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

TL;DR

This paper introduces a saddle point optimization method using approximate minimization oracles, demonstrating theoretical convergence, practical efficiency, and application to robust berthing control under uncertainties.

Contribution

It presents a novel saddle point optimization approach with convergence guarantees and applies it to real-world berthing control problems.

Findings

Linear convergence to saddle point proven theoretically

Outperforms existing methods on test problems

Effective in robust berthing control under uncertainties

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.