Maxmin_Qlearning.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a6e54614",
   "metadata": {
    "id": "a6e54614"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a7abf2ce",
   "metadata": {
    "id": "a7abf2ce"
   },
   "outputs": [],
   "source": [
    "N = 3\n",
    "alpha = 0.01\n",
    "gamma = 1\n",
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ea4d225f",
   "metadata": {
    "id": "ea4d225f"
   },
   "outputs": [],
   "source": [
    "def rewardnstate(a, s):\n",
    "    r, state, terminal = P[s][a]\n",
    "    if s==1 and a==0:\n",
    "        r = r + np.random.uniform(-1, 1)\n",
    "    return r, state, terminal\n",
    "#     if s==1:\n",
    "#         r = r + np.random.uniform(-1, 1)\n",
    "#     return r, state, terminal\n",
    "\n",
    "def act_functn(Q, state):\n",
    "    eps = 0.1\n",
    "    #eps = 1/np.power(state_visits[state], 0.2)\n",
    "#     eps = 1/np.sqrt(state_visits[state])\n",
    "#     state_visits[state] += 1\n",
    "    if np.random.choice([True, False], p=[1-eps, eps]):\n",
    "        action = np.argmax(Q)\n",
    "    else:\n",
    "        action = np.random.choice(nAfes[state])\n",
    "    return action"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a60ab27d",
   "metadata": {},
   "outputs": [],
   "source": [
    "nAfes = [2, 2]\n",
    "def maxmin_q_train(N, epochs, alpha, gamma, rewardnstate, act_functn, P, seed):\n",
    "    np.random.seed(seed)\n",
    "    nS = 2\n",
    "    nA = 2\n",
    "    Q_list = np.random.rand(N, nS, nA)\n",
    "#     for i in range(N):\n",
    "#         Q = np.random.rand(nS, nA)\n",
    "#         Q_list.append(Q)\n",
    "#     Q_list = np.array(Q_list)\n",
    "    Q_list[:, 0] = 0\n",
    "    D = [] #replay buffer2\n",
    "    diff_list = []\n",
    "    len_d = 0\n",
    "    for i in range(epochs):\n",
    "        state = 2\n",
    "        terminal = False\n",
    "        while not terminal:\n",
    "            Qmin = np.min(Q_list[:, state, :nAfes[state]], axis=0)\n",
    "            action = act_functn(Qmin, state)\n",
    "#             print(Qmin)\n",
    "            r, next_state, terminal = rewardnstate(action, state)\n",
    "            D.append((state, action, r, next_state))\n",
    "            len_d += 1\n",
    "            n = np.random.randint(N)\n",
    "            sd, ad, rd, nsd  = D[np.random.choice(len_d)]\n",
    "#             sd, ad, rd, nsd = state, action, r, next_state \n",
    "            Qmin = np.min(Q_list[:, nsd, :nAfes[nsd]], axis=0)\n",
    "            Y = rd + gamma*np.max(Qmin)\n",
    "            q = Q_list[n, sd, ad]\n",
    "            Q_list[n, sd, ad] = q + alpha*(Y-q)\n",
    "            state = next_state\n",
    "        diff = 0.\n",
    "        for i in range(N):\n",
    "            diff += Q_list[i][2][0] - Q_list[i][2][1] #preference of left over right\n",
    "        diff /= float(N)\n",
    "        diff_list.append(diff)\n",
    "    return diff_list, Q_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "9f5b0f44",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.3995798  0.27817748]\n",
      " [0.82408744 0.63343138]\n",
      " [0.58600935 0.56425505]]\n"
     ]
    }
   ],
   "source": [
    "Q_list = []\n",
    "for i in range(N):\n",
    "    Q = np.random.rand(3, 8)\n",
    "    Q_list.append(Q)\n",
    "Q_list = np.array(Q_list)\n",
    "print(Q_list[:, 2, :nAfes[2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "nTzL0sT81TAJ",
   "metadata": {
    "id": "nTzL0sT81TAJ"
   },
   "outputs": [],
   "source": [
    "mu = 1\n",
    "P = {\n",
    "    0:{0: (0, 0, True)}, #state:{action: (reward, next state, terminal)}\n",
    "    1:{0: (mu, 0, True),\n",
    "       1: (mu, 0, True),\n",
    "       2: (mu, 0, True),\n",
    "       3: (mu, 0, True),\n",
    "       4: (mu, 0, True),\n",
    "       5: (mu, 0, True),\n",
    "       6: (mu, 0, True),\n",
    "       7: (mu, 0, True)}, \n",
    "    2:{0: (0, 1, False),\n",
    "       1: (0, 0, True)}\n",
    "}\n",
    "diff_list_over, Q_list_over = maxmin_q_train(N = 10, epochs = 5000, \n",
    "                                             alpha = 0.01, gamma = 1,  \n",
    "                                             rewardnstate = rewardnstate, \n",
    "                                             act_functn = act_functn, \n",
    "                                             P = P, seed = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "5p_95hSz2Gah",
   "metadata": {
    "id": "5p_95hSz2Gah"
   },
   "outputs": [],
   "source": [
    "mu = -1\n",
    "P = {\n",
    "    0:{0: (0, 0, True)}, #state:{action: (reward, next state, terminal)}\n",
    "    1:{0: (mu, 0, True),\n",
    "       1: (mu, 0, True),\n",
    "       2: (mu, 0, True),\n",
    "       3: (mu, 0, True),\n",
    "       4: (mu, 0, True),\n",
    "       5: (mu, 0, True),\n",
    "       6: (mu, 0, True),\n",
    "       7: (mu, 0, True)}, \n",
    "    2:{0: (0, 1, False),\n",
    "       1: (0, 0, True)}\n",
    "}\n",
    "diff_list_under, Q_list_under = maxmin_q_train(N = 4, epochs = 5000, \n",
    "                                               alpha = 0.01, gamma = 1,  \n",
    "                                               rewardnstate = rewardnstate, \n",
    "                                               act_functn = act_functn, \n",
    "                                               P = P, seed = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "-pPcMXro2MBB",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 282
    },
    "id": "-pPcMXro2MBB",
    "outputId": "83d2689f-3891-48c8-e8ae-de2ac2ce6386",
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7477045464651761 -0.1683328212644948\n"
     ]
    }
   ],
   "source": [
    "plt.plot(diff_list_over, color = \"b\", label = \"over\")\n",
    "plt.axhline(y = 0.1, color = \"b\", linestyle = \"--\", linewidth = 1)\n",
    "plt.axhline(y = -0.1, color = \"r\", linestyle = \"--\", linewidth = 1)\n",
    "plt.plot(diff_list_under, color = \"r\", label = \"under\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "print(diff_list_over[-1], diff_list_under[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f256db04",
   "metadata": {},
   "source": [
    "# mu = 1, mu = -1\n",
    "\n",
    "# 0.16413845575626063, 0.22977469936721467 1000 epochs \n",
    "# 0.5342581497100699, -0.02164709207862111 3000 epochs\n",
    "# 0.7477045464651761, -0.1683328212644948  5000 epochs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "mjicA_64FigA",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "mjicA_64FigA",
    "outputId": "8038efd8-87ac-43f3-a1ba-d9e8809909ac"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6634052379335809"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(diff_list_under[2000:]) + 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "af8a3e66",
   "metadata": {
    "id": "af8a3e66"
   },
   "outputs": [],
   "source": [
    "#This code was written for a different setting (8 actions and 2 states)\n",
    "nAfes = [1, 8, 2]\n",
    "def maxmin_q_train(N, epochs, alpha, gamma, rewardnstate, act_functn, P, seed):\n",
    "    np.random.seed(seed)\n",
    "    nS = 3\n",
    "    nA = 8\n",
    "    Q_list = np.random.rand(N, nS, nA)\n",
    "#     for i in range(N):\n",
    "#         Q = np.random.rand(nS, nA)\n",
    "#         Q_list.append(Q)\n",
    "#     Q_list = np.array(Q_list)\n",
    "    Q_list[:, 0] = 0\n",
    "    D = [] #replay buffer2\n",
    "    diff_list = []\n",
    "    len_d = 0\n",
    "    for i in range(epochs):\n",
    "        state = 2\n",
    "        terminal = False\n",
    "        while not terminal:\n",
    "            Qmin = np.min(Q_list[:, state, :nAfes[state]], axis=0)\n",
    "            action = act_functn(Qmin, state)\n",
    "#             print(Qmin)\n",
    "            r, next_state, terminal = rewardnstate(action, state)\n",
    "            D.append((state, action, r, next_state))\n",
    "            len_d += 1\n",
    "            n = np.random.randint(N)\n",
    "            sd, ad, rd, nsd  = D[np.random.choice(len_d)]\n",
    "#             sd, ad, rd, nsd = state, action, r, next_state \n",
    "            Qmin = np.min(Q_list[:, nsd, :nAfes[nsd]], axis=0)\n",
    "            Y = rd + gamma*np.max(Qmin)\n",
    "            q = Q_list[n, sd, ad]\n",
    "            Q_list[n, sd, ad] = q + alpha*(Y-q)\n",
    "            state = next_state\n",
    "        diff = 0.\n",
    "        for i in range(N):\n",
    "            diff += Q_list[i][2][0] - Q_list[i][2][1] #preference of left over right\n",
    "        diff /= float(N)\n",
    "        diff_list.append(diff)\n",
    "    return diff_list, Q_list"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "include_colab_link": true,
   "name": "Maxmin Qlearning.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}