chapter eight

8 Satisfying extra constraints with constrained optimization

 

This chapter covers

  • The problem of black-box optimization with constraints
  • Taking constraints into account when making decisions in Bayesian optimization
  • Implementing constraint-aware Bayesian optimization policies

In previous chapters, we tackled black-box optimization problems where we aimed solely to maximize the objective function without any other considerations. This is called an unconstrained optimization problem, as we are free to explore the search space to look for the global optimum of the objective function. Many real-life situations might not follow this unconstrained formulation, however, and there might be a cost associated with the objective function’s global optimum that makes the optimum infeasible to achieve in practice.

8.1 Accounting for constraints in a constrained optimization problem

8.1.1 Constraints can change the solution of an optimization problem

8.1.2 The constraint-aware Bayesian optimization framework

8.2 Constraint-aware decision making in Bayesian optimization

8.3 Exercise 1: Manual computation of constrained Expected Improvement

8.4 Implementing constrained Expected Improvement with BoTorch

8.5 Summary

8.6 Exercise 2: Constrained optimization of airplane design