r\"PQL ($\\lambda = 0.1$)\")\n",
    "plt.plot(res_PQL_09, label=r\"PQL ($\\lambda = 0.9$)\")\n",
    "plt.legend()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "結果から何が分かるでしょうか？\n",
    "\n",
    "TBLとRetraceのような補正をするアルゴリズムがちゃんと収束していることがわかります。この２つが$Q_\\pi$と$Q_*$に収束することは原著で証明されています。\n",
    "\n",
    "一方で、PQLは$\\lambda$の値次第では収束ができていません。これは[Revisiting Peng's Q(λ) for Modern Reinforcement Learning](https://arxiv.org/abs/2103.00107)で証明されてますが、PQLは$Q^{\\lambda \\mu+(1-\\lambda) \\pi_{\\dagger}}$に収束します。\n",
    "ここで、$\\pi_\\dagger$は任意の$\\pi$で$Q^{\\lambda \\mu+(1-\\lambda) \\pi_{\\dagger}} \\geq Q^{\\lambda \\mu+(1-\\lambda) \\pi}$を満たす方策です。\n",
    "つまり、$\\lambda$の値が$1$に近いほど学習する$Q$値にバイアスが乗ります。"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## マルチステップ制御\n",
    "\n",
    "これまでのアルゴリズムでは１ステップについて貪欲な方策を考えていましたが、必ずしもこれは１ステップである必要がありません。\n",
    "例えばMonte Carlo木探索やモデル予測制御は複数ステップについて貪欲な方策を吐き出しています。\n",
    "ここからはマルチステップな制御を行うアルゴリズムを見ていきましょう。\n",
    "\n",
    "\n",
    "### On-policyのアルゴリズム\n",
    "\n",
    "---\n",
    "**$h$-Greedy policy** \n",
    "\n",
    "* 参考文献: [Multiple-Step Greedy Policies in Online and Approximate Reinforcement Learning](https://arxiv.org/abs/1805.07956)\n",
    "\n",
    "$h$-貪欲方策では$h$ステップだけ貪欲な方策を考えます。つまり、$h=1$ならVIと同じです。\n",
    "推定の方は省略します。\n",
    "次の方策集合$\\mathcal{G}_h$の要素を$h$-貪欲方策と呼びます。\n",
    "\n",
    "* 準備: $\\forall v, \\pi, T_{h}^{\\pi} v \\stackrel{\\text { def }}{=} T^{\\pi} T^{h-1} v$\n",
    "* 制御: $\\forall v, \\mathcal{G}_{h}(v) =\\left\\{\\pi: T_{h}^{\\pi} v=T^{h} v\\right\\}$\n",
    "\n",
    "---\n",
    "\n",
    "---\n",
    "\n",
    "**$\\kappa$-Greedy policy** \n",
    "\n",
    "$\\lambda$-PIは無限ステップの重み付き推定を考えていましたが、同様にして無限ステップの重み付き貪欲方策も考えることができます。\n",
    "\n",
    "次の方策集合の要素を$\\kappa$-貪欲方策と呼びます。\n",
    "\n",
    "* 準備: $\\forall v, \\pi, T_{\\kappa}^{\\pi} v \\stackrel{\\text { def }}{=}(1-\\kappa) \\sum_{j=0}^{\\infty} \\kappa^{j}\\left(T^{\\pi}\\right)^{j+1} v$\n",
    "* 制御: $\\forall v, \\mathcal{G}_{\\kappa}(v)=\\left\\{\\pi: T_{\\kappa}^{\\pi} v=T_{\\kappa} v\\right\\}$\n",
    "\n",
    "また、$\\kappa$-貪欲方策では次が成立します。\n",
    "$$\n",
    "\\forall v, \\pi, T_{\\kappa}^{\\pi} v =\\left(I-\\kappa \\gamma P^{\\pi}\\right)^{-1}\\left(r^{\\pi}+(1-\\kappa) \\gamma P^{\\pi} v\\right) \n",
    "$$\n",
    "\n",
    "これを$v^{*}=\\left(I-\\gamma P^{\\pi^{*}}\\right)^{-1} r^{\\pi^{*}}$と比較すると、$\\kappa$-貪欲方策は「割引率が$\\kappa\\gamma$かつ報酬関数が$\\hat{r}^{\\pi, v} \\stackrel{\\text { def }}{=} r^{\\pi}+(1-\\kappa) \\gamma P^{\\pi} v$で定義されたMDP (Surrogate MDP) の最適方策」と一致することがわかります。\n",
    "\n",
    "---\n",
    "\n",
    "さっそく実験してみましょう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fbf3c5e0e50>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@partial(jax.jit, static_argnames=(\"h_step\"))\n",
    "def h_step_control(mdp: MDP, Q: np.ndarray, h_step: int):\n",
    "    # n-step 制御をします\n",
    "    S, A = Q.shape\n",
    "    for i in range(h_step-1):\n",
    "        Q_max = Q.max(axis=1).reshape(1, 1, S)\n",
    "        next_v = np.sum(mdp.P * Q_max, axis=-1)\n",
    "        assert next_v.shape == (S, A)\n",
    "        Q = mdp.rew + mdp.gamma * next_v\n",
    "        assert Q.shape == (S, A)\n",
    "    h_step_greedy_policy = compute_greedy_policy(Q)\n",
    "    return h_step_greedy_policy\n",
    "\n",
    "\n",
    "@partial(jax.jit)\n",
    "def kappa_control(mdp: MDP, Q: np.ndarray, kappa: float):\n",
    "    # kappa-貪欲方策を計算します。\n",
    "    S, A = Q.shape\n",
    "    max_Q = Q.max(axis=-1)\n",
    "    rew = mdp.rew + (1 - kappa) * mdp.gamma * mdp.P @ max_Q\n",
    "\n",
    "    # surrogate MDPの最適Qを計算します。\n",
    "    def backup(optimal_Q):\n",
    "        max_Q = optimal_Q.max(axis=-1)\n",
    "        next_v = mdp.P @ max_Q\n",
    "        assert next_v.shape == (S, A)\n",
    "        return rew + mdp.gamma * kappa * next_v\n",
    "    \n",
    "    optimal_Q = jnp.zeros((S, A))\n",
    "    body_fn = lambda i, Q: backup(Q)\n",
    "    optimal_Q = jax.lax.fori_loop(0, mdp.horizon + 1000, body_fn, optimal_Q)\n",
    "\n",
    "    # 貪欲方策を返します\n",
    "    return compute_greedy_policy(optimal_Q)\n",
    "\n",
    "\n",
    "\n",
    "def do_table_value_iteration(mdp: MDP, h_step: int, kappa: float, iteration: int):\n",
    "    optimality_gaps = []\n",
    "    Q_gaps = []\n",
    "    \n",
    "    # >>>> Do value iteration >>>>\n",
    "    Q_table = np.zeros((mdp.S, mdp.A))\n",
    "    for i in range(iteration):\n",
    "        if kappa is None:\n",
    "            greedy_policy = h_step_control(mdp, Q_table, h_step)\n",
    "        elif h_step is None:\n",
    "            greedy_policy = kappa_control(mdp, Q_table, kappa)\n",
    "        Q_table = n_step_evaluate(mdp, Q_table, greedy_policy, 1)\n",
    "        optimality_gaps.append(compute_optimality_gap(mdp, greedy_policy))\n",
    "        Q_gaps.append(np.abs(Q_table - mdp.optimal_Q).max())\n",
    "    # <<<< Do value iteration <<<<\n",
    "    return optimality_gaps, Q_gaps \n",
    "\n",
    "h_opt, h_q = do_table_value_iteration(table_MDP, 10, None, 100)\n",
    "kap_opt, kap_q = do_table_value_iteration(table_MDP, None, 0.1, 100)\n",
    "\n",
    "\n",
    "plt.figure(figsize=(16, 4))\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(h_opt, label=r\"$h$-Greedy Policy (h=10)\")\n",
    "plt.plot(kap_opt, label=r\"$\\kappa$-Greedy Policy ($\\kappa=0.1$)\")\n",
    "plt.xlabel(\"Iteration\")\n",
    "plt.ylabel(r\"$\\|q^* - q_{\\pi_k}\\|_\\infty$\")\n",
    "plt.title(\"Optimality Gap\")\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.plot(h_q, label=r\"$h$-Greedy Policy (h=10)\")\n",
    "plt.plot(kap_q, label=r\"$\\kappa$-Greedy Policy ($\\kappa=0.1$)\")\n",
    "plt.xlabel(\"Iteration\")\n",
    "plt.ylabel(r\"$\\|q^* - q_{k}\\|_\\infty$\")\n",
    "plt.title(\"Learned Q vs Optimal Q\")\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.legend()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MDPが小さすぎてあんまり差が出ないですね。まあ実装がわかったのでOKとします。\n",
    "重要な性質: 「$\\kappa$-貪欲方策と$\\lambda$-推定は、どちらもちゃんと最適方策への収束が保証されています」"
   ]
  }
 ],
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