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Convergence Analysis of Gradient-Based Learning with Non-Uniform Learning Rates in Non-Cooperative Multi-Agent Settings

Chasnov, Benjamin and Ratliff, Lillian J. and Mazumdar, Eric and Burden, Samuel A. (2019) Convergence Analysis of Gradient-Based Learning with Non-Uniform Learning Rates in Non-Cooperative Multi-Agent Settings. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210903-213656891

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Abstract

Considering a class of gradient-based multi-agent learning algorithms in non-cooperative settings, we provide local convergence guarantees to a neighborhood of a stable local Nash equilibrium. In particular, we consider continuous games where agents learn in (i) deterministic settings with oracle access to their gradient and (ii) stochastic settings with an unbiased estimator of their gradient. Utilizing the minimum and maximum singular values of the game Jacobian, we provide finite-time convergence guarantees in the deterministic case. On the other hand, in the stochastic case, we provide concentration bounds guaranteeing that with high probability agents will converge to a neighborhood of a stable local Nash equilibrium in finite time. Different than other works in this vein, we also study the effects of non-uniform learning rates on the learning dynamics and convergence rates. We find that much like preconditioning in optimization, non-uniform learning rates cause a distortion in the vector field which can, in turn, change the rate of convergence and the shape of the region of attraction. The analysis is supported by numerical examples that illustrate different aspects of the theory. We conclude with discussion of the results and open questions.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1906.00731arXivDiscussion Paper
ORCID:
AuthorORCID
Chasnov, Benjamin0000-0003-3484-2997
Ratliff, Lillian J.0000-0001-8936-0229
Mazumdar, Eric0000-0002-1815-269X
Record Number:CaltechAUTHORS:20210903-213656891
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210903-213656891
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110720
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:07 Sep 2021 16:25
Last Modified:07 Sep 2021 19:24

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