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Multiplicative Weights Update with Constant Step-Size in Congestion Games: Convergence, Limit Cycles and Chaos
Gerasimos Palaiopanos · Ioannis Panageas · Georgios Piliouras

Tue Dec 05 03:40 PM -- 03:45 PM (PST) @ Hall C
in Theory »
The Multiplicative Weights Update (MWU) method is a ubiquitous meta-algorithm that works as follows: A distribution is maintained on a certain set, and at each step the probability assigned to action $\gamma$ is multiplied by $(1 -\epsilon C(\gamma))>0$ where $C(\gamma)$ is the ``cost" of action $\gamma$ and then rescaled to ensure that the new values form a distribution. We analyze MWU in congestion games where agents use \textit{arbitrary admissible constants} as learning rates $\epsilon$ and prove convergence to \textit{exact Nash equilibria}. Interestingly, this convergence result does not carry over to the nearly homologous MWU variant where at each step the probability assigned to action $\gamma$ is multiplied by $(1 -\epsilon)^{C(\gamma)}$ even for the most innocuous case of two-agent, two-strategy load balancing games, where such dynamics can provably lead to limit cycles or even chaotic behavior.

Author Information

Gerasimos Palaiopanos (SUTD)
Ioannis Panageas (Singapore University of Technology and Design)
Georgios Piliouras (Singapore University of Technology and Design)

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