Sample-Based Trust Region Dynamics in Contextual Global Optimization

Abstract

The problem of contextual global optimization is treated, in which a generally non-convex scalar objective (possibly black-box) depends not only on the decision variables, but also on uncontrollable, observable context variables. Assuming Lipschitz continuity of the objective function with respect to its arguments, the proposed approach builds a Set Membership model from observed samples. According to the observed context, a submodel that relates the objective to the decision variables is isolated, and used by a zeroth-order technique to pick the appropriate decision variable for sampling. A novel trust region dynamic is introduced, adjusting its size with samples instead of iterations. Such a technique makes the resulting contextual optimization algorithm more flexible with respect to the context behavior, whether it is changing smoothly, abruptly, or a combination of both. Benchmark tests and a case study demonstrate the efficacy of the proposed method.