Saddle Point Optimization with Approximate Minimization Oracle and its Application to Robust Berthing Control
arXiv:2105.11586 · doi:10.1145/3510425
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.
arXiv commentAccepted for ACM TELO
References in corpus (12)
- Robust Adversarial Reinforcement Learning
- A Tutorial on Bayesian Optimization
- The Numerics of GANs
- Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methods
- 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
- The Implicit and the Inverse Function theorems: easy proofs
- Local Saddle Point Optimization: A Curvature Exploitation Approach
- Frank-Wolfe Algorithms for Saddle Point Problems
- On the Application of Danskin's Theorem to Derivative-Free Minimax Optimization
- Saddle Point Optimization with Approximate Minimization Oracle
- System Parameter Exploration of Ship Maneuvering Model for Automatic Docking / Berthing using CMA-ES