Papers › DoCoM: Compressed Decentralized Optimization with Near-Optimal Sample Complexity
DoCoM: Compressed Decentralized Optimization with Near-Optimal Sample Complexity
Chung-Yiu Yau, Hoi-To Wai
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 𝔼[ ∇f( θ) ² ] = 𝒪( 1 / T^(2/3) ) in T iterations, where f(θ) 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-{\L}ojasiewicz condition. Numerical experiments demonstrate that our algorithm outperforms several state-of-the-art algorithms in practice.
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