mlsanityData to 7 Oct 2026

Data-Driven Minimax Optimization with Expectation Constraints

arXiv 2202.07868 ↗First posted 16 Feb 2022cs.LG math.OCcited by 5

Not on the map. Why?

Abstract (arXiv)

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 O(frac1√N). We demonstrate the practical efficiency of our algorithms by conducting numerical experiments on large-scale real-world applications.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 18 of its 66 references that are in the map. First posted on arXiv 16 Feb 2022.

Builds on

18 of 66 references.

References · 18

  1. 2019Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methodscited by 148
  2. 2017Online Convex Optimization with Stochastic Constraintscited by 94
  3. 2020Model-Based Multi-Agent RL in Zero-Sum Markov Games with Near-Optimal Sample Complexitycited by 91
  4. 2018Lower complexity bounds of first-order methods for convex-concave bilinear saddle-point problemscited by 75
  5. 2013Challenges of Big Data Analysiscited by 47
  6. 2019Stochastic First-order Methods for Convex and Nonconvex Functional Constrained Optimizationcited by 38
  7. 2014Accelerated Schemes For A Class of Variational Inequalitiescited by 30
  8. 2020Efficient Generation of Structured Objects with Constrained Adversarial Networkscited by 27
  9. 2020Optimal Algorithms for Convex Nested Stochastic Composite Optimizationcited by 20
  10. 2013Optimal Primal-Dual Methods for a Class of Saddle Point Problemscited by 19
  11. 2019Constrained Generative Adversarial Networks for Interactive Image Generationcited by 10
  12. 2013Mirror Prox Algorithm for Multi-Term Composite Minimization and Semi-Separable Problemscited by 7
6 more
  1. 2014On the solution of stochastic optimization and variational problems in imperfect information regimescited by 5
  2. 2017Sample average approximation with heavier tails I: non-asymptotic bounds with weak assumptions and stochastic constraintscited by 4
  3. 2019A Data Efficient and Feasible Level Set Method for Stochastic Convex Optimization with Expectation Constraintscited by 4
  4. 2020Conditional Gradient Methods for Convex Optimization with General Affine and Nonlinear Constraintscited by 4
  5. 2019Stochastic Approximation Proximal Method of Multipliers for Convex Stochastic Programmingcited by 2
  6. 2017Sample average approximation with heavier tails II: localization in stochastic convex optimization and persistence results for the Lassocited by 1

Built on by

Cited by year

Citing papers per year: 2022: 2; 2023: 1; 2024: 1; 2025: 1.

5 papers.

  1. 2022Stochastic Methods for AUC Optimization subject to AUC-based Fairness Constraintscited by 9
  2. 2022Stochastic Compositional Optimization with Compositional Constraintscited by 4
  3. 2024Developing Lagrangian-based Methods for Nonsmooth Nonconvex Optimizationcited by 2
  4. 2023First-order methods for Stochastic Variational Inequality problems with Function Constraintscited by 0
  5. 2025Simultaneous Learning and Optimization via Misspecified Saddle Point Problemscited by 0