Data-Driven Minimax Optimization with Expectation Constraints

• URL: http://arxiv.org/abs/2202.07868v1
• Date: Wed, 16 Feb 2022 05:23:27 GMT
• Title: Data-Driven Minimax Optimization with Expectation Constraints
• Authors: Shuoguang Yang, Xudong Li, Guanghui Lan
• Abstract summary: We propose a class of efficient primal-dual algorithms to tackle the minimax expectation-constrained problem. We show that our algorithms converge at the optimal rate of $mathcalO(frac1sqrtN)$.
• Score: 9.373649142701803
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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