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   "source": [
    "# Contextual Multi-Armed Bandit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the contextual multi-armed bandit (sMAB) when user information is available (context), we implemented a generalisation of Thompson sampling algorithm ([Agrawal and Goyal, 2014](https://arxiv.org/pdf/1209.3352.pdf)) based on PyMC3."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![title](img/cmab.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following notebook contains an example of usage of the class Cmab, which implements the algorithm above."
   ]
  },
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   "execution_count": null,
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   "source": [
    "import numpy as np\n",
    "\n",
    "from pybandits.cmab import CmabBernoulli\n",
    "from pybandits.model import BayesianLogisticRegression, StudentT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_samples = 1000\n",
    "n_features = 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we need to define the input context matrix $X$ of size ($n\\_samples, n\\_features$) and the mapping of possible actions $a_i \\in A$ to their associated model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "# context\n",
    "X = 2 * np.random.random_sample((n_samples, n_features)) - 1  # random float in the interval (-1, 1)\n",
    "print(\"X: context matrix of shape (n_samples, n_features)\")\n",
    "print(X[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define action model\n",
    "actions = {\n",
    "    \"a1\": BayesianLogisticRegression(alpha=StudentT(mu=1, sigma=2), betas=n_features * [StudentT()]),\n",
    "    \"a2\": BayesianLogisticRegression(alpha=StudentT(mu=1, sigma=2), betas=n_features * [StudentT()]),\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now init the bandit given the mapping of actions $a_i$ to their model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# init contextual Multi-Armed Bandit model\n",
    "cmab = CmabBernoulli(actions=actions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The predict function below returns the action selected by the bandit at time $t$: $a_t = argmax_k P(r=1|\\beta_k, x_t)$. The bandit selects one action per each sample of the contect matrix $X$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# predict action\n",
    "pred_actions, _, _ = cmab.predict(X)\n",
    "print(\"Recommended action: {}\".format(pred_actions[:10]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we observe the rewards and the context from the environment. In this example rewards and the context are randomly simulated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# simulate reward from environment\n",
    "simulated_rewards = np.random.randint(2, size=n_samples)\n",
    "# simulate context from environment\n",
    "simulated_context = 2 * np.random.random_sample((n_samples, n_features)) - 1  # random float in the interval (-1, 1)\n",
    "print(\"Simulated rewards: {}\".format(simulated_rewards[:10]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we update the model providing per each action sample: (i) its context $x_t$ (ii) the action $a_t$ selected by the bandit, (iii) the corresponding reward $r_t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# update model\n",
    "cmab.update(context=X, actions=pred_actions, rewards=simulated_rewards)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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