A Hybrid Algorithm for Monotone Variational Inequalities

TL;DR

This paper introduces two new algorithms inspired by aGRAAL for solving monotone variational inequalities, demonstrating improved convergence through momentum parameter tuning and validating performance on various machine learning and control problems.

Contribution

The paper proposes novel methods that enhance convergence speed by adjusting momentum parameters, extending the adaptive Golden Ratio Algorithm for broader applications.

Findings

Improved convergence speed with larger momentum parameters.

Effective performance on Nash equilibrium, minimization, MDPs, and zero-sum games.

Outperforms existing methods in tested variational inequality problems.

Abstract

Inspired by the adaptive Golden Ratio Algorithm (aGRAAL), we propose two new methods for solving monotone variational inequalities. We show that by selecting the momentum parameter beyond the golden ratio in aGRAAL, the convergence speed can be improved, which motivates us to study the switching between small and large momentum parameters to accelerate convergence. We validate the performance of our proposed algorithms on several classes of variational inequality problems studied in the machine learning and control literature, including Nash equilibrium seeking, composite minimization, Markov decision processes, and zero-sum games, and compare them to that of existing methods.