# Accelerating Distributed Stochastic Optimization via Self-Repellent Random Walks

arXiv: https://arxiv.org/abs/2401.09665 · HTML: https://mlsanity.com/paper/2401.09665/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 72 references that are in the map.
- First posted on arXiv 18 Jan 2024.

## Builds on (most cited first, 30 of 36)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [How to Escape Saddle Points Efficiently](https://mlsanity.com/paper/1703.00887/) (2017)
- [Minimizing Finite Sums with the Stochastic Average Gradient](https://mlsanity.com/paper/1309.2388/) (2013)
- [Better Theory for SGD in the Nonconvex World](https://mlsanity.com/paper/2002.03329/) (2020)
- [A Two-Timescale Framework for Bilevel Optimization: Complexity Analysis and Application to Actor-Critic](https://mlsanity.com/paper/2007.05170/) (2020)
- [On Linear Stochastic Approximation: Fine-grained Polyak-Ruppert and Non-Asymptotic Concentration](https://mlsanity.com/paper/2004.04719/) (2020)
- [MATCHA: Speeding Up Decentralized SGD via Matching Decomposition Sampling](https://mlsanity.com/paper/1905.09435/) (2019)
- [Finite-Sample Analysis of Nonlinear Stochastic Approximation with Applications in Reinforcement Learning](https://mlsanity.com/paper/1905.11425/) (2019)
- [Accelerated Gradient Descent Escapes Saddle Points Faster than Gradient Descent](https://mlsanity.com/paper/1711.10456/) (2017)
- [On Markov Chain Gradient Descent](https://mlsanity.com/paper/1809.04216/) (2018)
- [Convergence and Dynamical Behavior of the ADAM Algorithm for Non-Convex Stochastic Optimization](https://mlsanity.com/paper/1810.02263/) (2018)
- [Non-asymptotic Analysis of Biased Stochastic Approximation Scheme](https://mlsanity.com/paper/1902.00629/) (2019)
- [Stochastic Heavy Ball](https://mlsanity.com/paper/1609.04228/) (2016)
- [State Dependent Performative Prediction with Stochastic Approximation](https://mlsanity.com/paper/2110.00800/) (2021)
- [RelaySum for Decentralized Deep Learning on Heterogeneous Data](https://mlsanity.com/paper/2110.04175/) (2021)
- [Stochastic Gradient Descent under Markovian Sampling Schemes](https://mlsanity.com/paper/2302.14428/) (2023)
- [A Two-Time-Scale Stochastic Optimization Framework with Applications in Control and Reinforcement Learning](https://mlsanity.com/paper/2109.14756/) (2021)
- [Online Statistical Inference for Nonlinear Stochastic Approximation with Markovian Data](https://mlsanity.com/paper/2302.07690/) (2023)
- [Finite-Sample Analysis of Stochastic Approximation Using Smooth Convex Envelopes](https://mlsanity.com/paper/2002.00874/) (2020)
- [Explicit Mean-Square Error Bounds for Monte-Carlo and Linear Stochastic Approximation](https://mlsanity.com/paper/2002.02584/) (2020)
- [A principled framework for the design and analysis of token algorithms](https://mlsanity.com/paper/2205.15015/) (2022)
- [On the Convergence of Decentralized Federated Learning Under Imperfect Information Sharing](https://mlsanity.com/paper/2303.10695/) (2023)
- [Convergence Rates of Accelerated Markov Gradient Descent with Applications in Reinforcement Learning](https://mlsanity.com/paper/2002.02873/) (2020)
- [Private Weighted Random Walk Stochastic Gradient Descent](https://mlsanity.com/paper/2009.01790/) (2020)
- [Q-learning with Uniformly Bounded Variance: Large Discounting is Not a Barrier to Fast Learning](https://mlsanity.com/paper/2002.10301/) (2020)
- [Stochastic optimization with momentum: convergence, fluctuations, and traps avoidance](https://mlsanity.com/paper/2012.04002/) (2020)
- [Finite-Time Convergence Rates of Nonlinear Two-Time-Scale Stochastic Approximation under Markovian Noise](https://mlsanity.com/paper/2104.01627/) (2021)

## Built on by (most cited first, 2 of 2)

- [Does Worst-Performing Agent Lead the Pack? Analyzing Agent Dynamics in Unified Distributed SGD](https://mlsanity.com/paper/2409.17499/) (2024)
- [Beyond Self-Repellent Kernels: History-Driven Target Towards Efficient Nonlinear MCMC on General Graphs](https://mlsanity.com/paper/2505.18300/) (2025)

## Abstract (arXiv)

We study a family of distributed stochastic optimization algorithms where gradients are sampled by a token traversing a network of agents in random-walk fashion. Typically, these random-walks are chosen to be Markov chains that asymptotically sample from a desired target distribution, and play a critical role in the convergence of the optimization iterates. In this paper, we take a novel approach by replacing the standard linear Markovian token by one which follows a nonlinear Markov chain - namely the Self-Repellent Radom Walk (SRRW). Defined for any given 'base' Markov chain, the SRRW, parameterized by a positive scalar α, is less likely to transition to states that were highly visited in the past, thus the name. In the context of MCMC sampling on a graph, a recent breakthrough in Doshi et al. (2023) shows that the SRRW achieves O(1/α) decrease in the asymptotic variance for sampling. We propose the use of a 'generalized' version of the SRRW to drive token algorithms for distributed stochastic optimization in the form of stochastic approximation, termed SA-SRRW. We prove that the optimization iterate errors of the resulting SA-SRRW converge to zero almost surely and prove a central limit theorem, deriving the explicit form of the resulting asymptotic covariance matrix corresponding to iterate errors. This asymptotic covariance is always smaller than that of an algorithm driven by the base Markov chain and decreases at rate O(1/α2) - the performance benefit of using SRRW thereby amplified in the stochastic optimization context. Empirical results support our theoretical findings.