Update composite BO tutorial with HOGP notebook reference (#2738)

Summary:
# PR Summary
Small PR - Commit b3f6a38 moved the composite BO tutorial with HOGP notebook. This PR adjusts sources to changes. It also fixes a few typos along the way.

Pull Request resolved: #2738

Reviewed By: esantorella

Differential Revision: D69354421

Pulled By: saitcakmak

fbshipit-source-id: 902f6eacf8b5a2848ef00ef9a5c098a4e5c8b0f1

tutorials/composite_mtbo/composite_mtbo.ipynb

@@ -14,7 +14,7 @@
         "\n",
         "**Multi-task Bayesian Optimization** was first proposed by [Swersky et al, NeurIPS, '13](https://papers.neurips.cc/paper/2013/hash/f33ba15effa5c10e873bf3842afb46a6-Abstract.html) in the context of fast hyper-parameter tuning for neural network models; however, we demonstrate a more advanced use-case of **[composite Bayesian optimization](https://proceedings.mlr.press/v97/astudillo19a.html)** where the overall function that we wish to optimize is a cheap-to-evaluate (and known) function of the outputs. In general, we expect that using more information about the function should yield improved performance when attempting to optimize it, particularly if the metric function itself is quickly varying.\n",
         "\n",
-        "See [the composite BO tutorial w/ HOGP](https://github.com/pytorch/botorch/blob/main/tutorials/composite_bo_with_hogp.ipynb) for a more technical introduction. In general, we suggest using MTGPs for unstructured task outputs and the HOGP for matrix / tensor structured outputs.\n",
+        "See [the composite BO tutorial w/ HOGP](https://github.com/pytorch/botorch/blob/main/tutorials/composite_bo_with_hogp/composite_bo_with_hogp.ipynb) for a more technical introduction. In general, we suggest using MTGPs for unstructured task outputs and the HOGP for matrix / tensor structured outputs.\n",
         "\n",
         "\n",
         "We will use a Multi-Task Gaussian process ([MTGP](https://papers.nips.cc/paper/2007/hash/66368270ffd51418ec58bd793f2d9b1b-Abstract.html)) with an ICM kernel to model all of the outputs in this problem. MTGPs can be easily accessed in Botorch via the `botorch.models.KroneckerMultiTaskGP` model class (for the \"block design\" case of fully observed outputs at all inputs). Given $T$ tasks (outputs) and $n$ data points, they assume that the responses, $Y \\sim \\mathbb{R}^{n \\times T},$ are distributed as $\\text{vec}(Y) \\sim \\mathcal{N}(f, D)$ and $f \\sim \\mathcal{GP}(\\mu_{\\theta}, K_{XX} \\otimes K_{T}),$ where $D$ is a (diagonal) noise term."
@@ -162,7 +162,7 @@
         "$$g(f) = \\sum_{i=1}^T \\cos(f_i^2 + f_i w_i)$$\n",
         "where $w$ is a weight vector (drawn randomly once at the start of the optimization). As this function is a non-linear function of the outputs $f,$ we cannot compute acquisition functions via computation of the posterior mean and variance, but rather have to compute posterior samples and evaluate acquisitions with Monte Carlo sampling. \n",
         "\n",
-        "For greater than $10$ or so tasks, it is computationally challenging to sample the posterior over all tasks jointly using conventional approaches, except that [Maddox et al, '21](https://arxiv.org/abs/2106.12997) have devised an efficient method for exploiting the structure in the posterior distribution of the MTGP, enabling efficient MC based optimization of objectives using MTGPs. In this tutorial, we choose 6  contexts/tasks for demostration. "
+        "For greater than $10$ or so tasks, it is computationally challenging to sample the posterior over all tasks jointly using conventional approaches, except that [Maddox et al, '21](https://arxiv.org/abs/2106.12997) have devised an efficient method for exploiting the structure in the posterior distribution of the MTGP, enabling efficient MC based optimization of objectives using MTGPs. In this tutorial, we choose 6  contexts/tasks for demonstration. "
       ]
     },
     {
@@ -348,7 +348,7 @@
         "        bounds=bounds,\n",
         "        q=batch_size,\n",
         "        num_restarts=10,\n",
-        "        raw_samples=512,  # used for intialization heuristic\n",
+        "        raw_samples=512,  # used for initialization heuristic\n",
         "        options={\"batch_limit\": 5, \"maxiter\": MAXITER, \"init_batch_limit\": 5},\n",
         "    )\n",
         "    mtgp_train_x = torch.cat((mtgp_train_x, new_mtgp_x), dim=0)\n",