Data-Driven Minimax Optimization with Expectation Constraints

TL;DR

This paper introduces efficient primal-dual algorithms for non-smooth convex-concave stochastic minimax problems with expectation constraints, addressing computational challenges and demonstrating optimal convergence and practical effectiveness.

Contribution

It develops a novel class of primal-dual algorithms for minimax expectation-constrained problems, achieving optimal convergence rates and applicability to real-world large-scale problems.

Findings

Algorithms converge at the optimal rate of 1/√N

Demonstrated practical efficiency on large-scale applications

Addresses computational challenges of data-driven constraints

Abstract

Attention to data-driven optimization approaches, including the well-known stochastic gradient descent method, has grown significantly over recent decades, but data-driven constraints have rarely been studied, because of the computational challenges of projections onto the feasible set defined by these hard constraints. In this paper, we focus on the non-smooth convex-concave stochastic minimax regime and formulate the data-driven constraints as expectation constraints. The minimax expectation constrained problem subsumes a broad class of real-world applications, including two-player zero-sum game and data-driven robust optimization. We propose a class of efficient primal-dual algorithms to tackle the minimax expectation-constrained problem, and show that our algorithms converge at the optimal rate of $\mathcal{O}(\frac{1}{\sqrt{N}})$. We demonstrate the practical efficiency of our algorithms by conducting numerical experiments on large-scale real-world applications.