DoCoM: Compressed Decentralized Optimization with Near-Optimal Sample Complexity

• URL: http://arxiv.org/abs/2202.00255v2
• Date: Mon, 31 Jul 2023 04:34:34 GMT
• Title: DoCoM: Compressed Decentralized Optimization with Near-Optimal Sample Complexity
• Authors: Chung-Yiu Yau, Hoi-To Wai
• Abstract summary: This paper proposes the Doubly Compressed Momentum-assisted tracking algorithm $ttDoCoM$ for communication. We show that our algorithm outperforms several state-of-the-art algorithms in practice.
• Score: 25.775517797956237
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper proposes the Doubly Compressed Momentum-assisted stochastic gradient tracking algorithm $\texttt{DoCoM}$ for communication-efficient decentralized optimization. The algorithm features two main ingredients to achieve a near-optimal sample complexity while allowing for communication compression. First, the algorithm tracks both the averaged iterate and stochastic gradient using compressed gossiping consensus. Second, a momentum step is incorporated for adaptive variance reduction with the local gradient estimates. We show that $\texttt{DoCoM}$ finds a near-stationary solution at all participating agents satisfying $\mathbb{E}[ \| \nabla f( \theta ) \|^2 ] = \mathcal{O}( 1 / T^{2/3} )$ in $T$ iterations, where $f(\theta)$ is a smooth (possibly non-convex) objective function. Notice that the proof is achieved via analytically designing a new potential function that tightly tracks the one-iteration progress of $\texttt{DoCoM}$. As a corollary, our analysis also established the linear convergence of $\texttt{DoCoM}$ to a global optimal solution for objective functions with the Polyak-{\L}ojasiewicz condition. Numerical experiments demonstrate that our algorithm outperforms several state-of-the-art algorithms in practice.

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