DoCoM: Compressed Decentralized Optimization with Near-Optimal Sample Complexity

Chung-Yiu Yau, Hoi To Wai

Abstract: This paper proposes the Doubly Compressed Momentum-assisted stochastic gradient tracking algorithm (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 DoCoM finds a near-stationary solution at all participating agents satisfying $\mathbb{E}[ \| \nabla f( \theta ) \|^2 ] = {\cal O}( 1 / T^{2/3} )$ 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 DoCoM. As a corollary, our analysis also established the linear convergence of DoCoM to a global optimal solution for objective functions with the Polyak-Łojasiewicz condition. Numerical experiments demonstrate that our algorithm outperforms several state-of-the-art algorithms in practice.

Submission Length: Regular submission (no more than 12 pages of main content)

Video: https://youtu.be/3ZNmkE9ryEs

Code: https://github.com/OscarYau525/docom

Assigned Action Editor: ~Lijun_Zhang1

License: Creative Commons Attribution 4.0 International (CC BY 4.0)

Submission Number: 1173