Distributed Online Optimization in Time-Varying Unbalanced Networks without Explicit Subgradients

TL;DR

This paper introduces a novel distributed online optimization algorithm for time-varying unbalanced networks that uses a zeroth-order oracle and achieves sublinear regret without relying on explicit subgradients.

Contribution

It proposes a new consensus-based distributed online algorithm with a local randomized zeroth-order oracle and a rescaling technique for unbalanced digraphs, extending existing methods.

Findings

Achieves sublinear average dynamic regret under mild conditions.

Demonstrates effectiveness through simulations on sensor network problems.

Shows convergence is unaffected by the use of a zeroth-order oracle.

Abstract

This paper studies a distributed online constrained optimization problem over time-varying unbalanced digraphs without explicit subgradients. In sharp contrast to the existing algorithms, we design a novel consensus-based distributed online algorithm with a local randomized zeroth-order oracle and then rescale the oracle by constructing row-stochastic matrices, which aims to address the unbalancedness of time-varying digraphs. Under mild conditions, the average dynamic regret over a time horizon is shown to asymptotically converge at a sublinear rate provided that the accumulated variation grows sublinearly with a specific order. Moreover, the counterpart of the proposed algorithm when subgradients are available is also provided, along with its dynamic regret bound, which reflects that the convergence of our algorithm is essentially not affected by the zeroth-order oracle. Simulations on distributed targets tracking problem and dynamic sparse signal recovery problem in sensor networks are employed to demonstrate the effectiveness of the proposed algorithm.