# Finite-Time Performance of Distributed Two-Time-Scale Stochastic Approximation

arXiv: https://arxiv.org/abs/1912.10155 · HTML: https://mlsanity.com/paper/1912.10155/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2019.

## Built on by (most cited first, 3 of 3)

- [A Two-Time-Scale Stochastic Optimization Framework with Applications in Control and Reinforcement Learning](https://mlsanity.com/paper/2109.14756/) (2021)
- [Stochastic Optimization Algorithms for Instrumental Variable Regression with Streaming Data](https://mlsanity.com/paper/2405.19463/) (2024)
- [Finite-Time Analysis of Projected Two-Time-Scale Stochastic Approximation](https://mlsanity.com/paper/2604.00179/) (2026)

## Abstract (arXiv)

Two-time-scale stochastic approximation is a popular iterative method for finding the solution of a system of two equations. Such methods have found broad applications in many areas, especially in machine learning and reinforcement learning. In this paper, we propose a distributed variant of this method over a network of agents, where the agents use two graphs representing their communication at different speeds due to the nature of their two-time-scale updates. Our main contribution is to provide a finite-time analysis for the performance of the proposed method. In particular, we establish an upper bound for the convergence rates of the mean square errors at the agents to zero as a function of the step sizes and the network topology.