examples/quickstart/replay.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quickstart Example of Off-Policy Evaluation of Online Bandit Algorithms\n",
    "---\n",
    "This notebook provides an example of conducting OPE of online bandit algorithms using Replay Method (RM) with synthetic bandit feedback data.\n",
    "RM uses a subset of the logged bandit feedback data where actions selected by the behavior policy are the same as that of the evaluation policy.\n",
    "Theoretically, RM is unbiased when the behavior policy is uniformly random and the evaluation policy is fixed.\n",
    "However, empirically, RM works well when evaluation policies are learning algorithms.\n",
    "Please refer to https://arxiv.org/abs/1003.5956 about the details of RM.\n",
    "\n",
    "Our example with online bandit algorithms contains the following three major steps:\n",
    "- (1) Synthetic Data Generation\n",
    "- (2) Off-Policy Evaluation (OPE)\n",
    "- (3) Evaluation of OPE\n",
    "\n",
    "Please see [../examples/online](../online) for a more sophisticated example of the evaluation of OPE of online bandit algorithms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# needed when using Google Colab\n",
    "# !pip install obp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import open bandit pipeline (obp)\n",
    "import obp\n",
    "from obp.dataset import (\n",
    "    SyntheticBanditDataset,\n",
    "    logistic_reward_function\n",
    ")\n",
    "from obp.policy import EpsilonGreedy, LinTS, LinUCB\n",
    "from obp.ope import (\n",
    "    OffPolicyEvaluation, \n",
    "    ReplayMethod\n",
    ")\n",
    "from obp.simulator import (\n",
    "    calc_ground_truth_policy_value,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5.4\n"
     ]
    }
   ],
   "source": [
    "# obp version\n",
    "print(obp.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (1) Synthetic Data Generation\n",
    "We prepare easy-to-use synthetic data generator: `SyntheticBanditDataset` class in the dataset module.\n",
    "\n",
    "It takes number of actions (`n_actions`), dimension of context vectors (`dim_context`), reward function (`reward_function`), and behavior policy (`behavior_policy_function`) as inputs and generates a synthetic bandit dataset that can be used to evaluate the performance of decision making policies (obtained by `off-policy learning`) and OPE estimators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'n_rounds': 10000,\n",
       " 'n_actions': 10,\n",
       " 'context': array([[-0.20470766,  0.47894334, -0.51943872, -0.5557303 ,  1.96578057],\n",
       "        [ 1.39340583,  0.09290788,  0.28174615,  0.76902257,  1.24643474],\n",
       "        [ 1.00718936, -1.29622111,  0.27499163,  0.22891288,  1.35291684],\n",
       "        ...,\n",
       "        [-1.27028221,  0.80914602, -0.45084222,  0.47179511,  1.89401115],\n",
       "        [-0.68890924,  0.08857502, -0.56359347, -0.41135069,  0.65157486],\n",
       "        [ 0.51204121,  0.65384817, -1.98849253, -2.14429131, -0.34186901]]),\n",
       " 'action_context': array([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "        [0, 1, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "        [0, 0, 1, 0, 0, 0, 0, 0, 0, 0],\n",
       "        [0, 0, 0, 1, 0, 0, 0, 0, 0, 0],\n",
       "        [0, 0, 0, 0, 1, 0, 0, 0, 0, 0],\n",
       "        [0, 0, 0, 0, 0, 1, 0, 0, 0, 0],\n",
       "        [0, 0, 0, 0, 0, 0, 1, 0, 0, 0],\n",
       "        [0, 0, 0, 0, 0, 0, 0, 1, 0, 0],\n",
       "        [0, 0, 0, 0, 0, 0, 0, 0, 1, 0],\n",
       "        [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]),\n",
       " 'action': array([9, 3, 2, ..., 0, 2, 7]),\n",
       " 'position': None,\n",
       " 'reward': array([1, 1, 0, ..., 0, 0, 1]),\n",
       " 'expected_reward': array([[0.81612381, 0.62585527, 0.3867853 , ..., 0.62527072, 0.58635322,\n",
       "         0.38638404],\n",
       "        [0.52901819, 0.30298844, 0.47277431, ..., 0.67711224, 0.55584904,\n",
       "         0.60472268],\n",
       "        [0.47070198, 0.44459997, 0.40016028, ..., 0.71193979, 0.49769816,\n",
       "         0.71876507],\n",
       "        ...,\n",
       "        [0.85229627, 0.60343336, 0.18287765, ..., 0.54555271, 0.77112271,\n",
       "         0.18843358],\n",
       "        [0.78101646, 0.68586084, 0.40700551, ..., 0.45177062, 0.63841605,\n",
       "         0.48128186],\n",
       "        [0.88757249, 0.75954519, 0.82721872, ..., 0.3422384 , 0.33609074,\n",
       "         0.84539856]]),\n",
       " 'pi_b': array([[[0.13284158],\n",
       "         [0.10982506],\n",
       "         [0.08647184],\n",
       "         ...,\n",
       "         [0.10976088],\n",
       "         [0.10557132],\n",
       "         [0.08643715]],\n",
       " \n",
       "        [[0.10165762],\n",
       "         [0.08109171],\n",
       "         [0.09609782],\n",
       "         ...,\n",
       "         [0.11788441],\n",
       "         [0.1044221 ],\n",
       "         [0.10965236]],\n",
       " \n",
       "        [[0.09128276],\n",
       "         [0.08893092],\n",
       "         [0.08506539],\n",
       "         ...,\n",
       "         [0.11618686],\n",
       "         [0.09378061],\n",
       "         [0.11698258]],\n",
       " \n",
       "        ...,\n",
       " \n",
       "        [[0.13979975],\n",
       "         [0.10900003],\n",
       "         [0.07157834],\n",
       "         ...,\n",
       "         [0.10287015],\n",
       "         [0.12890008],\n",
       "         [0.07197713]],\n",
       " \n",
       "        [[0.12794035],\n",
       "         [0.11632739],\n",
       "         [0.08801904],\n",
       "         ...,\n",
       "         [0.09204875],\n",
       "         [0.11093714],\n",
       "         [0.0948057 ]],\n",
       " \n",
       "        [[0.1309115 ],\n",
       "         [0.11517978],\n",
       "         [0.1232442 ],\n",
       "         ...,\n",
       "         [0.0758826 ],\n",
       "         [0.07541753],\n",
       "         [0.12550525]]]),\n",
       " 'pscore': array([0.08643715, 0.11568983, 0.08506539, ..., 0.13979975, 0.08801904,\n",
       "        0.0758826 ])}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# generate a synthetic bandit dataset with 10 actions\n",
    "# we use `logistic function` as the reward function\n",
    "# we use the uniformly random behavior policy because it is desriable for RM\n",
    "# one can define their own reward function and behavior policy such as nonlinear ones. \n",
    "dataset = SyntheticBanditDataset(\n",
    "    n_actions=10,\n",
    "    dim_context=5,\n",
    "    reward_type=\"binary\", # \"binary\" or \"continuous\"\n",
    "    reward_function=logistic_reward_function,\n",
    "    behavior_policy_function=None, # uniformly random\n",
    "    random_state=12345,\n",
    ")\n",
    "# obtain a set of synthetic logged bandit feedback\n",
    "n_rounds = 10000\n",
    "bandit_feedback = dataset.obtain_batch_bandit_feedback(n_rounds=n_rounds)\n",
    "\n",
    "# `bandit_feedback` is a dictionary storing synthetic logged bandit data\n",
    "bandit_feedback"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (2) Off-Policy Evaluation (OPE)\n",
    "Our next step is OPE which aims to estimate the performance of online bandit algorithms using logged bandit data and RM.\n",
    "\n",
    "Here, we visualize the OPE results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10000/10000 [00:00<00:00, 72377.23it/s]\n",
      "100%|██████████| 10000/10000 [00:10<00:00, 924.59it/s]\n",
      "100%|██████████| 10000/10000 [00:00<00:00, 10100.23it/s]\n"
     ]
    }
   ],
   "source": [
    "# simulations of online bandit algorithms\n",
    "# obtain a deterministic action distribution representing which action is selected at each round in the simulation\n",
    "# policies are updated only when the selected action is the same as that of the logged data\n",
    "epsilon_greedy = EpsilonGreedy(\n",
    "    n_actions=dataset.n_actions,\n",
    "    epsilon=0.1,\n",
    "    random_state=12345\n",
    ")\n",
    "action_dist_epsilon_greedy = run_bandit_replay(\n",
    "    bandit_feedback=bandit_feedback,\n",
    "    policy=epsilon_greedy\n",
    ")\n",
    "\n",
    "lin_ts = LinTS(\n",
    "    dim=dataset.dim_context,\n",
    "    n_actions=dataset.n_actions,\n",
    "    random_state=12345\n",
    ")\n",
    "action_dist_lin_ts = run_bandit_replay(\n",
    "    bandit_feedback=bandit_feedback,\n",
    "    policy=lin_ts\n",
    ")\n",
    "\n",
    "lin_ucb = LinUCB(\n",
    "    dim=dataset.dim_context,\n",
    "    n_actions=dataset.n_actions,\n",
    "    random_state=12345\n",
    ")\n",
    "action_dist_lin_ucb = run_bandit_replay(\n",
    "    bandit_feedback=bandit_feedback,\n",
    "    policy=lin_ucb\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# estimate the policy value of the online bandit algorithms using RM\n",
    "ope = OffPolicyEvaluation(\n",
    "    bandit_feedback=bandit_feedback,\n",
    "    ope_estimators=[ReplayMethod()]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    95.0% CI (lower)  95.0% CI (upper)     mean\n",
      "rm          0.548577          0.633734  0.59423 \n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# estimate the policy value of EpsilonGreedy\n",
    "estimated_policy_value_epsilon_greedy, estimated_interval_epsilon_greedy = ope.summarize_off_policy_estimates(\n",
    "    action_dist=action_dist_epsilon_greedy\n",
    ")\n",
    "print(estimated_interval_epsilon_greedy, '\\n')\n",
    "\n",
    "# visualize estimated policy values of EpsilonGreedy by the three OPE estimators\n",
    "# and their 95% confidence intervals (estimated by nonparametric bootstrap method)\n",
    "ope.visualize_off_policy_estimates(\n",
    "    action_dist=action_dist_epsilon_greedy,\n",
    "    n_bootstrap_samples=10000, # number of resampling performed in bootstrap sampling\n",
    "    random_state=12345,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    95.0% CI (lower)  95.0% CI (upper)      mean\n",
      "rm          0.615827          0.712571  0.662281 \n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# estimate the policy value of LinTS\n",
    "estimated_policy_value_lin_ts, estimated_interval_lin_ts = ope.summarize_off_policy_estimates(\n",
    "    action_dist=action_dist_lin_ts\n",
    ")\n",
    "print(estimated_interval_lin_ts, '\\n')\n",
    "\n",
    "# visualize estimated policy values of LinTS by the three OPE estimators\n",
    "# and their 95% confidence intervals (estimated by nonparametric bootstrap method)\n",
    "ope.visualize_off_policy_estimates(\n",
    "    action_dist=action_dist_lin_ts,\n",
    "    n_bootstrap_samples=10000, # number of resampling performed in bootstrap sampling\n",
    "    random_state=12345,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    95.0% CI (lower)  95.0% CI (upper)      mean\n",
      "rm          0.581798          0.674513  0.626882 \n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# estimate the policy value of LinUCB\n",
    "estimated_policy_value_lin_ucb, estimated_interval_lin_ucb = ope.summarize_off_policy_estimates(\n",
    "    action_dist=action_dist_lin_ucb\n",
    ")\n",
    "print(estimated_interval_lin_ucb, '\\n')\n",
    "\n",
    "# visualize estimated policy values of LinUCB by the three OPE estimators\n",
    "# and their 95% confidence intervals (estimated by nonparametric bootstrap method)\n",
    "ope.visualize_off_policy_estimates(\n",
    "    action_dist=action_dist_lin_ucb,\n",
    "    n_bootstrap_samples=10000, # number of resampling performed in bootstrap sampling\n",
    "    random_state=12345,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RM estimates that LinTS is the best policy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (3) Evaluation of OPE\n",
    "Our final step is **the evaluation of OPE**, which evaluates and compares the estimation accuracy of OPE estimators.\n",
    "\n",
    "With synthetic data, we can calculate the policy value of the evaluation policies. \n",
    "Therefore, we can compare the policy values estimated by RM with the ground-turths to evaluate the accuracy of OPE."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 3/3 [00:18<00:00,  6.20s/it]\n",
      "100%|██████████| 3/3 [00:51<00:00, 17.10s/it]\n",
      "100%|██████████| 3/3 [00:21<00:00,  7.24s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "policy value of EpsilonGreedy: 0.6056001659264234\n",
      "policy value of LinTS: 0.7515744188226375\n",
      "policy value of LinUCB: 0.6689063585401301\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# we first calculate the policy values of the three evaluation policies\n",
    "# in synthetic data, we know p(r|x,a), the reward distribution, so we can perform simulations\n",
    "# here, a policy is updated at each round according to actions and rewards sampled from the policy and p(r|x,a)\n",
    "# the policy values are averaged over `n_sim` simulations\n",
    "policy_value_epsilon_greedy = calc_ground_truth_policy_value(\n",
    "    bandit_feedback=bandit_feedback,\n",
    "    reward_sampler=dataset.sample_reward, # p(r|x,a)\n",
    "    policy=epsilon_greedy,\n",
    "    n_sim=3 # the number of simulations\n",
    ")\n",
    "policy_value_lin_ts = calc_ground_truth_policy_value(\n",
    "    bandit_feedback=bandit_feedback,\n",
    "    reward_sampler=dataset.sample_reward, # p(r|x,a)\n",
    "    policy=lin_ts,\n",
    "    n_sim=3 # the number of simulations\n",
    ")\n",
    "policy_value_lin_ucb = calc_ground_truth_policy_value(\n",
    "    bandit_feedback=bandit_feedback,\n",
    "    reward_sampler=dataset.sample_reward, # p(r|x,a)\n",
    "    policy=lin_ucb,\n",
    "    n_sim=3 # the number of simulations\n",
    ")\n",
    "\n",
    "print(f'policy value of EpsilonGreedy: {policy_value_epsilon_greedy}')\n",
    "print(f'policy value of LinTS: {policy_value_lin_ts}')\n",
    "print(f'policy value of LinUCB: {policy_value_lin_ucb}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In fact, LinTS reveals the best performance among the three evaluation policies.\n",
    "\n",
    "Using the above policy values, we evaluate the estimation accuracy of the OPE estimators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>relative-ee</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>rm</th>\n",
       "      <td>0.02448</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    relative-ee\n",
       "rm      0.02448"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# evaluate the estimation performances of OPE estimators \n",
    "# by comparing the estimated policy values of EpsilonGreedy and its ground-truth.\n",
    "# `summarize_estimators_comparison` returns a pandas dataframe containing estimation performances of given estimators \n",
    "relative_ee_epsilon_greedy = ope.summarize_estimators_comparison(\n",
    "    ground_truth_policy_value=policy_value_epsilon_greedy,\n",
    "    action_dist=action_dist_epsilon_greedy,\n",
    "    metric=\"relative-ee\", # \"relative-ee\" (relative estimation error) or \"se\" (squared error)\n",
    ")\n",
    "\n",
    "# estimation performances of the three estimators (lower means accurate)\n",
    "relative_ee_epsilon_greedy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>relative-ee</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>rm</th>\n",
       "      <td>0.118454</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    relative-ee\n",
       "rm     0.118454"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# evaluate the estimation performance of OPE estimators \n",
    "# by comparing the estimated policy values of LinTS t and its ground-truth.\n",
    "# `summarize_estimators_comparison` returns a pandas dataframe containing estimation performances of given estimators \n",
    "relative_ee_lin_ts = ope.summarize_estimators_comparison(\n",
    "    ground_truth_policy_value=policy_value_lin_ts,\n",
    "    action_dist=action_dist_lin_ts,\n",
    "    metric=\"relative-ee\", # \"relative-ee\" (relative estimation error) or \"se\" (squared error)\n",
    ")\n",
    "\n",
    "# estimation performances of the three estimators (lower means accurate)\n",
    "relative_ee_lin_ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>relative-ee</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>rm</th>\n",
       "      <td>0.058522</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    relative-ee\n",
       "rm     0.058522"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# evaluate the estimation performance of OPE estimators \n",
    "# by comparing the estimated policy values of LinUCB and its ground-truth.\n",
    "# `summarize_estimators_comparison` returns a pandas dataframe containing estimation performances of given estimators \n",
    "relative_ee_lin_ucb = ope.summarize_estimators_comparison(\n",
    "    ground_truth_policy_value=policy_value_lin_ucb,\n",
    "    action_dist=action_dist_lin_ucb,\n",
    "    metric=\"relative-ee\", # \"relative-ee\" (relative estimation error) or \"se\" (squared error)\n",
    ")\n",
    "\n",
    "# estimation performances of the three estimators (lower means accurate)\n",
    "relative_ee_lin_ucb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please see [../examples/online](../online) for a more sophisticated example of the evaluation of OPE with online bandit algorithms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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