2023/03/01 by Nan, Tianlong, Gao, Yuan, Kroer, Christian · 1 citation
#Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Multiagent Systems (cs.MA) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2303.00506
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 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.