Multi-agent learning under uncertainty: Recurrence vs. concentration

Fuente: arXiv
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Main Authors: Lotidis, Kyriakos, Mertikopoulos, Panayotis, Bambos, Nicholas, Blanchet, Jose
Format: Preprint
Published: 2025
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_version_ 1866912755014959104
author Lotidis, Kyriakos
Mertikopoulos, Panayotis
Bambos, Nicholas
Blanchet, Jose
author_facet Lotidis, Kyriakos
Mertikopoulos, Panayotis
Bambos, Nicholas
Blanchet, Jose
contents In this paper, we examine the convergence landscape of multi-agent learning under uncertainty. Specifically, we analyze two stochastic models of regularized learning in continuous games -- one in continuous and one in discrete time with the aim of characterizing the long-run behavior of the induced sequence of play. In stark contrast to deterministic, full-information models of learning (or models with a vanishing learning rate), we show that the resulting dynamics do not converge in general. In lieu of this, we ask instead which actions are played more often in the long run, and by how much. We show that, in strongly monotone games, the dynamics of regularized learning may wander away from equilibrium infinitely often, but they always return to its vicinity in finite time (which we estimate), and their long-run distribution is sharply concentrated around a neighborhood thereof. We quantify the degree of this concentration, and we show that these favorable properties may all break down if the underlying game is not strongly monotone -- underscoring in this way the limits of regularized learning in the presence of persistent randomness and uncertainty.
format Preprint
id arxiv_https___arxiv_org_abs_2512_08132
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Multi-agent learning under uncertainty: Recurrence vs. concentration
Lotidis, Kyriakos
Mertikopoulos, Panayotis
Bambos, Nicholas
Blanchet, Jose
Computer Science and Game Theory
Machine Learning
Optimization and Control
Primary 91A10, 91A26, secondary 68Q32, 60J60, 60J70
In this paper, we examine the convergence landscape of multi-agent learning under uncertainty. Specifically, we analyze two stochastic models of regularized learning in continuous games -- one in continuous and one in discrete time with the aim of characterizing the long-run behavior of the induced sequence of play. In stark contrast to deterministic, full-information models of learning (or models with a vanishing learning rate), we show that the resulting dynamics do not converge in general. In lieu of this, we ask instead which actions are played more often in the long run, and by how much. We show that, in strongly monotone games, the dynamics of regularized learning may wander away from equilibrium infinitely often, but they always return to its vicinity in finite time (which we estimate), and their long-run distribution is sharply concentrated around a neighborhood thereof. We quantify the degree of this concentration, and we show that these favorable properties may all break down if the underlying game is not strongly monotone -- underscoring in this way the limits of regularized learning in the presence of persistent randomness and uncertainty.
title Multi-agent learning under uncertainty: Recurrence vs. concentration
topic Computer Science and Game Theory
Machine Learning
Optimization and Control
Primary 91A10, 91A26, secondary 68Q32, 60J60, 60J70
url https://arxiv.org/abs/2512.08132