# Improved Convergence Rate for a Distributed Two-Time-Scale Gradient Method under Random Quantization

arXiv: https://arxiv.org/abs/2105.14089 · HTML: https://mlsanity.com/paper/2105.14089/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2021.

## Built on by (most cited first, 5 of 5)

- [On the Convergence of Decentralized Federated Learning Under Imperfect Information Sharing](https://mlsanity.com/paper/2303.10695/) (2023)
- [Convergence Rates of Two-Time-Scale Gradient Descent-Ascent Dynamics for Solving Nonconvex Min-Max Problems](https://mlsanity.com/paper/2112.09579/) (2021)
- [Fast Nonlinear Two-Time-Scale Stochastic Approximation: Achieving O(1/k) Finite-Sample Complexity](https://mlsanity.com/paper/2401.12764/) (2024)
- [FedNMUT -- Federated Noisy Model Update Tracking Convergence Analysis](https://mlsanity.com/paper/2403.13247/) (2024)
- [Fast networked data selection via distributed smoothed quantile estimation](https://mlsanity.com/paper/2406.01929/) (2024)

## Abstract (arXiv)

We study the so-called distributed two-time-scale gradient method for solving convex optimization problems over a network of agents when the communication bandwidth between the nodes is limited, and so information that is exchanged between the nodes must be quantized. Our main contribution is to provide a novel analysis, resulting to an improved convergence rate of this method as compared to the existing works. In particular, we show that the method converges at a rate O(log2 k/√ k) to the optimal solution, when the underlying objective function is strongly convex and smooth. The key technique in our analysis is to consider a Lyapunov function that simultaneously captures the coupling of the consensus and optimality errors generated by the method.