tutorials/GIBBON_for_efficient_batch_entropy_search.ipynb

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        "## The GIBBON (General-purpose Information-Based Bayesian OptimisatioN) acquisition function\n",
        "\n",
        "A particularly intuitive and empirically effective class of acquisition functions has arisen based on information theory. Information-theoretic Bayesian Optimisation (BO) seeks to reduce uncertainty in the location of high-performing areas of the search space, as measured in terms of differential entropy. BoTorch already supports information-theoretic BO through an implementation of the Max-value Entropy Search (MES) acquisition function [1] (see the [Max-Value Entropy tutorial](./max_value_entropy) for details), which makes evaluations that reduce uncertainty in the maximum value attained by the objective function. However, in order to support batch and multi-fidelity BO, our implementation of MES employs numerical integrations and fantasy observations  (i. e., we generate one point each time and when we try to generate the 𝑖-th point of a batch, we condition the models on the 𝑖−1 points generated prior to this). Unfortunately,  Each of these calculations can can add significantly to the computational overhead incurred by BO.\n",
        "\n",
        "In this notebook, we provide an information-theoretic acquisition function for tasks where objective function query costs are not large enough to overshadow significant optimisation overheads known as General-purpose Information-Based Bayesian OptimisatioN (GIBBON) [2]. In this tutorial, we present a very high-level overview of GIBBON and demonstrate its use within BoTorch.\n",
        "\n",
        "### Calculating GIBBON\n",
        "\n",
        "Following a principled information-theoretic construction, the GIBBON acquisition function measures the utility of evaluating a candidate batch of $B$ points $\\{\\textbf{x}\\}_{i=1}^B$ as\n",
        "\\begin{align}\n",
        "    \\alpha_{\\text{GIBBON}}(\\{\\textbf{x}\\}_{i=1}^B)\n",
        "    &= \\frac{1}{2}\\log |C| + \\sum_{i=1}^B  \\hat{\\alpha}_{\\text{MES}}(\\textbf{x}_i)\n",
        "\\end{align}\n",
        "where $|C|$ is the determinant of the $B\\times B$ correlation matrix between the batch elements and $\\hat{\\alpha}_{\\text{MES}}$ is an analytical approximation of the standard (non-batch) MES acquisition function. The GIBBON acquisition function forms a lower bound on the exact (but intractable) batch MES function and is consequently referred to as the `qLowerBoundMaxValueEntropy` in BoTorch. Crucially, GIBBON can be computed in closed-form and so incurs substantially lower overheads than batch MES via fantasies.\n",
        "\n",
        "### Interpretating GIBBON\n",
        "Note that the above decomposition of GIBBON has two terms and each has a helpful intuitive justification. In particular, the first term encourages diversity within the batch (achieving high values for points with low predictive correlation), whereas the second term ensures that evaluations are targeted in areas of the search space that provide large amounts of information about the maximum value attained by the objective function.\n",
        "\n",
        "\n",
        "<br>\n",
        "__References__\n",
        "\n",
        "\n",
        "[1] [Wang, Z., Jegelka, S., _Max-value Entropy Search for Efficient Bayesian Optimization._ arXiv:1703.01968v3, 2018](https://arxiv.org/abs/1703.01968)\n",
        "\n",
        "[2] [Moss, M., et al., _GIBBON: General-purpose Information-Based Bayesian Optimisation._  arXiv:2102.03324, 2020](https://arxiv.org/abs/2102.03324)\n"
      ]
    },
    {
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      "execution_count": 1,
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      "outputs": [],
      "source": [
        "import os\n",
        "\n",
        "SMOKE_TEST = os.environ.get(\"SMOKE_TEST\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "### 1. Setting up a toy model\n",
        "We will fit a standard SingleTaskGP model on noisy observations of the synthetic 2D SixHumpCamel function."
      ]
    },
    {
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      "execution_count": 2,
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      "source": [
        "import math\n",
        "import torch\n",
        "\n",
        "from botorch.test_functions import SixHumpCamel\n",
        "from botorch.fit import fit_gpytorch_mll\n",
        "from botorch.models import SingleTaskGP\n",
        "from botorch.utils.transforms import standardize, normalize\n",
        "from gpytorch.mlls import ExactMarginalLogLikelihood\n",
        "\n",
        "torch.manual_seed(123456)\n",
        "\n",
        "bounds = torch.tensor(SixHumpCamel._bounds).T\n",
        "bounds_norm = torch.tensor([[0.0, 0.0], [1.0, 1.0]])\n",
        "train_X = bounds[0] + (bounds[1] - bounds[0]) * torch.rand(5, 2)\n",
        "train_Y = SixHumpCamel(negate=True)(train_X).unsqueeze(-1)\n",
        "\n",
        "train_X = normalize(train_X, bounds=bounds)\n",
        "train_Y = standardize(train_Y + 0.05 * torch.randn_like(train_Y))\n",
        "\n",
        "model = SingleTaskGP(train_X, train_Y)\n",
        "mll = ExactMarginalLogLikelihood(model.likelihood, model)\n",
        "fit_gpytorch_mll(mll, max_attempts=10);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "originalKey": "1b900ec1-ec7a-4330-bf79-d16b72e53304"
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      "source": [
        "### 2. Defining the GIBBON acquisition function\n",
        "\n",
        "GIBBON is implemented in BoTorch as `qLowerBoundMaxValueEntropy` and supports pending points through its `X_pending` argument. Required arguments for the constructor are `model` and `candidate_set` (the discretized candidate points in the design space that will be used to draw max value samples). There are also other optional parameters, such as number of max value samples. Just like in our implementation of MES, two different sampling algorithms are supported for the max value samples: discretized Thompson sampling and Gumbel sampling (the default choice). \n",
        "   "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "collapsed": false,
        "executionStartTime": 1648577015914,
        "executionStopTime": 1648577016144,
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        "requestMsgId": "ad226a16-8b53-418e-bfb2-d3460b270acd"
      },
      "outputs": [],
      "source": [
        "from botorch.acquisition.max_value_entropy_search import qLowerBoundMaxValueEntropy\n",
        "\n",
        "candidate_set_size = 1000 if not SMOKE_TEST else 5\n",
        "candidate_set = torch.rand(\n",
        "    candidate_set_size, bounds_norm.size(1), device=bounds.device, dtype=bounds.dtype\n",
        ")\n",
        "qGIBBON = qLowerBoundMaxValueEntropy(model, candidate_set)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "originalKey": "d7ad6371-414c-4daa-b00a-253c7dbf0dd0"
      },
      "source": [
        "### 3. Optimizing the GIBBON acquisition function to get the next candidate points\n",
        "\n",
        "In order to obtain the next candidate point(s) to query, we need to optimize the acquisition function over the design space. For $q=1$ case, we can simply call the `optimize_acqf` function in the library. For $q>1$,  we greedily build batches using sequential optimization. \n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "collapsed": false,
        "executionStartTime": 1648577016206,
        "executionStopTime": 1648577016782,
        "originalKey": "6b2f24f7-93cb-419b-a36a-626e48077b6c",
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      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(tensor([[ 0.1199, -0.0158]]), tensor(0.0085))"
            ]
          },
          "execution_count": 4,
          "metadata": {
            "bento_obj_id": "140516803885120"
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "from botorch.optim import optimize_acqf\n",
        "\n",
        "NUM_RESTARTS = 10 if not SMOKE_TEST else 2\n",
        "RAW_SAMPLES = 512 if not SMOKE_TEST else 4\n",
        "\n",
        "# for q = 1\n",
        "candidates, acq_value = optimize_acqf(\n",
        "    acq_function=qGIBBON,\n",
        "    bounds=bounds,\n",
        "    q=1,\n",
        "    num_restarts=NUM_RESTARTS,\n",
        "    raw_samples=RAW_SAMPLES,\n",
        ")\n",
        "candidates, acq_value"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "collapsed": false,
        "executionStartTime": 1648577016794,
        "executionStopTime": 1648577017848,
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        "requestMsgId": "270506a8-d7dc-42d6-a6f5-b54f77746900"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(tensor([[ 0.1194, -0.0160],\n",
              "         [ 1.4241,  0.4417]]),\n",
              " tensor([0.0085, 0.0104]))"
            ]
          },
          "execution_count": 5,
          "metadata": {
            "bento_obj_id": "140516803794560"
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "from botorch.optim import optimize_acqf\n",
        "\n",
        "# for q = 2, sequential optimsiation\n",
        "candidates, acq_value = optimize_acqf(\n",
        "    acq_function=qGIBBON,\n",
        "    bounds=bounds,\n",
        "    q=2,\n",
        "    num_restarts=NUM_RESTARTS,\n",
        "    raw_samples=RAW_SAMPLES,\n",
        "    sequential=True,\n",
        ")\n",
        "candidates, acq_value"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "originalKey": "5e590a09-d151-4578-8558-79a9d9aa20d6"
      },
      "source": [
        "### 4. Comparing GIBBON with other acquisition functions\n",
        "\n",
        "We now perform an illustrative comparison between GIBBON and the other low-cost acquisition functions implemented in BoTorch. We plot points chosen by each of the acquisition functions, each acquisition function's surface.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "originalKey": "669f1fbe-f713-4158-a10a-9fa70ce3f14f"
      },
      "source": [
        "#### Sequential BO (q=1)\n",
        "\n",
        "Firstly, we investigate GIBBON in the purely sequential case, comparing agaisnt MES, Expected Improvement (EI) and Probability of Improvement (PI). We see that GIBBON provides a very high-quality approximation of MES, choosing essentially the same location.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
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        "executionStartTime": 1648577017895,
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      "outputs": [
        {
          "data": {
            "text/plain": [
              "Text(-0.1, 0.5, 'x_2')"
            ]
          },
          "execution_count": 6,
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          "output_type": "execute_result"
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",
            "text/plain": [
              "<Figure size 720x360 with 4 Axes>"
            ]
          },
          "metadata": {
            "bento_obj_id": "140516819586640",
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "from botorch.acquisition import (\n",
        "    ExpectedImprovement,\n",
        "    ProbabilityOfImprovement,\n",
        "    qMaxValueEntropy,\n",
        ")\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "%matplotlib inline\n",
        "\n",
        "# prep different acqusition functions\n",
        "acqs = {}\n",
        "candidate_set = torch.rand(\n",
        "    10000, bounds.size(1), device=bounds.device, dtype=bounds.dtype\n",
        ")\n",
        "acqs[\"GIBBON\"] = qLowerBoundMaxValueEntropy(model, candidate_set)\n",
        "acqs[\"MES\"] = qMaxValueEntropy(model, candidate_set)\n",
        "acqs[\"EI\"] = ExpectedImprovement(model, best_f=train_Y.max())\n",
        "acqs[\"PI\"] = ProbabilityOfImprovement(model, best_f=train_Y.max())\n",
        "\n",
        "# prep grid to evaluate acq functions\n",
        "n = 100 if not SMOKE_TEST else 2\n",
        "xv, yv = torch.meshgrid([torch.linspace(0, 1, n), torch.linspace(0, 1, n)])\n",
        "test_x = torch.stack([xv.reshape(n * n, 1), yv.reshape(n * n, 1)], -1)\n",
        "\n",
        "# eval and maximise acq functions\n",
        "evals = {}\n",
        "candidates = {}\n",
        "for acq in acqs.keys():\n",
        "    evals[acq] = acqs[acq](test_x).detach().reshape(n, n)\n",
        "    candidates[acq], _ = optimize_acqf(\n",
        "        acq_function=acqs[acq], bounds=bounds_norm, q=1, num_restarts=5, raw_samples=100\n",
        "    )\n",
        "\n",
        "# plot acqusition function values and chosen points\n",
        "fig, (ax1, ax2, ax3, ax4) = plt.subplots(\n",
        "    nrows=1, ncols=4, sharex=True, sharey=True, figsize=(10, 5)\n",
        ")\n",
        "ax1.contourf(xv.numpy(), yv.numpy(), evals[\"GIBBON\"].numpy(), levels=20)\n",
        "ax1.scatter(candidates[\"GIBBON\"][:, 0], candidates[\"GIBBON\"][:, 1], marker=\"X\", c=\"r\")\n",
        "ax1.set_title(\"GIBBON\")\n",
        "ax2.contourf(xv.numpy(), yv.numpy(), evals[\"MES\"].numpy(), levels=20)\n",
        "ax2.scatter(candidates[\"MES\"][:, 0], candidates[\"MES\"][:, 1], marker=\"X\", c=\"r\")\n",
        "ax2.set_title(\"MES\")\n",
        "ax3.contourf(xv.numpy(), yv.numpy(), evals[\"EI\"].numpy(), levels=20)\n",
        "ax3.scatter(candidates[\"EI\"][:, 0], candidates[\"EI\"][:, 1], marker=\"X\", c=\"r\")\n",
        "ax3.set_title(\"EI\")\n",
        "ax4.contourf(xv.numpy(), yv.numpy(), evals[\"PI\"].numpy(), levels=20)\n",
        "ax4.scatter(candidates[\"PI\"][:, 0], candidates[\"PI\"][:, 1], marker=\"X\", c=\"r\")\n",
        "ax4.set_title(\"PI\")\n",
        "fig.text(0.5, -0.1, \"x_1\", ha=\"center\")\n",
        "fig.text(-0.1, 0.5, \"x_2\", va=\"center\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "originalKey": "aa853e07-b322-4e26-ad5b-db81b8a47a33"
      },
      "source": [
        "#### Batch BO (q=3)\n",
        "\n",
        "For the batch BO case, GIBBON selects similar points to MES but with an order-of-magnitude lower computational overhead, i.e perfoming information-theoretic BO at the cost of much simpler acqusition functions like EI and PI. We stress that this gap in computational overhead between GIBBON and MES grows substantially as the optimisation progresses (see [2])."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "collapsed": false,
        "executionStartTime": 1648577020385,
        "executionStopTime": 1648577031509,
        "originalKey": "31ac3a12-eb78-4226-9170-31a22816f6c5",
        "requestMsgId": "a7e5671c-1735-46dc-b2f0-6f8b85a997e6"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Text(0.5, 0, 'Acquisition Function')"
            ]
          },
          "execution_count": 7,
          "metadata": {
            "bento_obj_id": "140516625083456"
          },
          "output_type": "execute_result"
        },
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 720x360 with 4 Axes>"
            ]
          },
          "metadata": {
            "bento_obj_id": "140516819231504",
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "bento_obj_id": "140516625042544",
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "from botorch.acquisition import qNoisyExpectedImprovement, qProbabilityOfImprovement\n",
        "from time import time\n",
        "\n",
        "# prep different acqusition functions\n",
        "acqs = {}\n",
        "candidate_set = torch.rand(\n",
        "    10000, bounds.size(1), device=bounds.device, dtype=bounds.dtype\n",
        ")\n",
        "acqs[\"GIBBON\"] = qLowerBoundMaxValueEntropy(model, candidate_set)\n",
        "acqs[\"MES\"] = qMaxValueEntropy(model, candidate_set)\n",
        "acqs[\"EI\"] = qNoisyExpectedImprovement(model, train_X)\n",
        "acqs[\"PI\"] = qProbabilityOfImprovement(model, best_f=train_Y.max())\n",
        "\n",
        "# prep grid to evaluate acq functions\n",
        "n = 100 if not SMOKE_TEST else 2\n",
        "xv, yv = torch.meshgrid([torch.linspace(0, 1, n), torch.linspace(0, 1, n)])\n",
        "test_x = torch.stack([xv.reshape(n * n, 1), yv.reshape(n * n, 1)], -1)\n",
        "\n",
        "# eval and maximise acq functions\n",
        "evals = {}\n",
        "candidates = {}\n",
        "times = {}\n",
        "for acq in acqs.keys():\n",
        "    evals[acq] = acqs[acq](test_x).detach().reshape(n, n)\n",
        "    t_0 = time()\n",
        "    candidates[acq], _ = optimize_acqf(\n",
        "        acq_function=acqs[acq],\n",
        "        bounds=bounds_norm,\n",
        "        q=3,\n",
        "        num_restarts=5,\n",
        "        raw_samples=100,\n",
        "        sequential=True,\n",
        "    )\n",
        "    times[acq] = time() - t_0\n",
        "\n",
        "# plot acqusition function values and chosen points\n",
        "fig, (ax1, ax2, ax3, ax4) = plt.subplots(\n",
        "    nrows=1, ncols=4, sharex=True, sharey=True, figsize=(10, 5)\n",
        ")\n",
        "ax1.contourf(xv.numpy(), yv.numpy(), evals[\"GIBBON\"].numpy(), levels=20)\n",
        "ax1.scatter(candidates[\"GIBBON\"][:, 0], candidates[\"GIBBON\"][:, 1], marker=\"X\", c=\"r\")\n",
        "ax1.set_title(\"GIBBON\")\n",
        "ax2.contourf(xv.numpy(), yv.numpy(), evals[\"MES\"].numpy(), levels=20)\n",
        "ax2.scatter(candidates[\"MES\"][:, 0], candidates[\"MES\"][:, 1], marker=\"X\", c=\"r\")\n",
        "ax2.set_title(\"MES\")\n",
        "ax3.contourf(xv.numpy(), yv.numpy(), evals[\"EI\"].numpy(), levels=20)\n",
        "ax3.scatter(candidates[\"EI\"][:, 0], candidates[\"EI\"][:, 1], marker=\"X\", c=\"r\")\n",
        "ax3.set_title(\"EI\")\n",
        "ax4.contourf(xv.numpy(), yv.numpy(), evals[\"PI\"].numpy(), levels=20)\n",
        "ax4.scatter(candidates[\"PI\"][:, 0], candidates[\"PI\"][:, 1], marker=\"X\", c=\"r\")\n",
        "ax4.set_title(\"PI\")\n",
        "fig.text(0.5, -0.1, \"x_1\", ha=\"center\")\n",
        "fig.text(-0.1, 0.5, \"x_2\", va=\"center\")\n",
        "\n",
        "# plot computational overheads\n",
        "plt.figure()\n",
        "heights = [times[acq] for acq in acqs.keys()]\n",
        "plt.bar(acqs.keys(), heights)\n",
        "plt.ylabel(\"Computation Time\")\n",
        "plt.xlabel(\"Acquisition Function\")"
      ]
    }
  ],
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