Regularization_CancerSim.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "F8MHh3Z48GV9",
        "outputId": "86a743a0-a8c8-4298-9911-e48dabf7319d"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Mounted at /content/gdrive\n"
          ]
        }
      ],
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/gdrive')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "AyMzXHo6NVaS"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import torch\n",
        "import random\n",
        "from matplotlib.ticker import FormatStrFormatter\n",
        "from matplotlib.ticker import MaxNLocator\n",
        "from matplotlib.ticker import PercentFormatter"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s_H1Q0j9HpD-"
      },
      "source": [
        "## Cancer Simulator"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lwUpgfxPTu_b"
      },
      "outputs": [],
      "source": [
        "################ Cancer Simulator ####################\n",
        "\n",
        "#code from:\n",
        "#Omer Gottesman, Joseph Futoma, Yao Liu, Sonali Parbhoo, Leo Celi, Emma Brunskill,\n",
        "#and Finale Doshi-Velez. Interpretable off-policy evaluation in reinforcement learning by\n",
        "#highlighting influential transitions. In International Conference on Machine Learning,\n",
        "#pages 3658–3667. PMLR, 2020.\n",
        "\n",
        "# This cancer simulator is built on the paper\n",
        "#   * Ribba 2012 (https://pubmed.ncbi.nlm.nih.gov/22761472/)\n",
        "#   * Yauney 2018 (http://proceedings.mlr.press/v85/yauney18a/yauney18a.pdf)\n",
        "\n",
        "# The simulator approximate the dynamics of tumor growth, with actions consisting administration of chemotherapy TMZ at each timestep representing one month.\n",
        "\n",
        "# * State space: 4-dimensional where the first dimension associates with drug concerntration and the last three with tumor diameter\n",
        "# * Action space: TODO\n",
        "# * Maximum Treatment cycle: 30\n",
        "\n",
        "\n",
        "class EnvCancer:\n",
        "    ############# Initialization #############\n",
        "    # dose_penalty -- 0 - no penalty; 1 - small; 10 - large; default no penalty;\n",
        "    # max_steps -- max treatment cycle; default 30 days\n",
        "    # transition_noise -- default 0 (i.e. deterministic)\n",
        "\n",
        "    def __init__(self, dose_penalty=0, max_steps=30, transition_noise=0.0):\n",
        "        # PDE parameter initialization (See Ribba 2012 Sec model & Table 1)\n",
        "        self.kde = 0.32\n",
        "        self.lambda_p = 0.114\n",
        "        self.k_qpp = 0.0045\n",
        "        self.k_pq = 0.0226\n",
        "        self.gamma = 0.842\n",
        "        self.delta_qp = 0.0214\n",
        "        self.k = 100\n",
        "\n",
        "        self.dose_penalty = dose_penalty\n",
        "        self.max_steps = max_steps\n",
        "        self.time_step = None\n",
        "        self.transition_noise = transition_noise\n",
        "\n",
        "    def reset(self):\n",
        "        C = 0\n",
        "        P = 0.924\n",
        "        Q = 42.3\n",
        "        Q_p = 0\n",
        "\n",
        "        self.state = np.array([C, P, Q, Q_p])\n",
        "        self.time_step = 0\n",
        "\n",
        "        #SVR adding noise to start\n",
        "        noise = 1 + self.transition_noise * np.random.randn(4)\n",
        "        self.state *= noise\n",
        "\n",
        "        #start at random state by taking n steps with random actions\n",
        "        #steps = random.randint(0,self.max_steps)\n",
        "        #for s in range(steps):\n",
        "        #  a = np.random.binomial(1,.1)\n",
        "        #  self.perform_action(a)\n",
        "        #self.time_step=0\n",
        "\n",
        "    def is_done(self):\n",
        "        return self.time_step >= self.max_steps\n",
        "\n",
        "    def observe(self):\n",
        "        return self.state\n",
        "\n",
        "    def perform_action(self, action):\n",
        "        # current state\n",
        "        C, P, Q, Q_p = self.state\n",
        "        P_star = P + Q + Q_p\n",
        "        # perform_action\n",
        "        if action == 1:\n",
        "            C += 1\n",
        "        C = C - self.kde * C\n",
        "        P = (P + self.lambda_p * P * (1-P_star/self.k) + self.k_qpp * Q_p\n",
        "             - self.k_pq * P - self.gamma * C * self.kde * P)\n",
        "        Q = Q + self.k_pq * P - self.gamma * C * self.kde * Q\n",
        "        Q_p = (Q_p + self.gamma * C * self.kde * Q - self.k_qpp * Q_p\n",
        "               - self.delta_qp * Q_p)\n",
        "        # new state\n",
        "        next_state = np.array([C, P, Q, Q_p])\n",
        "        # add noise if any\n",
        "        noise = 1 + self.transition_noise * np.random.randn(4)\n",
        "        next_state *= noise\n",
        "        self.state = next_state\n",
        "\n",
        "        # define reward function\n",
        "        P_star_new = P + Q + Q_p\n",
        "        reward = (P_star - P_star_new) - self.dose_penalty * C\n",
        "        self.time_step += 1\n",
        "        return next_state, reward"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WYT6dp_hHshd"
      },
      "source": [
        "## Generate data from simulator\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9U0TLWFlI3vK"
      },
      "source": [
        "## Discretize states\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NH1CD27IzOGO"
      },
      "source": [
        "### Generate data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "e-4yYWLYT_7s",
        "outputId": "6e7764d9-f25c-42df-c01d-ceca8bae0b3f"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "n 0\n"
          ]
        }
      ],
      "source": [
        "num_runs = 100000\n",
        "\n",
        "#initialize -- only saving off states so we can look at the distribution of each dimension to discretize\n",
        "C_list = []  #first dim of state\n",
        "P_list = []  #second dim of state\n",
        "Q_list = []  #third dim of state\n",
        "Qp_list = [] #fourt dim of state\n",
        "\n",
        "for n in range(num_runs):\n",
        "  if n%100000 == 0:\n",
        "    print('n',n)\n",
        "  csim = EnvCancer(dose_penalty=10,transition_noise=0.25)\n",
        "  csim.reset()\n",
        "\n",
        "  C_list.append(csim.state[0])\n",
        "  P_list.append(csim.state[1])\n",
        "  Q_list.append(csim.state[2])\n",
        "  Qp_list.append(csim.state[3])\n",
        "\n",
        "  while csim.time_step < csim.max_steps:\n",
        "    a = np.random.binomial(1,.5)\n",
        "    s_prime,r = csim.perform_action(a)\n",
        "    C_list.append(s_prime[0])\n",
        "    P_list.append(s_prime[1])\n",
        "    Q_list.append(s_prime[2])\n",
        "    Qp_list.append(s_prime[3])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZoBR7eVXRXb7"
      },
      "source": [
        "### Histograms with quantiles for each state dimension"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Kg8zYuw0Q24U"
      },
      "outputs": [],
      "source": [
        "C_25 = np.quantile(C_list,.25)\n",
        "C_50 = np.quantile(C_list,.5)\n",
        "C_75 = np.quantile(C_list,.75)\n",
        "\n",
        "P_25 = np.quantile(P_list,.25)\n",
        "P_50 = np.quantile(P_list,.5)\n",
        "P_75 = np.quantile(P_list,.75)\n",
        "\n",
        "Q_25 = np.quantile(Q_list,.25)\n",
        "Q_50 = np.quantile(Q_list,.5)\n",
        "Q_75 = np.quantile(Q_list,.75)\n",
        "\n",
        "Qp_25 = np.quantile(Qp_list,.25)\n",
        "Qp_50 = np.quantile(Qp_list,.5)\n",
        "Qp_75 = np.quantile(Qp_list,.75)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nLJkPkRlNUFz",
        "outputId": "bb131918-05c7-4bbb-cd94-dab2a0cab505"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<matplotlib.lines.Line2D at 0x7f8cebc71ea0>"
            ]
          },
          "execution_count": 6,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
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\n",
            "text/plain": [
              "<Figure size 1500x1500 with 4 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "fig,ax = plt.subplots(2,2,figsize=(15,15))\n",
        "ax[0][0].hist(C_list,bins=25)\n",
        "ax[0][0].set_title('C: drug concentration')\n",
        "ax[0][0].axvline(C_25,color='r',linestyle = \":\")\n",
        "ax[0][0].axvline(C_50,color='r',linestyle = \":\")\n",
        "ax[0][0].axvline(C_75,color='r',linestyle = \":\")\n",
        "\n",
        "ax[0][1].hist(P_list,bins=25)\n",
        "ax[0][1].set_title('P: Proliferative Tissue (mm)')\n",
        "ax[0][1].axvline(P_25,color='r',linestyle = \":\")\n",
        "ax[0][1].axvline(P_50,color='r',linestyle = \":\")\n",
        "ax[0][1].axvline(P_75,color='r',linestyle = \":\")\n",
        "\n",
        "ax[1][0].hist(Q_list,bins=25)\n",
        "ax[1][0].set_title('Q: quiescent tissue (mm)')\n",
        "ax[1][0].axvline(Q_25,color='r',linestyle = \":\")\n",
        "ax[1][0].axvline(Q_50,color='r',linestyle = \":\")\n",
        "ax[1][0].axvline(Q_75,color='r',linestyle = \":\")\n",
        "\n",
        "ax[1][1].hist(Qp_list,bins=25)\n",
        "ax[1][1].set_title('Qp: Damaged quiescent tissue')\n",
        "ax[1][1].axvline(Qp_25,color='r',linestyle = \":\")\n",
        "ax[1][1].axvline(Qp_50,color='r',linestyle = \":\")\n",
        "ax[1][1].axvline(Qp_75,color='r',linestyle = \":\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6DKfyk9cWT5B",
        "outputId": "d04b1c7b-c645-4ab6-aa5d-98af5ba03db8"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "-0.41977313896331464\n",
            "6.345657931975775\n",
            "-4.863372601962225\n",
            "495.37397688236285\n",
            "-1.552854263573678\n",
            "17.21502030222788\n",
            "-8.99573565693143\n",
            "3529.818815805774\n"
          ]
        }
      ],
      "source": [
        "print(min(C_list))\n",
        "print(max(C_list))\n",
        "\n",
        "print(min(Q_list))\n",
        "print(max(Q_list))\n",
        "\n",
        "print(min(P_list))\n",
        "print(max(P_list))\n",
        "\n",
        "print(min(Qp_list))\n",
        "print(max(Qp_list))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9ss61dyPSGEi"
      },
      "source": [
        "## Helper function to discretize and convert from 4-d to 1-d state space"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ot0co1s-NUEi"
      },
      "outputs": [],
      "source": [
        "def convert_state(s):\n",
        "  \"\"\"Convert cancer simulation state to 1-d discrete\n",
        "\n",
        "  input is 4-d continuous state as defined in cancer simulator\n",
        "  output is numerical tabular state\n",
        "\n",
        "  \"\"\"\n",
        "  C,P,Q,Qp = s\n",
        "\n",
        "  #first convert each dimension to quantile\n",
        "  C_discrete = 0*(s[0]< C_25) + 1*((s[0] >= C_25) & (s[0] < C_50)) + 2*((s[0] >= C_50) & (s[0] < C_75)) + 3*(s[0]> C_75)\n",
        "  P_discrete = 0*(s[1]< P_25) + 1*((s[1] >= P_25) & (s[1] < P_50)) + 2*((s[1] >= P_50) & (s[1] < P_75)) + 3*(s[1]> P_75)\n",
        "  Q_discrete = 0*(s[2]< Q_25) + 1*((s[2] >= Q_25) & (s[2] < Q_50)) + 2*((s[2] >= Q_50) & (s[2] < Q_75)) + 3*(s[2]> Q_75)\n",
        "  Qp_discrete = 0*(s[3]< Qp_25) + 1*((s[3] >= Qp_25) & (s[3] < Qp_50)) + 2*((s[3] >= Qp_50) & (s[3] < Qp_75)) + 3*(s[3]> Qp_75)\n",
        "  s_4d_discrete = [C_discrete,P_discrete,Q_discrete,Qp_discrete]\n",
        "\n",
        "  # then convert to 1D\n",
        "  one_d_state = np.ravel_multi_index(tuple(s_4d_discrete),(4,4,4,4))\n",
        "  return one_d_state"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mpwjB9aZuLL0"
      },
      "source": [
        "## Generate trajectory from one run of simulator"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9HTZjCtfTtPk"
      },
      "outputs": [],
      "source": [
        "def single_run(pct_treat = .1):\n",
        "  csim = EnvCancer(dose_penalty = 10, transition_noise=.25)\n",
        "\n",
        "  csim.reset()\n",
        "  #initialize -- only saving off states so we can look at the distribution of each dimension to discretize\n",
        "  state_list = []\n",
        "  action_list = []\n",
        "  reward_list = []\n",
        "\n",
        "  state_list.append(convert_state(csim.state))\n",
        "\n",
        "  max_steps = random.randint(0,csim.max_steps) #length of traj\n",
        "\n",
        "  while csim.time_step < max_steps:\n",
        "\n",
        "    #take action\n",
        "    a = np.random.binomial(1,pct_treat)\n",
        "    s_prime,r = csim.perform_action(a)\n",
        "\n",
        "    #save data\n",
        "    state_list.append(convert_state(s_prime))\n",
        "    action_list.append(a)\n",
        "    reward_list.append(r)\n",
        "\n",
        "  return state_list,action_list,reward_list"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_7drhDKyvPql"
      },
      "source": [
        "## Helper functions to estimate MDP\n",
        "data  = [[state_list,action_list,reward_list],[state_list,action_list,reward_list],...]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "2FGRLPqOvQAV"
      },
      "outputs": [],
      "source": [
        "def estimate_mdp(data):\n",
        "  num_states = 4*4*4*4\n",
        "  num_actions = 2\n",
        "  T_counts = np.zeros((num_actions,num_states,num_states))\n",
        "  R_sum = np.zeros((num_actions,num_states))\n",
        "\n",
        "  T_default = (1./num_states)*np.ones(num_states)\n",
        "  R_default = 0\n",
        "\n",
        "  for d in data:\n",
        "\n",
        "    #add transition data to count matrix\n",
        "    state_list = d[0]\n",
        "    action_list = d[1]\n",
        "    reward_list = d[2]\n",
        "    for i in range(len(state_list)-1):\n",
        "      a = action_list[i]\n",
        "      s = state_list[i]\n",
        "      s_prime = state_list[i+1]\n",
        "      T_counts[a][s][s_prime] +=1\n",
        "      R_sum[a][s_prime] += reward_list[i]\n",
        "\n",
        "  #estimate T and R\n",
        "  T_hat = np.zeros((num_actions,num_states,num_states))\n",
        "  r_hat = np.zeros((num_actions,num_states))\n",
        "\n",
        "  for a in range(num_actions):\n",
        "    for s in range(num_states):\n",
        "      total_counts = np.sum(T_counts[a][s])\n",
        "      if total_counts == 0:\n",
        "        T_hat[a][s] = T_default\n",
        "        r_hat[a][s] = R_default\n",
        "      else:\n",
        "        T_hat[a][s] = T_counts[a][s]/total_counts\n",
        "        r_hat[a][s] = R_sum[a][s]/total_counts\n",
        "\n",
        "  return T_hat,r_hat,T_counts\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hpG69rfqKfkZ"
      },
      "outputs": [],
      "source": [
        "#frequency of each state in \"True\" data set\n",
        "def state_weights(data):\n",
        "  num_states = 4*4*4*4\n",
        "  state_count = np.zeros(num_states)\n",
        "\n",
        "  for d in data:\n",
        "    state_list = d[0]\n",
        "    for s in state_list:\n",
        "      state_count[s]+=1\n",
        "  return state_count/float(sum(state_count))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T5m_0QdTuJbE"
      },
      "source": [
        "## Estimate T, R for n runs of simulator\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "HE_hznuTuIoe"
      },
      "outputs": [],
      "source": [
        "def get_data_and_estimate(pct_treat,num_trajectories):\n",
        "  data = []\n",
        "  for n in range(num_trajectories):\n",
        "    s,a,r = single_run(pct_treat)\n",
        "    data.append([s,a,r])\n",
        "\n",
        "  return estimate_mdp(data),state_weights(data)\n",
        "\n",
        "# Define True MDP for below and also ground truth for simulations\n",
        "[T_true,R_true,T_counts],true_weights = get_data_and_estimate(pct_treat = .50,num_trajectories = 100000)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_Gm9VjmlCHmV"
      },
      "source": [
        "## Dynamic Programming\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "O1FNwgQLIBd2"
      },
      "outputs": [],
      "source": [
        "def value_iter(gamma, T_list,R_list, theta = .0001):\n",
        "  \"\"\"Value Iteration\n",
        "  \"\"\"\n",
        "  num_states = T_list.shape[1]\n",
        "\n",
        "  T = torch.tensor(np.array([np.array(x) for x in T_list]))\n",
        "  R = torch.tensor(np.array(R_list))\n",
        "\n",
        "  #V = torch.tensor(np.zeros(10))\n",
        "  V = torch.tensor(np.random.uniform(0,1,num_states))\n",
        "  delta = 10.\n",
        "\n",
        "  while delta > theta:\n",
        "      v = V\n",
        "      V = torch.max(R + gamma*torch.einsum(\"bij,j->bi\", T, V),dim=0).values\n",
        "      delta= torch.max(torch.abs(v-V)).item()\n",
        "\n",
        "  #get greedy policy\n",
        "  P = torch.max(R + gamma*torch.einsum(\"bij,j->bi\", T, V),dim=0).indices\n",
        "\n",
        "  return np.array(P),np.array(V)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "y5hiln6cP59J"
      },
      "outputs": [],
      "source": [
        "def eval_policy(gamma,policy,T_list,R_list,theta):\n",
        "  \"\"\"Policy evaluation\n",
        "  \"\"\"\n",
        "  num_states = T_list[0].shape[0]\n",
        "\n",
        "  index = list(zip(policy,range(num_states)))\n",
        "  T_pi = np.matrix([T_list[i][j] for (i,j) in index])\n",
        "  #R_pi = np.transpose(np.matrix(R_list))\n",
        "  R_pi = np.array([R_list[i][j] for (i,j) in index])\n",
        "\n",
        "  value = np.linalg.solve(np.eye(num_states)-gamma*T_pi,R_pi)\n",
        "\n",
        "  return value"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tzXUA1pyO2Z-"
      },
      "source": [
        "## Regularization"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q1lC-xO8PB8n"
      },
      "source": [
        "### global param for all states"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "MRmy0Y7bO2rm"
      },
      "outputs": [],
      "source": [
        "def uniform_prior(eps,sa_count_list):\n",
        "    T_unif_list = []\n",
        "    num_actions = sa_count_list.shape[0]\n",
        "    num_states = sa_count_list.shape[1]\n",
        "    unif_prior = np.ones((num_states,num_states))\n",
        "\n",
        "    total_sa_count = 0\n",
        "    for sa_count in sa_count_list:\n",
        "      total_sa_count += np.sum(sa_count)\n",
        "    avg_count = total_sa_count/(num_states*num_actions)\n",
        "    mag = eps/(1-eps)*avg_count/num_states\n",
        "\n",
        "    for sa_count in sa_count_list:\n",
        "        if eps == 1:\n",
        "            alpha_post = 0*sa_count+unif_prior\n",
        "        else:\n",
        "            alpha_post = sa_count + mag*unif_prior\n",
        "\n",
        "        T_post = np.zeros((num_states,num_states))\n",
        "        default = (1./num_states)*np.ones(num_states) #uniform default, as above\n",
        "        for i in range(num_states):\n",
        "            sum_state = alpha_post[i].sum()\n",
        "            if sum_state == 0: # never visited state i and took action \"act\"\n",
        "                T_post[i] = default\n",
        "            else:\n",
        "                T_post[i] = (1./sum_state)*alpha_post[i]\n",
        "        T_unif_list.append(T_post)\n",
        "\n",
        "    return T_unif_list"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IBgZWzNpPFAF"
      },
      "source": [
        "### State-specific"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Go1MxHaBO--f"
      },
      "outputs": [],
      "source": [
        "def epsilon_star_unif(T_sa,num_samples):\n",
        "  \"\"\"Calculate optimal value of epsilon for uniform prior\n",
        "\n",
        "  Optimal epsilon if we knew true value of T\n",
        "\n",
        "  \"\"\"\n",
        "  num_states = len(T_sa)\n",
        "  numerator = 0\n",
        "  denominator = 0\n",
        "  for s_prime in range(num_states):\n",
        "    numerator += (1./num_samples)*T_sa[s_prime]*(1-T_sa[s_prime])\n",
        "    denominator += ((1./num_samples)*T_sa[s_prime]*(1-T_sa[s_prime]) + T_sa[s_prime]**2 - 2/num_states*T_sa[s_prime] + 1/(num_states**2))\n",
        "  return numerator/denominator\n",
        "\n",
        "def mse_unif(T_sa,epsilon,num_samples):\n",
        "  mse = 0\n",
        "  num_states = len(T_sa)\n",
        "  for s_prime in range(num_states):\n",
        "    mse += (1-epsilon)**2*(1/num_samples)*T_sa[s_prime]*(1-T_sa[s_prime])+epsilon**2*((1/num_states)-T_sa[s_prime])**2\n",
        "\n",
        "  return mse"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bjEUAEEFPQ5J"
      },
      "outputs": [],
      "source": [
        "def epsilon_star_hat_unif(sa_count_list):\n",
        "\n",
        "  \"\"\"Calculate optimal value of epsilon for uniform prior\n",
        "\n",
        "  Optimal epsilon for single s-a pair for when we do not know true T\n",
        "\n",
        "  \"\"\"\n",
        "  epsilon_list = np.linspace(0,1,100)\n",
        "  num_resamples = 25\n",
        "  prior_mag = .10\n",
        "\n",
        "  max_mse_by_eps = []\n",
        "  mean_mse_by_eps = []\n",
        "  mse = 0\n",
        "  num_samples = np.sum(sa_count_list)\n",
        "\n",
        "  #define posterior. T_sa ~ dirichlet(alpha)\n",
        "  alpha = tuple(x+prior_mag for x in sa_count_list)\n",
        "  for e in epsilon_list:\n",
        "\n",
        "    mse_list = []\n",
        "    for n in range(num_resamples):\n",
        "\n",
        "      #sample new T-hat from posterior\n",
        "      T_samp = np.random.dirichlet(alpha)\n",
        "\n",
        "      #calc MSE\n",
        "      if num_samples > 0:\n",
        "        mse = mse_unif(T_samp,e,num_samples)\n",
        "      else:\n",
        "        mse = mse_unif(T_samp,e,1)\n",
        "      mse_list.append(mse)\n",
        "\n",
        "    #max_mse_by_eps.append(max(mse_list))\n",
        "    mean_mse_by_eps.append(np.mean(mse_list))\n",
        "\n",
        "  #min_index = max_mse_by_eps.index(min(max_mse_by_eps))\n",
        "  min_index = mean_mse_by_eps.index(min(mean_mse_by_eps))\n",
        "\n",
        "\n",
        "  return epsilon_list[min_index]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "pw7PQKEzPQ4G"
      },
      "outputs": [],
      "source": [
        "def T_reg_unif_per_state(T_mle_list,sa_count_list,cross_validate=False):\n",
        "\n",
        "  num_states = T_mle_list[0].shape[0]\n",
        "  num_actions = len(T_mle_list)\n",
        "  T_reg_list = []\n",
        "  T_unif = (1./num_states)*np.ones(num_states)\n",
        "\n",
        "  T_sa_reg_list = [] #list of regularized transition matrixes for each action\n",
        "  for a in range(num_actions):\n",
        "    T_sa_reg = [] #action a regularized matrix\n",
        "    num_samples_a = sa_count_list[a].sum(axis=1).tolist()\n",
        "    for row_num in range(num_states):\n",
        "      num_sa_samples = num_samples_a[row_num]\n",
        "      if cross_validate==True:\n",
        "        eps_sa = epsilon_star_hat_unif(sa_count_list[a].tolist()[row_num])\n",
        "      else:\n",
        "        try:\n",
        "          eps_sa = epsilon_star_unif(T_mle_list[a].tolist()[row_num],num_sa_samples)\n",
        "        except:\n",
        "          eps_sa = 1\n",
        "\n",
        "      T_sa_reg.append([(1-eps_sa)*x + eps_sa*y for (x,y) in zip(T_mle_list[a].tolist()[row_num],T_unif)])\n",
        "    T_sa_reg_list.append(np.array(T_sa_reg))\n",
        "\n",
        "  return T_sa_reg_list"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6Z3stFZoPeIm"
      },
      "outputs": [],
      "source": [
        "def T_reg_unif_per_state_trueT(T_list,T_mle_list,sa_count_list):\n",
        "\n",
        "  \"\"\"State-specific regularization calculating epsilon* using true T\n",
        "\n",
        "  (Theoretical minimum loss using our method)\n",
        "\n",
        "  \"\"\"\n",
        "  num_states = T_list[0].shape[0]\n",
        "  num_actions = len(T_list)\n",
        "  T_reg_list = []\n",
        "  T_unif = (1./num_states)*np.ones(num_states)\n",
        "\n",
        "  T_sa_reg_list = [] #list of regularized transition matrixes for each action\n",
        "  for a in range(num_actions):\n",
        "    T_sa_reg = [] #action a regularized matrix\n",
        "    num_samples_a = sa_count_list[a].sum(axis=1).tolist()\n",
        "    for row_num in range(num_states):\n",
        "      num_sa_samples = num_samples_a[row_num]\n",
        "      if num_sa_samples > 0:\n",
        "        eps_sa = epsilon_star_unif(T_list[a][row_num],num_sa_samples)\n",
        "      else:\n",
        "        eps_sa = 1\n",
        "      #print('num_sa_samples',num_sa_samples)\n",
        "      #print('epsilon',eps_sa)\n",
        "      T_sa_reg.append([(1-eps_sa)*x + eps_sa*y for (x,y) in zip(T_mle_list[a][row_num],T_unif)])\n",
        "    T_sa_reg_list.append(np.array(T_sa_reg))\n",
        "\n",
        "  return T_sa_reg_list"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jGl8B8hFNRWW"
      },
      "source": [
        "## Compare Loss by Regularization Method"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "D_hEmCvHCH8F"
      },
      "outputs": [],
      "source": [
        "def calc_loss(num_trajectories,num_datasets,T_true,R_true):\n",
        "\n",
        "  gamma_eval = 0.99\n",
        "  theta = .0001\n",
        "  epsilon_list = [0,.1,.2,.3,.4,.5,.6,.7,.8,.9,.95,.99]\n",
        "  pct_treat = .50\n",
        "\n",
        "  #store loss for each value of epsilon\n",
        "  loss_dict_disc = {} #discount regularization\n",
        "  loss_dict_unif = {} #uniform prior with equal magnitude\n",
        "  for e in epsilon_list:\n",
        "    loss_dict_disc[e] = []\n",
        "    loss_dict_unif[e] = []\n",
        "\n",
        "  #loss for state-specfic\n",
        "  loss_list_unif_ss_cv = [] #state specific with epsilon found by cv\n",
        "  loss_list_unif_ss_MLE = [] #state specific with epsilon found using t-mle\n",
        "  loss_list_unif_ss_TrueT = [] #state specific with epsilon found using true T\n",
        "\n",
        "  # True MDP, policy, value\n",
        "  #T_true,R_true,T_counts_true = get_data_and_estimate(1000)  #move this outside as global variable if running multiple times\n",
        "  p,v = value_iter(gamma_eval,T_true,R_true,theta)\n",
        "  num_states = T_true.shape[1]\n",
        "  start_state_weights = (1./num_states)*np.ones(num_states) #evalulation\n",
        "\n",
        "  for n in range(num_datasets):\n",
        "    print('n',n)\n",
        "    [T_mle,R_mle,T_counts],w = get_data_and_estimate(pct_treat,num_trajectories)\n",
        "    #print('T_counts',T_counts.sum(axis=1))\n",
        "\n",
        "    #state specific epsilon losses - unif WITH CV\n",
        "    T_unif_ss_list = T_reg_unif_per_state(T_mle,T_counts,cross_validate=True)\n",
        "    p_unif_ss,v_unif_ss = value_iter(gamma_eval,np.array(T_unif_ss_list),R_true)\n",
        "    v_unif_ss = eval_policy(gamma_eval,np.array(p_unif_ss),T_true,R_true,theta) #calculate value of policy in true MDP\n",
        "    loss_unif_ss = v - np.array(v_unif_ss)\n",
        "    loss_unif_ss = np.average(loss_unif_ss,axis=None,weights=true_weights)\n",
        "    loss_list_unif_ss_cv.append(loss_unif_ss)\n",
        "    print('loss_unif_ss',loss_unif_ss)\n",
        "\n",
        "    #state specific - Using true T to get theoretical min loss\n",
        "    T_unif_ss_list2 = T_reg_unif_per_state_trueT(T_true,T_mle,T_counts)\n",
        "    p_unif_ss2,v_unif_ss2 = value_iter(gamma_eval,np.array(T_unif_ss_list2),R_true)\n",
        "    v_unif_ss2 = eval_policy(gamma_eval,np.array(p_unif_ss2),T_true,R_true,theta) #calculate value of policy in true MDP\n",
        "    loss_unif_ss2 = v - np.array(v_unif_ss2)\n",
        "    loss_unif_ss2 = np.average(loss_unif_ss2,axis=None,weights=true_weights)\n",
        "    loss_list_unif_ss_TrueT.append(loss_unif_ss2)\n",
        "    print('loss_unif_ss2',loss_unif_ss2)\n",
        "\n",
        "    #state specific epsilon losses - unif WITHOUT CV\n",
        "    T_unif_ss_list3 = T_reg_unif_per_state(T_mle,T_counts,cross_validate=False)\n",
        "    p_unif_ss3,v_unif_ss3 = value_iter(gamma_eval,np.array(T_unif_ss_list3),R_true)\n",
        "    v_unif_ss3 = eval_policy(gamma_eval,np.array(p_unif_ss3),T_true,R_true,theta) #calculate value of policy in true MDP\n",
        "    loss_unif_ss3 = v - np.array(v_unif_ss3)\n",
        "    loss_unif_ss3 = np.average(loss_unif_ss3,axis=None,weights=true_weights)\n",
        "    loss_list_unif_ss_MLE.append(loss_unif_ss3)\n",
        "\n",
        "    for e in epsilon_list:\n",
        "      T_hat_unif = uniform_prior(e,T_counts)\n",
        "\n",
        "      #calculate optimal policy and its value for regularized MDPs\n",
        "      #assume R known\n",
        "      p_disc,v_disc = value_iter((1-e)*gamma_eval,T_mle,R_true,theta)\n",
        "      p_unif,v_unif = value_iter(gamma_eval,np.array(T_hat_unif),R_true,theta)\n",
        "\n",
        "      #calculate value of policies above using true MDP\n",
        "      v_disc = eval_policy(gamma_eval,p_disc,T_true,R_true,theta)\n",
        "      v_unif = eval_policy(gamma_eval,p_unif,T_true,R_true,theta)\n",
        "\n",
        "      #loss = expected value over starting state distrib\n",
        "      loss_disc = v - np.array(v_disc)\n",
        "      loss_unif = v - np.array(v_unif)\n",
        "\n",
        "      loss_dict_disc[e].append(np.average(loss_disc,axis=None,weights=true_weights))\n",
        "      loss_dict_unif[e].append(np.average(loss_unif,axis=None,weights=true_weights))\n",
        "\n",
        "    #mean loss\n",
        "    mean_loss_disc = []\n",
        "    mean_loss_unif = []\n",
        "    for e in epsilon_list:\n",
        "        mean_loss_disc.append(np.mean(loss_dict_disc[e]))\n",
        "        mean_loss_unif.append(np.mean(loss_dict_unif[e]))\n",
        "\n",
        "    #stdev loss of MEAN loss\n",
        "    stdev_loss_disc = []\n",
        "    stdev_loss_unif = []\n",
        "    for e in epsilon_list:\n",
        "        stdev_loss_disc.append(np.std(loss_dict_disc[e])/np.sqrt(num_datasets))\n",
        "        stdev_loss_unif.append(np.std(loss_dict_unif[e])/np.sqrt(num_datasets))\n",
        "\n",
        "  return mean_loss_disc,mean_loss_unif,stdev_loss_disc,stdev_loss_unif,np.mean(loss_list_unif_ss_cv),np.mean(loss_list_unif_ss_TrueT),np.mean(loss_list_unif_ss_MLE),np.std(loss_list_unif_ss_cv)/np.sqrt(num_datasets),np.std(loss_list_unif_ss_MLE)/np.sqrt(num_datasets)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "#.25 transition noise\n",
        "# dose_penalty = 10\n",
        "# start state: .1 transition_noise\n",
        "# length: random lengths to increase uneven distrib of data\n",
        "# 50 traj\n",
        "# 50% treat\n",
        "# 500 resamples\n",
        "\n",
        "num_traj = 50\n",
        "num_datasets = 100\n",
        "mean_loss_disc, mean_loss_unif,stdev_loss_disc,stdev_loss_unif,loss_unif_ss_cv,loss_list_unif_ss_trueT,loss_unif_ss_mle,stdev_loss_ss_cv,stdev_loss_ss_mle=calc_loss(num_traj,num_datasets,T_true,R_true)\n",
        "epsilon_list = [0,.1,.2,.3,.4,.5,.6,.7,.8,.9,.95,.99]\n",
        "\n",
        "fig,ax = plt.subplots(1,1,figsize=(8,6))\n",
        "#ax.plot(epsilon_list,eg_normalized,label = 'Epsilon-Greedy',alpha=.5,linewidth = 5.0,color='mediumseagreen')\n",
        "#ax.plot(epsilon_list,mean_loss_unif,label = 'Uniform Prior',alpha=.8,linewidth = 5.0,color='#3a98c7')\n",
        "ax.errorbar(epsilon_list, mean_loss_unif, yerr=[2*j for j in stdev_loss_unif],label = 'Uniform Prior',linewidth =5.0,color='mediumseagreen')\n",
        "#ax.plot(epsilon_list,mean_loss_disc,label = 'Discount Regularization',alpha=.8,linewidth = 5.0,color='#ed6a47')\n",
        "ax.errorbar(epsilon_list, mean_loss_disc, yerr=[2*j for j in stdev_loss_disc],label = 'Discount Regularization',linewidth = 5.0,color='dodgerblue')\n",
        "#ax.axhline(y=loss_unif_ss_cv, color='darkblue', linestyle='-',linewidth = 5.0,alpha = .7, label = r\"State-action specfic $\\epsilon$ (CV)\")\n",
        "ax.errorbar(epsilon_list,[loss_unif_ss_cv for i in epsilon_list],yerr=[2*stdev_loss_ss_cv for j in epsilon_list],color='firebrick',linewidth = 5.0,alpha = .7,label = r\"State-Action Specfic $\\epsilon$\")\n",
        "#ax.axhline(y=loss_unif_ss_mle, color='teal', linestyle='-',linewidth = 5.0,alpha = .7, label = r\"State-action specfic $\\epsilon$ (MLE)\")\n",
        "#ax.errorbar(epsilon_list,[loss_unif_ss_mle for i in epsilon_list],yerr=[2*stdev_loss_ss_mle for j in epsilon_list],color='teal',linewidth = 5.0,alpha = .7,label = r\"State-action specfic $\\epsilon$ (MLE)\")\n",
        "\n",
        "ax.set_xlabel(\"Epsilon\",fontsize=18)\n",
        "ax.set_ylabel(\"Loss\",fontsize=18)\n",
        "ax.xaxis.set_major_locator(MaxNLocator(5))\n",
        "ax.yaxis.set_major_locator(MaxNLocator(5))\n",
        "ax.tick_params(axis='both', which='major', labelsize=14)\n",
        "ax.legend(fontsize=16)\n",
        "\n",
        "ax.legend(fontsize=18)\n",
        "\n",
        "fig.tight_layout(rect=[0.05, 0, 1, 0.85])\n",
        "plt.savefig('/content/gdrive/My Drive/cancer.pdf')"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "machine_shape": "hm",
      "provenance": [],
      "collapsed_sections": [
        "ZoBR7eVXRXb7",
        "9ss61dyPSGEi"
      ]
    },
    "gpuClass": "standard",
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}