# 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 a (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 for Monte Carlo acquistion functions is to multiply
the acquisition utility by the feasibility indicator of the modeled outcome
(^{[1]}, ^{[2]}). The approach can be utilized by passing
`constraints`

to the constructors of compatible acquisition functions,
e.g. any `SampleReducingMCAcqquisitionFunction`

with a positive acquisition utility,
like expected improvement.
Notably, if the constraint and objective models are statistically independent,
the constrained expected improvement variant is mathematically equivalent to the
unconstrained expected improvement of the objective, multiplied by the probability of
feasibility under the modeled outcome constraint.

See the Closed-Loop Optimization tutorial for an example of using outcome constraints in BoTorch.