# Distributed stochastic optimization via matrix exponential learning

arXiv: https://arxiv.org/abs/1606.01190 · HTML: https://mlsanity.com/paper/1606.01190/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2016.

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

- [Doubly Optimal No-Regret Online Learning in Strongly Monotone Games with Bandit Feedback](https://mlsanity.com/paper/2112.02856/) (2021)
- [Robust Distributed Optimization With Randomly Corrupted Gradients](https://mlsanity.com/paper/2106.14956/) (2021)
- [Exploiting hidden structures in non-convex games for convergence to Nash equilibrium](https://mlsanity.com/paper/2312.16609/) (2023)
- [Payoff-based learning with matrix multiplicative weights in quantum games](https://mlsanity.com/paper/2311.02423/) (2023)
- [Multi-agent learning under uncertainty: Recurrence vs. concentration](https://mlsanity.com/paper/2512.08132/) (2025)
- [Guiding Agents of Quantum Games to Equilibrium using Matrix Exponential Fixed-Point Iteration](https://mlsanity.com/paper/2609.21944/) (2026)

## Abstract (arXiv)

In this paper, we investigate a distributed learning scheme for a broad class of stochastic optimization problems and games that arise in signal processing and wireless communications. The proposed algorithm relies on the method of matrix exponential learning (MXL) and only requires locally computable gradient observations that are possibly imperfect and/or obsolete. To analyze it, we introduce the notion of a stable Nash equilibrium and we show that the algorithm is globally convergent to such equilibria - or locally convergent when an equilibrium is only locally stable. We also derive an explicit linear bound for the algorithm's convergence speed, which remains valid under measurement errors and uncertainty of arbitrarily high variance. To validate our theoretical analysis, we test the algorithm in realistic multi-carrier/multiple-antenna wireless scenarios where several users seek to maximize their energy efficiency. Our results show that learning allows users to attain a net increase between 100% and 500% in energy efficiency, even under very high uncertainty.