English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The Multiplicative Weights Update (MWU) method is a ubiquitous meta-algorithmthat works as follows: A distribution is maintained on a certain set, and ateach step the probability assigned to element $\gamma$ is multiplied by $(1-\epsilon C(\gamma))>0$ where $C(\gamma)$ is the "cost" of element $\gamma$ andthen rescaled to ensure that the new values form a distribution. We analyze MWUin congestion games where agents use \textit{arbitrary admissible constants} aslearning rates $\epsilon$ and prove convergence to \textit{exact Nashequilibria}. Our proof leverages a novel connection between MWU and theBaum-Welch algorithm, the standard instantiation of theExpectation-Maximization (EM) algorithm for hidden Markov models (HMM).Interestingly, this convergence result does not carry over to the nearlyhomologous MWU variant where at each step the probability assigned to element$\gamma$ is multiplied by $(1 -\epsilon)^{C(\gamma)}$ even for the mostinnocuous case of two-agent, two-strategy load balancing games, where suchdynamics can provably lead to limit cycles or even chaotic behavior.

Multiplicative Weights Update with Constant Step-Size in Congestion Games: Convergence, Limit Cycles and Chaos