# An Online Feasible Point Method for Benign Generalized Nash Equilibrium Problems

arXiv: https://arxiv.org/abs/2410.02400 · HTML: https://mlsanity.com/paper/2410.02400/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 31 references that are in the map.
- First posted on arXiv 3 Oct 2024.

## Builds on (most cited first, 9 of 9)

- [Optimization, Learning, and Games with Predictable Sequences](https://mlsanity.com/paper/1311.1869/) (2013)
- [Near-Optimal No-Regret Learning in General Games](https://mlsanity.com/paper/2108.06924/) (2021)
- [Online Convex Optimization with Time-Varying Constraints](https://mlsanity.com/paper/1702.04783/) (2017)
- [Multi-agent online learning in time-varying games](https://mlsanity.com/paper/1809.03066/) (2018)
- [Simultaneously Achieving Sublinear Regret and Constraint Violations for Online Convex Optimization with Time-varying Constraints](https://mlsanity.com/paper/2111.07707/) (2021)
- [First-Order Algorithms for Nonlinear Generalized Nash Equilibrium Problems](https://mlsanity.com/paper/2204.03132/) (2022)
- [Online Learning under Adversarial Nonlinear Constraints](https://mlsanity.com/paper/2306.03655/) (2023)
- [A New Inexact Gradient Descent Method with Applications to Nonsmooth Convex Optimization](https://mlsanity.com/paper/2303.08785/) (2023)
- [Distributed forward-backward (half) forward algorithms for generalized Nash equilibrium seeking](https://mlsanity.com/paper/1910.13903/) (2019)

## Abstract (arXiv)

We consider a repeatedly played generalized Nash equilibrium game. This induces a multi-agent online learning problem with joint constraints. An important challenge in this setting is that the feasible set for each agent depends on the simultaneous moves of the other agents and, therefore, varies over time. As a consequence, the agents face time-varying constraints, which are not adversarial but rather endogenous to the system. Prior work in this setting focused on convergence to a feasible solution in the limit via integrating the constraints in the objective as a penalty function. However, no existing work can guarantee that the constraints are satisfied for all iterations while simultaneously guaranteeing convergence to a generalized Nash equilibrium. This is a problem of fundamental theoretical interest and practical relevance. In this work, we introduce a new online feasible point method. Under the assumption that limited communication between the agents is allowed, this method guarantees feasibility. We identify the class of benign generalized Nash equilibrium problems, for which the convergence of our method to the equilibrium is guaranteed. We set this class of benign generalized Nash equilibrium games in context with existing definitions and illustrate our method with examples.