# Distributed Learning for Stochastic Generalized Nash Equilibrium Problems

arXiv: https://arxiv.org/abs/1608.00039 · HTML: https://mlsanity.com/paper/1608.00039/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2016.

## Built on by (most cited first, 6 of 6)

- [Robust Distributed Optimization With Randomly Corrupted Gradients](https://mlsanity.com/paper/2106.14956/) (2021)
- [Competing Adaptive Networks](https://mlsanity.com/paper/2103.15664/) (2021)
- [Federated Learning Robust to Byzantine Attacks: Achieving Zero Optimality Gap](https://mlsanity.com/paper/2308.10427/) (2023)
- [Online Parameter Identification of Generalized Non-cooperative Game](https://mlsanity.com/paper/2310.09511/) (2023)
- [Diffusion Stochastic Learning Over Adaptive Competing Networks](https://mlsanity.com/paper/2504.19635/) (2025)
- [Input-to-State Stability Framework for Fully Distributed Primal-Dual Dynamics for Quadratic GNEPs Without Multiplier Consensus](https://mlsanity.com/paper/2609.06983/) (2026)

## Abstract (arXiv)

This work examines a stochastic formulation of the generalized Nash equilibrium problem (GNEP) where agents are subject to randomness in the environment of unknown statistical distribution. We focus on fully-distributed online learning by agents and employ penalized individual cost functions to deal with coupled constraints. Three stochastic gradient strategies are developed with constant step-sizes. We allow the agents to use heterogeneous step-sizes and show that the penalty solution is able to approach the Nash equilibrium in a stable manner within O(μmax), for small step-size value μmax and sufficiently large penalty parameters. The operation of the algorithm is illustrated by considering the network Cournot competition problem.