# Decentralized Optimal Equilibrium Learning Over Dynamic Networks

arXiv: https://arxiv.org/abs/2609.17601 · HTML: https://mlsanity.com/paper/2609.17601/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 17 references that are in the map.
- First posted on arXiv 13 Sep 2026.

## Builds on (most cited first, 10 of 10)

- [Fully Decentralized Multi-Agent Reinforcement Learning with Networked Agents](https://mlsanity.com/paper/1802.08757/) (2018)
- [Distributed optimization over time-varying directed graphs](https://mlsanity.com/paper/1303.2289/) (2013)
- [Pareto Actor-Critic for Equilibrium Selection in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2209.14344/) (2022)
- [Decentralized Learning for Optimality in Stochastic Dynamic Teams and Games with Local Control and Global State Information](https://mlsanity.com/paper/1903.05812/) (2019)
- [Distributed Discrete-time Optimization in Multi-agent Networks Using only Sign of Relative State](https://mlsanity.com/paper/1709.08360/) (2017)
- [Single Bit and Reduced Dimension Diffusion Strategies Over Distributed Networks](https://mlsanity.com/paper/1306.1665/) (2013)
- [Distributed State Estimation over Time-Varying Graphs: Exploiting the Age-of-Information](https://mlsanity.com/paper/2001.07006/) (2020)
- [Logit-Q Dynamics for Efficient Learning in Stochastic Teams](https://mlsanity.com/paper/2302.09806/) (2023)
- [Learning with Episodic Hypothesis Testing in General Games: A Framework for Equilibrium Selection](https://mlsanity.com/paper/2507.23149/) (2025)
- [Achieving Pareto Optimality in Games via Single-bit Feedback](https://mlsanity.com/paper/2509.25921/) (2025)

## Abstract (arXiv)

This paper studies decentralized learning of socially optimal equilibria in finite normal-form games over dynamic communication networks. Each agent observes only its own realized payoffs, does not know the game a priori, and can communicate only with time-varying neighbors using low-bandwidth messages. We propose networked decentralized optimal equilibrium learning dynamics in which agents generate randomized semantic content/discontent signals from local payoff comparisons and exchange time-stamped time-stacked tables rather than raw actions, payoff information or local estimates/parameters. The method combines table fusion with temporal majority reconstruction to mitigate dynamic communication while preserving fully decentralized operation. We establish finite-time logarithmic regret guarantees, with an in-phase exploration perturbation, for optimal equilibrium selection under utilitarian and proportional-fair social welfare objectives. Simulation results further show that the proposed approach can effectively select socially desirable equilibria over dynamic communication networks.