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.

Accepted for ACM TELO

References in corpus (6)

• Robust Adversarial Reinforcement Learning
• On Neural Network Identification for Low-Speed Ship Maneuvering Model
• Optimization on Planning of Trajectory and Control of Autonomous Berthing and Unberthing for the Realistic Port Geometry
• Frank-Wolfe Algorithms for Saddle Point Problems
• Saddle Point Optimization with Approximate Minimization Oracle
• System Parameter Exploration of Ship Maneuvering Model for Automatic Docking / Berthing using CMA-ES

Cited by in corpus (1)

• Black-Box Min--Max Continuous Optimization Using CMA-ES with Worst-case Ranking Approximation