The Entrapment Problem in Random Walk Decentralized Learning

TL;DR

This paper addresses the entrapment problem in random walk-based decentralized learning by proposing the MHLJ algorithm, which introduces jumps to improve convergence speed and overcome node entrapment.

Contribution

We introduce the MHLJ algorithm that enhances decentralized SGD by incorporating Lévy jumps, overcoming entrapment issues caused by the Metropolis-Hastings method.

Findings

MHLJ accelerates convergence compared to traditional MH-based methods.

Theoretical analysis confirms the convergence rate and error bounds of MHLJ.

Numerical experiments demonstrate improved performance and robustness of MHLJ.

Abstract

This paper explores decentralized learning in a graph-based setting, where data is distributed across nodes. We investigate a decentralized SGD algorithm that utilizes a random walk to update a global model based on local data. Our focus is on designing the transition probability matrix to speed up convergence. While importance sampling can enhance centralized learning, its decentralized counterpart, using the Metropolis-Hastings (MH) algorithm, can lead to the entrapment problem, where the random walk becomes stuck at certain nodes, slowing convergence. To address this, we propose the Metropolis-Hastings with L\'evy Jumps (MHLJ) algorithm, which incorporates random perturbations (jumps) to overcome entrapment. We theoretically establish the convergence rate and error gap of MHLJ and validate our findings through numerical experiments.