Robust expected improvement for Bayesian optimization
This work addresses the need for robust solutions in optimization when inputs are imprecise or multiple solutions are desired, representing an incremental improvement over existing Bayesian optimization methods.
The paper tackled the problem of finding robust optima in Bayesian optimization, where standard acquisition functions like expected improvement fail to prefer solutions with wider domains of attraction. They proposed robust expected improvement (REI), a method that integrates adversarial techniques into the GP framework, and demonstrated its performance on synthetic benchmarks and real-world problems.
Bayesian Optimization (BO) links Gaussian Process (GP) surrogates with sequential design toward optimizing expensive-to-evaluate black-box functions. Example design heuristics, or so-called acquisition functions, like expected improvement (EI), balance exploration and exploitation to furnish global solutions under stringent evaluation budgets. However, they fall short when solving for robust optima, meaning a preference for solutions in a wider domain of attraction. Robust solutions are useful when inputs are imprecisely specified, or where a series of solutions is desired. A common mathematical programming technique in such settings involves an adversarial objective, biasing a local solver away from ``sharp'' troughs. Here we propose a surrogate modeling and active learning technique called robust expected improvement (REI) that ports adversarial methodology into the BO/GP framework. After describing the methods, we illustrate and draw comparisons to several competitors on benchmark synthetic exercises and real problems of varying complexity.