Saddle Point Optimization with Approximate Minimization Oracle and Its Application to Robust Berthing Control

Abstract

We propose an approach to saddle point optimization relying only on oracles that solve minimization problems approximately. We analyze its convergence property on a strongly convex-concave problem and show its linear convergence toward the global min-max saddle point. Based on the convergence analysis, we develop a heuristic approach to adapt the learning rate. An implementation of the developed approach using the (1+1)-CMA-ES as the minimization oracle, namely, Adversarial-CMA-ES, is shown to outperform several existing approaches on test problems. Numerical evaluation confirms the tightness of the theoretical convergence rate bound as well as the efficiency of the learning rate adaptation mechanism. As an example of real-world problems, the suggested optimization method is applied to automatic berthing control problems under model uncertainties, showing its usefulness in obtaining solutions robust to uncertainty.