Fast and Interpretable Dynamics for Fisher Markets via Block-Coordinate Updates
Keywords:GTEP: Equilibrium, GTEP: Fair Division, MAS: Agent/AI Theories and Architectures
AbstractWe 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 tâtonnement-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.
How to Cite
Nan, T., Gao, Y., & Kroer, C. (2023). Fast and Interpretable Dynamics for Fisher Markets via Block-Coordinate Updates. Proceedings of the AAAI Conference on Artificial Intelligence, 37(5), 5832-5840. https://doi.org/10.1609/aaai.v37i5.25723
AAAI Technical Track on Game Theory and Economic Paradigms