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

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.

arXiv comment13 pages, 8 figures

References in corpus (7)

• Constrained Consensus
• A linear algorithm for optimization over directed graphs with geometric convergence
• Online Distributed Optimization on Dynamic Networks
• An Optimal Algorithm for Bandit and Zero-Order Convex Optimization with Two-Point Feedback
• An Exact Quantized Decentralized Gradient Descent Algorithm
• Privacy-Preserving Distributed Optimization via Subspace Perturbation: A General Framework
• Convergence Rates of Distributed Nesterov-like Gradient Methods on Random Networks

Cited by in corpus (1)

• Online Convex Optimization Using Coordinate Descent Algorithms