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arXiv · 2303.00506

Fast and Interpretable Dynamics for Fisher Markets via Block-Coordinate Updates

Tianlong Nan·Yuan Gao·Christian Kroer
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Abstract

We consider the problem of large-scale Fisher market equilibrium computation through scalable first-order optimization methods. It is well-known that market equilibria can be captured using structured convex programs such as the Eisenberg-Gale and Shmyrev convex programs. Highly performant deterministic full-gradient first-order methods have been developed for these programs. In this paper, we develop new block-coordinate first-order methods for computing Fisher market equilibria, and show that these methods have interpretations as t\^atonnement-style or proportional response-style dynamics where either buyers or items show up one at a time. We reformulate these convex programs and solve them using proximal block coordinate descent methods, a class of methods that update only a small number of coordinates of the decision variable in each iteration. Leveraging recent advances in the convergence analysis of these methods and structures of the equilibrium-capturing convex programs, we establish fast convergence rates of these methods.

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Tianlong Nan, Yuan Gao, Christian Kroer. 2023-03-01. Fast and Interpretable Dynamics for Fisher Markets via Block-Coordinate Updates. https://arxiv.org/abs/2303.00506

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