Add docs describing constraints on a high level (#730)

Summary:
First stab at addressing #729

Pull Request resolved: #730

Reviewed By: ldworkin

Differential Revision: D29428625

Pulled By: Balandat

fbshipit-source-id: bc75064556ee5b361ab2d5aa24bd903a6ced6619

docs/constraints.md

@@ -0,0 +1,46 @@
+---
+id: constraints
+title: Constraints
+---
+
+BoTorch supports two distinct types of constraints: Parameter constraints
+and outcome constraints.
+
+
+### Parameter Constraints
+
+Parameter constraints are constraints on the input space that restrict the
+values of the generated candidates. That is, rather than just living inside
+a bounding box defined by the `bounds` argument to `optimize_acqf` (or its
+derivates), candidate points may be further constrained by linear (in)equality
+constraints, specified by the `inequality_constraints` and `equality_constraints`
+arguments to `optimize_acqf`.
+
+Parameter constraints are used e.g. when certain configurations are infeasible
+to implement, or would result in excessive costs. These constraints do not affect
+the model directly, only indirectly in the sense that all newly generated and
+later observed points will satisfy these constraints. In particular, you may
+have a model that is fit on points that do not satisfy a certain set of parameter
+constraints, but still generate candidates subject to those constraints.
+
+
+### Outcome Constraints
+
+In the context of Bayesian Optimization, outcome constraints usually mean
+constraints on some (black-box) outcome that needs to be modeled, just like
+the objective function is modeled by a surrogate model. Various approaches
+for handling these types of constraints have been proposed, a popular one that
+is also adopted by BoTorch (and available in the form of `ConstrainedMCObjective`)
+is to use variant of expected improvement in which the improvement in the objective
+is weighted by the probability of feasibility under the (modeled) outcome
+constraint ([^Gardner2014], [^Letham2017]).
+
+See the [Closed-Loop Optimization](../tutorials/closed_loop_botorch_only)
+tutorial for an example of using outcome constraints in BoTorch.
+
+
+
+[^Gardner2014]: J.R. Gardner, M. J. Kusner, Z. E. Xu, K. Q. Weinberger and
+J. P. Cunningham. Bayesian Optimization with Inequality Constraints. ICML 2014.
+
+[^Letham2017]: B. Letham, B. Karrer, G. Ottoni and E. Bakshy. Constrained Bayesian optimization with noisy experiments. Bayesian Analysis 14(2), 2019.

website/sidebars.json

@@ -3,7 +3,7 @@
     "About": ["introduction", "design_philosophy", "botorch_and_ax", "papers"],
     "General": ["getting_started"],
     "Basic Concepts": ["overview", "models", "posteriors", "acquisition", "optimization"],
-    "Advanced Topics": ["batching", "objectives", "samplers"],
+    "Advanced Topics": ["constraints", "objectives", "batching", "samplers"],
     "Multi-Objective Optimization": ["multi_objective"]
   }
 }