loaded_dice_demo.ipynb

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  "metadata": {
    "colab": {
      "name": "loaded_dice_demo.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
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  "cells": [
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      "cell_type": "code",
      "metadata": {
        "id": "rkyeRFdSfy2h",
        "colab_type": "code",
        "outputId": "a306d1b0-002f-430c-9193-509ff2673a23",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        }
      },
      "source": [
        "import torch\n",
        "from torch.distributions.categorical import Categorical\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "!pip install pymdptoolbox\n",
        "import mdptoolbox.example\n",
        "import pickle\n",
        "\n",
        "plt.rcParams.update({\"font.size\": 20})"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: pymdptoolbox in /usr/local/lib/python3.6/dist-packages (4.0b3)\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from pymdptoolbox) (1.3.1)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from pymdptoolbox) (1.16.5)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Tm6nbDnkgCKa",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def magic_box(x):\n",
        "    \"\"\"Magic Box Operator. x are log-probabilities\"\"\"\n",
        "    return torch.exp(x - x.detach())\n",
        "\n",
        "def gae(rewards, values, mask, tau=1.0, gamma_weighted=False):\n",
        "    \"\"\"Generalised Advantage Estimation https://arxiv.org/abs/1506.02438\"\"\"\n",
        "    values = values * mask\n",
        "    deltas = rewards + gamma * values[:,1:] - values[:,:-1]\n",
        "    advantages = torch.zeros_like(deltas).float()\n",
        "    gae = torch.zeros_like(deltas[:,0]).float()\n",
        "    for i in range(deltas.size(1) - 1, -1, -1):\n",
        "        gae = gae * gamma * tau + deltas[:, i]\n",
        "        advantages[:,i] = gae\n",
        "    if gamma_weighted:\n",
        "        gamma_weights = torch.cumprod(torch.ones_like(advantages) * gamma, 1) / gamma\n",
        "        advantages = advantages * gamma_weights\n",
        "    return advantages\n",
        "\n",
        "def make_objective(batch_data, v_fn, tau=1.0, dice_lambda=1.0, use_dice=False, gamma_weighted=True):\n",
        "    \"\"\"Make objective for DiCE, Loaded DiCE, or classic surrogate loss\"\"\"\n",
        "    (batch_states, batch_pi_taken, batch_a_taken,\n",
        "        batch_r, batch_dones, batch_mask, ep_returns) = batch_data\n",
        "    empty_mask = (1 - batch_mask[:,:-1]).type(torch.ByteTensor)\n",
        "    batch_pi_taken[empty_mask] = 1.0\n",
        "    log_pi = torch.log(batch_pi_taken)\n",
        "    batch_values = v_fn(batch_states).detach()\n",
        "    advantages = gae(batch_r, batch_values, batch_mask, tau=tau, gamma_weighted=gamma_weighted)\n",
        "    if use_dice == \"old\":\n",
        "        log_pi_cumsum = torch.cumsum(log_pi, 1)\n",
        "        deps = magic_box(log_pi_cumsum)\n",
        "        batch_r[:,-1] = batch_r[:,-1] + batch_values[:,-1]*gamma\n",
        "        if gamma_weighted:\n",
        "            gamma_weights = torch.cumprod(torch.ones_like(advantages) * gamma, 1) / gamma\n",
        "            batch_r = batch_r * gamma_weights\n",
        "        obj = (batch_r * deps).sum(1).mean()\n",
        "    elif use_dice == \"loaded\":\n",
        "        weighted_cumsum = torch.zeros_like(log_pi)\n",
        "        weighted_cumsum[:,0] = log_pi[:,0]\n",
        "        for t in range(1, log_pi.size(1)):\n",
        "            weighted_cumsum[:,t] = dice_lambda * weighted_cumsum[:,t-1] + log_pi[:,t]\n",
        "        deps_exclusive = weighted_cumsum - log_pi\n",
        "        full_deps = magic_box(weighted_cumsum) - magic_box(deps_exclusive)\n",
        "        obj = (advantages * full_deps).sum(1).mean()\n",
        "    else:\n",
        "        obj = (advantages * log_pi).sum(1).mean()\n",
        "    return obj\n",
        "\n",
        "def get_P_pi(P, pi):\n",
        "    \"\"\"State transition function induced by MDP transition P and policy pi\"\"\"\n",
        "    return (pi.softmax(0).unsqueeze(-1) * P).sum(0)\n",
        "\n",
        "def get_V(S0, P_pi, R, gamma):\n",
        "    \"\"\"Analytically compute V for small MDPs\"\"\"\n",
        "    return (S0 @ torch.inverse(torch.eye(S0.size(0)) - gamma*P_pi) * R).sum()\n",
        "\n",
        "def sample(batch_size, max_steps=50, params=None):\n",
        "    \"\"\"Sample a batch of episodes from the MDP\"\"\"\n",
        "    ep_returns = []\n",
        "    if params is None:\n",
        "        params = pi\n",
        "\n",
        "    batch_states = torch.zeros([batch_size, max_steps+1])\n",
        "    batch_pi_taken = torch.zeros([batch_size, max_steps])\n",
        "    batch_a_taken = torch.zeros([batch_size, max_steps])\n",
        "    batch_r = torch.zeros([batch_size, max_steps])\n",
        "    batch_dones = torch.zeros([batch_size, max_steps])\n",
        "    batch_mask = torch.ones([batch_size, max_steps+1])\n",
        "    \n",
        "    state = Categorical(S0.unsqueeze(0).repeat(batch_size,1)).sample()\n",
        "    \n",
        "    for t in range(max_steps):\n",
        "        r = R[state]\n",
        "        probs = params[:,state].softmax(0).transpose(0,1)\n",
        "        actions = Categorical(probs).sample()\n",
        "        pi_taken = probs.gather(1, actions.unsqueeze(1)).squeeze(1)\n",
        "        p_next = P[actions,state]\n",
        "        next_state = Categorical(p_next).sample()\n",
        "\n",
        "        batch_states[:,t] = state\n",
        "        batch_pi_taken[:,t] = pi_taken\n",
        "        batch_r[:,t] = r\n",
        "        state = next_state\n",
        "    batch_states[:, -1] = state\n",
        "\n",
        "    return batch_states, batch_pi_taken, batch_a_taken, batch_r, batch_dones, batch_mask, ep_returns\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vlSpYTRDgfsj",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "np.random.seed(0)\n",
        "torch.manual_seed(0)\n",
        "n_states = 5\n",
        "n_actions = 4\n",
        "S0 = torch.ones(n_states) / n_states\n",
        "P, R = mdptoolbox.example.rand(n_states, n_actions)\n",
        "P = torch.tensor(P, dtype=torch.float)\n",
        "R = (torch.randn(n_states) + 5) * 10\n",
        "noise = 0.0\n",
        "gamma = 0.95\n",
        "pi = torch.randn(n_actions, n_states, requires_grad=True)\n",
        "\n",
        "P_pi = get_P_pi(P, pi)\n",
        "V = get_V(S0, P_pi, R, gamma)\n",
        "V_s = torch.zeros(n_states)\n",
        "for s in range(n_states):\n",
        "    V_s[s] = get_V(torch.eye(n_states)[s], P_pi, R, gamma).detach() + torch.randn_like(V) * noise\n",
        "    \n",
        "v_fn = lambda s: V_s[s.long()].detach()\n",
        "\n",
        "# batch_sizes = [4**n for n in range(3,9)] # bigger batches take longer, show estimator unbiasedness\n",
        "batch_sizes = [4**n for n in range(3,7)]\n",
        "n_orders = 3\n",
        "n_seeds = 5"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "G5Ea_qLMggyG",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def corr_obj(tau, dice_method, lam=1.0):\n",
        "    \"\"\"Get derivatives up to n_orders\"\"\"\n",
        "    data = {}  # bs: [order: [seed1, ...]]\n",
        "    print(f\"{dice_method}, tau={tau}, lambda={lam}\")\n",
        "    for batch_size in batch_sizes:\n",
        "        print(\"bs\", batch_size)\n",
        "        data[batch_size] = [[] for _ in range(n_orders)]\n",
        "        for seed in range(n_seeds):\n",
        "            batch_data = sample(batch_size)\n",
        "            obj = make_objective(batch_data, v_fn, tau, use_dice=dice_method,\n",
        "                                 dice_lambda=lam, gamma_weighted=True)\n",
        "\n",
        "            grad = torch.autograd.grad(obj, pi, retain_graph=True, create_graph=True)[0]\n",
        "            data[batch_size][0].append(grad.detach().numpy().flatten())\n",
        "            for order in range(1, n_orders):\n",
        "                # We only differentiate one element of the derivative to the next order\n",
        "                grad = torch.autograd.grad(grad[0][0], pi, retain_graph=True, create_graph=True)[0]\n",
        "                data[batch_size][order].append(grad.detach().numpy().flatten())\n",
        "    return data\n",
        "\n",
        "def get_true_grads():\n",
        "    true_grads = []\n",
        "    true_grad = torch.autograd.grad(V, pi, retain_graph=True, create_graph=True)[0]\n",
        "    true_grads.append(true_grad.detach().numpy().flatten())\n",
        "    for order in range(n_orders - 1):\n",
        "        true_grad = torch.autograd.grad(true_grad[0][0], pi, retain_graph=True, create_graph=True)[0]\n",
        "        true_grads.append(true_grad.detach().numpy().flatten())\n",
        "    return true_grads"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hZUFNcwOgmr9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def run_corr_exp():\n",
        "    old_dice_data = corr_obj(1.0, \"old\") # DiCE\n",
        "    betterbase_data = corr_obj(1.0, \"loaded\") # Mao et al. corresponds to Loaded DiCE with tau=1.0\n",
        "    lambda_data = corr_obj(0.0, \"loaded\") # Loaded DiCE, tau=0.0\n",
        "    lvc_data = corr_obj(1.0, \"loaded\", lam=0.0) # LVC corresponds to Loaded DiCE with tau=1.0, lamda=0.0\n",
        "    true_grads = get_true_grads()\n",
        "    full_data = [old_dice_data, betterbase_data, lambda_data, lvc_data, true_grads]\n",
        "\n",
        "    with open(\"corr_results_demo.pkl\", \"wb\") as f:\n",
        "        pickle.dump(full_data, f)\n",
        "\n",
        "def plot_corr_exp():\n",
        "    with open(\"corr_results_demo.pkl\", \"rb\") as f:\n",
        "        full_data = pickle.load(f)\n",
        "\n",
        "    true_grads = full_data[-1]\n",
        "    full_data = full_data[:-1]\n",
        "    full_corr_data = []\n",
        "\n",
        "    for data in full_data:\n",
        "        corr_data = {}\n",
        "        for bs in batch_sizes:\n",
        "            corr_data[bs] = [{} for _ in range(n_orders)]\n",
        "            for order in range(n_orders):\n",
        "                corrs = []\n",
        "                grads = []\n",
        "                for seed in range(n_seeds):\n",
        "                    corrs.append(np.corrcoef(data[bs][order][seed], true_grads[order])[0][1])\n",
        "                    grads.append(data[bs][order][seed])\n",
        "                grad_std = np.std(np.stack(grads), 0).mean()\n",
        "\n",
        "                corr_mean = np.mean(corrs)\n",
        "                corr_std = np.std(corrs)\n",
        "                corr_sem = corr_std / np.sqrt(n_seeds)\n",
        "                corr_data[bs][order][\"mean\"] = corr_mean\n",
        "                corr_data[bs][order][\"std\"] = corr_std\n",
        "                corr_data[bs][order][\"sem\"] = corr_sem\n",
        "                corr_data[bs][order][\"grad_std\"] = grad_std\n",
        "        full_corr_data.append(corr_data)\n",
        "\n",
        "    fig, axes = plt.subplots(1, n_orders, figsize=(22,6))\n",
        "\n",
        "    axes_labels = [\"1st Order\", \"2nd Order\", \"3rd Order\"]\n",
        "\n",
        "    for order in range(n_orders):\n",
        "        ax = axes[order]\n",
        "        for i, method in enumerate([\"DiCE\", \"Mao et al.\", \"Ours\", \"LVC\"]):\n",
        "            corr_data = full_corr_data[i]\n",
        "            ys = [corr_data[bs][order][\"mean\"] for bs in batch_sizes]\n",
        "            errs = [corr_data[bs][order][\"sem\"] for bs in batch_sizes]\n",
        "            ax.errorbar(batch_sizes, ys, yerr=errs, linestyle=\"None\", marker='x', label=method, markersize=12,\n",
        "                        elinewidth=2, markeredgewidth=2)\n",
        "        ax.set_xscale('log')\n",
        "        ax.set_ylim(-0.2,1.1)\n",
        "        ax.set_xlabel(axes_labels[order])\n",
        "    axes[0].set_ylabel(\"Correlation with true derivative\")\n",
        "    axes[0].legend(loc = \"lower right\")\n",
        "\n",
        "    fig.tight_layout()\n",
        "    fig.savefig(\"corr_demo.png\")"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t06z8BB4hH88",
        "colab_type": "code",
        "outputId": "877ea830-ed1b-4d7f-d480-905e7129cdbf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 787
        }
      },
      "source": [
        "# Check the correlation of different estimators with the true derivatives as a function of batch size\n",
        "\n",
        "run_corr_exp()\n",
        "plot_corr_exp()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "old, tau=1.0, lambda=1.0\n",
            "bs 64\n",
            "bs 256\n",
            "bs 1024\n",
            "bs 4096\n",
            "loaded, tau=1.0, lambda=1.0\n",
            "bs 64\n",
            "bs 256\n",
            "bs 1024\n",
            "bs 4096\n",
            "loaded, tau=0.0, lambda=1.0\n",
            "bs 64\n",
            "bs 256\n",
            "bs 1024\n",
            "bs 4096\n",
            "loaded, tau=1.0, lambda=0.0\n",
            "bs 64\n",
            "bs 256\n",
            "bs 1024\n",
            "bs 4096\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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cBKwCvhURX4uIv42IJRFxVvGjTrWWlFJaC6wGZgPvKTp8KbA/cG1K6alsZ0TM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\nzMzMGjmYYGZmZmZmZmZmZmZmjf4HvirzcGUfhxUAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 1584x432 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UwhNwRBrgr9S",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def run_lam_experiment():\n",
        "    data = {} # metric: [order: [seed1, ...]]\n",
        "\n",
        "    lams = [1.0, 0.75, 0.5, 0.25, 0.0]\n",
        "    batch_size = 512\n",
        "    n_orders = 3\n",
        "    n_seeds = 50\n",
        "    for lam in lams:\n",
        "        print(lam)\n",
        "        data[lam] = [[] for _ in range(n_orders)]\n",
        "        for seed in range(n_seeds):\n",
        "            batch_data = sample(batch_size, max_steps=50)\n",
        "            obj = make_objective(batch_data, v_fn, tau=0.0, use_dice=\"loaded\",\n",
        "                                 dice_lambda=lam, gamma_weighted=True)\n",
        "\n",
        "            grad = torch.autograd.grad(obj, pi, retain_graph=True, create_graph=True)[0]\n",
        "            data[lam][0].append(grad.detach().numpy().flatten())\n",
        "            for order in range(1, n_orders):\n",
        "                grad = torch.autograd.grad(grad[0][0], pi, retain_graph=True, create_graph=True)[0]\n",
        "                data[lam][order].append(grad.detach().numpy().flatten())\n",
        "\n",
        "    true_grads = []\n",
        "    true_grad = torch.autograd.grad(V, pi, retain_graph=True, create_graph=True)[0]\n",
        "    true_grads.append(true_grad.detach().numpy().flatten())\n",
        "    for order in range(n_orders - 1):\n",
        "        true_grad = torch.autograd.grad(true_grad[0][0], pi, retain_graph=True, create_graph=True)[0]\n",
        "        true_grads.append(true_grad.detach().numpy().flatten())\n",
        "\n",
        "    full_data = [data, true_grads]\n",
        "\n",
        "    with open(\"lam_results.pkl\", \"wb\") as f:\n",
        "        pickle.dump(full_data, f)\n",
        "\n",
        "def plot_lam_experiment(agg=True, param=0):\n",
        "    with open(\"lam_results.pkl\", \"rb\") as f:\n",
        "        full_data = pickle.load(f)\n",
        "\n",
        "    data, true_grads = full_data\n",
        "\n",
        "    proc_data = {}\n",
        "    n_orders = 3\n",
        "    n_seeds = 50\n",
        "\n",
        "    lams = list(data.keys())\n",
        "    for lam in lams:\n",
        "        proc_data[lam] = [{} for _ in range(n_orders)]\n",
        "        for order in range(n_orders):\n",
        "            diffs, grads = [], []\n",
        "            for seed in range(n_seeds):\n",
        "                diffs.append((data[lam][order][seed] - true_grads[order]))\n",
        "                grads.append(data[lam][order][seed])\n",
        "\n",
        "            diffs = np.stack(diffs)\n",
        "            grads = np.stack(grads)\n",
        "            grads_mean = np.mean(grads, 0)\n",
        "            stds = np.std(grads, 0)\n",
        "            if agg:\n",
        "                bias_mean = np.abs(diffs.mean(0)).mean()\n",
        "            else:\n",
        "                bias_mean = np.abs(diffs.mean(0))[param]\n",
        "\n",
        "            # picking a single param gives better error analysis but increases variance\n",
        "            if agg:\n",
        "                bias_std = np.std(diffs, 0).mean()\n",
        "            else:\n",
        "                bias_std = np.std(diffs, 0)[param]\n",
        "\n",
        "            bias_sem = bias_std / np.sqrt(n_seeds)\n",
        "            proc_data[lam][order][\"bias_mean\"] = bias_mean\n",
        "            proc_data[lam][order][\"bias_std\"] = bias_std\n",
        "            proc_data[lam][order][\"bias_sem\"] = bias_sem\n",
        "\n",
        "            if agg:\n",
        "                stds_mean = np.mean(stds)\n",
        "            else:\n",
        "                stds_mean = stds[param]\n",
        "            proc_data[lam][order][\"std_mean\"] = stds_mean\n",
        "            # https://stats.stackexchange.com/questions/631/standard-deviation-of-standard-deviation\n",
        "            proc_data[lam][order][\"std_sem\"] = stds_mean * np.sqrt(np.e * (1 - 1 / n_seeds) ** (n_seeds - 1) - 1)\n",
        "\n",
        "    fig, axes = plt.subplots(1, 2, figsize=(10,5))\n",
        "\n",
        "    min_bias, min_std = 9e9, 9e9\n",
        "    max_bias, max_std = -9e9, -9e9\n",
        "\n",
        "    labels = [\"1st\", \"2nd\", \"3rd\"]\n",
        "\n",
        "    for order in range(0, 3):\n",
        "        biases = [proc_data[lam][order][\"bias_mean\"] for lam in lams]\n",
        "        min_bias = min([min_bias] + biases)\n",
        "        max_bias = max([max_bias] + biases)\n",
        "        bias_errs = [proc_data[lam][order][\"bias_sem\"] for lam in lams]\n",
        "        axes[0].errorbar(lams, biases, yerr=bias_errs, linestyle=\"None\", marker='x', label=order+1, markersize=12,\n",
        "                        elinewidth=2, markeredgewidth=2)\n",
        "        stds = [proc_data[lam][order][\"std_mean\"] for lam in lams]\n",
        "        stds_err = [proc_data[lam][order][\"std_sem\"] for lam in lams]\n",
        "        min_std = min([min_std] + stds)\n",
        "        max_std = max([max_std] + stds)\n",
        "        axes[1].errorbar(lams, stds, yerr=stds_err, linestyle=\"None\", marker='x', label=labels[order], markersize=12,\n",
        "                        elinewidth=2, markeredgewidth=2)\n",
        "\n",
        "    axes[1].legend(title=\"Order\", loc=\"center left\")\n",
        "    axes[0].set_ylim(0, max_bias*1.1)\n",
        "    axes[1].set_ylim(min_std*0.9, max_std*1.1)\n",
        "    axes[0].set_ylabel(\"Bias\")\n",
        "    axes[1].set_ylabel(\"Std\")\n",
        "    axes[0].set_xlabel(r\"DiCE $\\lambda$\")\n",
        "    axes[1].set_xlabel(r\"DiCE $\\lambda$\")\n",
        "\n",
        "    fig.tight_layout()\n",
        "    fig.savefig(\"lambda_trade_demo.png\")"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CzMrNcPbig_t",
        "colab_type": "code",
        "outputId": "3918c42c-546a-4f6e-806a-879940631d51",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 435
        }
      },
      "source": [
        "# Trade off bias and variance in higher-order derivatives by discounting the effect of more distant causal dependencies\n",
        "\n",
        "run_lam_experiment()\n",
        "plot_lam_experiment()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1.0\n",
            "0.75\n",
            "0.5\n",
            "0.25\n",
            "0.0\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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UugDhL6nYl4iIUMGRSWUc3omCS6Ns5w852AvMbP1miYhkl5QEWRERSanJoXsD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\nSUFWRERERAJJQVZEREREAun/AWzaj0GIcv04AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 720x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "s-Etqaf3gyP6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def run_tau_experiment():\n",
        "    data = {} # metric: [order: [seed1, ...]]\n",
        "\n",
        "    taus = [1.0, 0.75, 0.5, 0.25, 0.0]\n",
        "    batch_size = 512\n",
        "    n_orders = 3\n",
        "    n_seeds = 50\n",
        "    for tau in taus:\n",
        "        print(tau)\n",
        "        data[tau] = [[] for _ in range(n_orders)]\n",
        "        for seed in range(n_seeds):\n",
        "            batch_data = sample(batch_size, max_steps=50)\n",
        "            obj = make_objective(batch_data, v_fn, tau=tau, use_dice=\"loaded\",\n",
        "                                 dice_lambda=1.0, gamma_weighted=True)\n",
        "\n",
        "            grad = torch.autograd.grad(obj, pi, retain_graph=True, create_graph=True)[0]\n",
        "            data[tau][0].append(grad.detach().numpy().flatten())\n",
        "            for order in range(1, n_orders):\n",
        "                grad = torch.autograd.grad(grad[0][0], pi, retain_graph=True, create_graph=True)[0]\n",
        "                data[tau][order].append(grad.detach().numpy().flatten())\n",
        "\n",
        "    true_grads = []\n",
        "    true_grad = torch.autograd.grad(V, pi, retain_graph=True, create_graph=True)[0]\n",
        "    true_grads.append(true_grad.detach().numpy().flatten())\n",
        "    for order in range(n_orders - 1):\n",
        "        true_grad = torch.autograd.grad(true_grad[0][0], pi, retain_graph=True, create_graph=True)[0]\n",
        "        true_grads.append(true_grad.detach().numpy().flatten())\n",
        "\n",
        "    full_data = [data, true_grads]\n",
        "\n",
        "    with open(\"tau_results.pkl\", \"wb\") as f:\n",
        "        pickle.dump(full_data, f)\n",
        "\n",
        "def plot_tau_experiment(agg=True, param=0):\n",
        "    with open(\"tau_results.pkl\", \"rb\") as f:\n",
        "        full_data = pickle.load(f)\n",
        "\n",
        "    data, true_grads = full_data\n",
        "\n",
        "    proc_data = {}\n",
        "    n_orders = 3\n",
        "    n_seeds = 50\n",
        "\n",
        "    taus = list(data.keys())\n",
        "    for tau in taus:\n",
        "        proc_data[tau] = [{} for _ in range(n_orders)]\n",
        "        for order in range(n_orders):\n",
        "            diffs, grads = [], []\n",
        "            for seed in range(n_seeds):\n",
        "                diffs.append((data[tau][order][seed] - true_grads[order]))\n",
        "                grads.append(data[tau][order][seed])\n",
        "            diffs = np.stack(diffs)\n",
        "            grads = np.stack(grads)\n",
        "            grads_mean = np.mean(grads, 0)\n",
        "            stds = np.std(grads, 0)\n",
        "\n",
        "            if agg:\n",
        "                bias_mean = np.abs(diffs.mean(0)).mean()\n",
        "            else:\n",
        "                bias_mean = np.abs(diffs.mean(0))[param]\n",
        "\n",
        "            bias_std = np.std(diffs, 0)[param]\n",
        "            bias_sem = bias_std / np.sqrt(n_seeds)\n",
        "            proc_data[tau][order][\"bias_mean\"] = bias_mean\n",
        "            proc_data[tau][order][\"bias_std\"] = bias_std\n",
        "            proc_data[tau][order][\"bias_sem\"] = bias_sem\n",
        "\n",
        "            if agg:\n",
        "                stds_mean = np.mean(stds)\n",
        "            else:\n",
        "                stds_mean = stds[param]\n",
        "            proc_data[tau][order][\"std_mean\"] = stds_mean\n",
        "\n",
        "            # https://stats.stackexchange.com/questions/631/standard-deviation-of-standard-deviation\n",
        "            proc_data[tau][order][\"std_sem\"] = stds_mean * np.sqrt(np.e * (1 - 1/n_seeds)**(n_seeds-1) - 1)\n",
        "\n",
        "    fig, axes = plt.subplots(1, 2, figsize=(10,5))\n",
        "\n",
        "    min_bias, min_std = 9e9, 9e9\n",
        "    max_bias, max_std = -9e9, -9e9\n",
        "\n",
        "    labels = [\"1st\", \"2nd\", \"3rd\"]\n",
        "\n",
        "    for order in range(0, 3):\n",
        "        biases = [proc_data[tau][order][\"bias_mean\"] for tau in taus]\n",
        "        min_bias = min([min_bias] + biases)\n",
        "        max_bias = max([max_bias] + biases)\n",
        "        bias_errs = [proc_data[tau][order][\"bias_sem\"] for tau in taus]\n",
        "        axes[0].errorbar(taus, biases, yerr=bias_errs, linestyle=\"None\", marker='x', markersize=12,\n",
        "                        elinewidth=2, markeredgewidth=2)\n",
        "        stds = [proc_data[tau][order][\"std_mean\"] for tau in taus]\n",
        "        stds_err = [proc_data[tau][order][\"std_sem\"] for tau in taus]\n",
        "        min_std = min([min_std] + stds)\n",
        "        max_std = max([max_std] + stds)\n",
        "        axes[1].errorbar(taus, stds, yerr=stds_err, linestyle=\"None\", marker='x', label=labels[order], markersize=12,\n",
        "                        elinewidth=2, markeredgewidth=2)\n",
        "\n",
        "    axes[1].legend(title=\"Order\", loc=\"upper left\")\n",
        "    axes[0].set_ylim(0, max_bias*1.1)\n",
        "    axes[1].set_ylim(min_std*0.9, max_std*1.1)\n",
        "    axes[0].set_ylabel(\"Bias\")\n",
        "    axes[1].set_ylabel(\"Std\")\n",
        "    axes[0].set_xlabel(r\"GAE $\\tau$\")\n",
        "    axes[1].set_xlabel(r\"GAE $\\tau$\")\n",
        "\n",
        "    fig.tight_layout()\n",
        "    fig.savefig(\"tau_trade_demo.png\")"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WvtTS1T0hJ-x",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Trade off bias and variance due to advantage estimator\n",
        "\n",
        "# For this we approximate a biased value function by adding some random noise\n",
        "# torch.manual_seed(0)\n",
        "noise = 10.0\n",
        "for s in range(n_states):\n",
        "  V_s[s] = get_V(torch.eye(n_states)[s], P_pi, R, gamma).detach() + torch.randn_like(V) * noise\n",
        "    \n",
        "v_fn = lambda s: V_s[s.long()].detach()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Bb6rJvwnNzNv",
        "colab_type": "code",
        "outputId": "676b3000-8bef-4397-ce02-b585a9a33b81",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 435
        }
      },
      "source": [
        "run_tau_experiment()\n",
        "plot_tau_experiment()"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1.0\n",
            "0.75\n",
            "0.5\n",
            "0.25\n",
            "0.0\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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RkXoMGTIEs7AV2EQi88Nsq+LDy1oVJzTEgoKsiIjkuflr5lP9eXXU7ao/r2b+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\nE1lJkiQ16T9cWezkQ8e7GwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 720x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MQUJaC-yjmA6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}