Improvements to botorch closed loop tutorial

Reviewed By: Balandat

Differential Revision: D15157204

fbshipit-source-id: 7361a7ba981208d11527ac124a73fa580346cd34

Author: Ashwin Murthy

tutorials/closed_loop_botorch_only.ipynb

@@ -19,7 +19,7 @@
     "\n",
     "over $x \\in [0,1]^6$ (parameter values can be found in `botorch/test_functions/hartmann6.py`).\n",
     "\n",
-    "In real BO applications, the design $x$ can influence multiple metrics in unknown ways, and the decision-maker often wants to optimize one metric without sacrificing another. To illustrate this, we add a synthetic constarint fo the form $\\|x\\|_1 - 3 \\le 0$. Both the objective and the constraint are observed with noise. \n",
+    "In real BO applications, the design $x$ can influence multiple metrics in unknown ways, and the decision-maker often wants to optimize one metric without sacrificing another. To illustrate this, we add a synthetic constraint fo the form $\\|x\\|_1 - 3 \\le 0$. Both the objective and the constraint are observed with noise. \n",
     "\n",
     "Since botorch assumes a maximization problem, we will attempt to maximize $-f(x)$ to achieve $\\max_{x} -f(x) = 3.32237$."
    ]
@@ -114,7 +114,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We will also need to define mappings that take the outputs of the GP and return the objective and the constraint. In general, these can be any `Callable`, but here we simply need to index the correct output."
+    "#### Define a construct to extract the objective and constraint from the GP\n",
+    "The methods below take the outputs of the GP and return the objective and the constraint. In general, these can be any `Callable`, but here we simply need to index the correct output."
    ]
   },
   {
@@ -198,7 +199,7 @@
     "3. update the surrogate model. \n",
     "\n",
     "\n",
-    "Just for illustration purposes, we run three trials of `N_BATCH=20` iterations. The acquisition function is approximated using `MC_SAMPLES=500` samples.\n",
+    "Just for illustration purposes, we run three trials each of which do `N_BATCH=20` rounds of optimization. The acquisition function is approximated using `MC_SAMPLES=500` samples.\n",
     "\n",
     "*Note*: Running this may take a little while."
    ]
@@ -337,7 +338,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "#### Plot the results"
+    "#### Plot the results\n",
+    "The plot below shows the best objective value observed at each step of the optimization for each of the algorithms. ",
+    "The confidence intervals represent the variance at that step in the optimization across the trial runs."
    ]
   },
   {