# Diffusion Stochastic Learning Over Adaptive Competing Networks

arXiv: https://arxiv.org/abs/2504.19635 · HTML: https://mlsanity.com/paper/2504.19635/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 58 references that are in the map.
- First posted on arXiv 28 Apr 2025.

## Builds on (most cited first, 25 of 25)

- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [Human-level performance in first-person multiplayer games with population-based deep reinforcement learning](https://mlsanity.com/paper/1807.01281/) (2018)
- [Faster Single-loop Algorithms for Minimax Optimization without Strong Concavity](https://mlsanity.com/paper/2112.05604/) (2021)
- [Decentralized Local Stochastic Extra-Gradient for Variational Inequalities](https://mlsanity.com/paper/2106.08315/) (2021)
- [Distributed Learning in Non-Convex Environments -- Part I: Agreement at a Linear Rate](https://mlsanity.com/paper/1907.01848/) (2019)
- [A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis](https://mlsanity.com/paper/1712.08277/) (2017)
- [Distributed Nash Equilibrium Seeking by A Consensus Based Approach](https://mlsanity.com/paper/1602.00771/) (2016)
- [Social Learning over Weakly-Connected Graphs](https://mlsanity.com/paper/1609.03703/) (2016)
- [Geometric Convergence of Gradient Play Algorithms for Distributed Nash Equilibrium Seeking](https://mlsanity.com/paper/1809.07383/) (2018)
- [Distributed Learning for Stochastic Generalized Nash Equilibrium Problems](https://mlsanity.com/paper/1608.00039/) (2016)
- [Information Exchange and Learning Dynamics over Weakly-Connected Adaptive Networks](https://mlsanity.com/paper/1412.1523/) (2014)
- [A Passivity-Based Approach to Nash Equilibrium Seeking over Networks](https://mlsanity.com/paper/1705.02424/) (2017)
- [Distributed Algorithms for Aggregative Games on Graphs](https://mlsanity.com/paper/1605.00267/) (2016)
- [Distributed generalized Nash equilibrium seeking in aggregative games on time-varying networks](https://mlsanity.com/paper/1907.00191/) (2019)
- [On the linear convergence of distributed Nash equilibrium seeking for multi-cluster games under partial-decision information](https://mlsanity.com/paper/2005.06923/) (2020)
- [Nash Equilibrium Computation in Subnetwork Zero-Sum Games with Switching Communications](https://mlsanity.com/paper/1312.7050/) (2013)
- [Game Design and Analysis for Price based Demand Response: An Aggregate Game Approach](https://mlsanity.com/paper/1508.02636/) (2015)
- [A Distributed Nash Equilibrium Seeking in Networked Graphical Games](https://mlsanity.com/paper/1703.09765/) (2017)
- [Diffusion Stochastic Optimization for Min-Max Problems](https://mlsanity.com/paper/2401.14585/) (2024)
- [Accelerated Stochastic Min-Max Optimization Based on Bias-corrected Momentum](https://mlsanity.com/paper/2406.13041/) (2024)
- [A Unified Strategy for Solution Seeking in Graphical N-coalition Noncooperative Games](https://mlsanity.com/paper/1708.02394/) (2017)
- [Competing Adaptive Networks](https://mlsanity.com/paper/2103.15664/) (2021)
- [Distributed Nash Equilibrium Seeking in Consistency-Constrained Multi-Coalition Games](https://mlsanity.com/paper/2106.10513/) (2021)
- [No-regret distributed learning in subnetwork zero-sum games](https://mlsanity.com/paper/2108.02144/) (2021)
- [Generalized Multi-cluster Game under Partial-decision Information with Applications to Management of Energy Internet](https://mlsanity.com/paper/2205.12027/) (2022)

## Abstract (arXiv)

This paper studies a stochastic dynamic game between two competing teams, each consisting of a network of collaborating agents. Unlike fully cooperative settings, where all agents share a common objective, each team in this game aims to minimize its own distinct objective. In the adversarial setting, their objectives could be conflicting as in zero-sum games. Throughout the competition, agents share strategic information within their own team while simultaneously inferring and adapting to the strategies of the opposing team. We propose diffusion learning algorithms to address two important classes of this network game: i) a zero-sum game characterized by weak cross-team subgraph interactions, and ii) a general non-zero-sum game exhibiting strong cross-team subgraph interactions. We analyze the stability performance of the proposed algorithms under reasonable assumptions and illustrate the theoretical results through experiments on Cournot team competition and decentralized GAN training.