DoCoM: Compressed Decentralized Optimization with Near-Optimal Sample Complexity
This work addresses communication bottlenecks in decentralized optimization for distributed machine learning systems, offering a novel method with strong theoretical guarantees and practical improvements.
The paper tackles the problem of communication-efficient decentralized optimization by proposing DoCoM, a doubly compressed momentum-assisted stochastic gradient tracking algorithm, which achieves a near-stationary solution with a sample complexity of O(1/T^{2/3}) and demonstrates superior performance in numerical experiments compared to state-of-the-art methods.
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 $\mathbb{E}[ \| \nabla f( θ) \|^2 ] = \mathcal{O}( 1 / T^{2/3} )$ 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 $\texttt{DoCoM}$. As a corollary, our analysis also established the linear convergence of $\texttt{DoCoM}$ to a global optimal solution for objective functions with the Polyak-Łojasiewicz condition. Numerical experiments demonstrate that our algorithm outperforms several state-of-the-art algorithms in practice.