Distributed Online Optimization with Coupled Inequality Constraints over Unbalanced Directed Networks

TL;DR

This paper introduces DUST, a distributed dual subgradient tracking algorithm for online convex optimization over unbalanced directed networks, achieving sublinear regret and constraint violations with improved bounds under Slater's condition.

Contribution

It presents a novel algorithm that handles unbalanced directed networks in distributed online optimization, allowing for coupled inequality constraints and improving convergence bounds.

Findings

DUST achieves sublinear dynamic regret and constraint violations.

Under Slater's condition, DUST has smaller constraint violation bounds.

Simulations demonstrate DUST's superior convergence in electric vehicle charging problems.

Abstract

This paper studies a distributed online convex optimization problem, where agents in an unbalanced network cooperatively minimize the sum of their time-varying local cost functions subject to a coupled inequality constraint. To solve this problem, we propose a distributed dual subgradient tracking algorithm, called DUST, which attempts to optimize a dual objective by means of tracking the primal constraint violations and integrating dual subgradient and push sum techniques. Different from most existing works, we allow the underlying network to be unbalanced with a column stochastic mixing matrix. We show that DUST achieves sublinear dynamic regret and constraint violations, provided that the accumulated variation of the optimal sequence grows sublinearly. If the standard Slater's condition is additionally imposed, DUST acquires a smaller constraint violation bound than the alternative existing methods applicable to unbalanced networks. Simulations on a plug-in electric vehicle charging problem demonstrate the superior convergence of DUST.