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

arXiv: https://arxiv.org/abs/2303.00506 · HTML: https://mlsanity.com/paper/2303.00506/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2023.

## Built on by (most cited first, 1 of 1)

- [Large-Scale Contextual Market Equilibrium Computation through Deep Learning](https://mlsanity.com/paper/2406.15459/) (2024)

## Abstract (arXiv)

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 tatonnement-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.