Communication-Efficient Distributed Online Nonconvex Optimization with Time-Varying Constraints

TL;DR

This paper introduces communication-efficient distributed online algorithms for nonconvex optimization with time-varying constraints, achieving sublinear regret and constraint violation bounds in networked settings.

Contribution

It proposes two novel distributed bandit primal-dual algorithms with compressed communication for nonconvex online optimization under dynamic constraints.

Findings

Achieves sublinear network regret bounds.

Reduces cumulative constraint violation under Slater's condition.

Validates theoretical results with simulation experiments.

Abstract

This paper considers distributed online nonconvex optimization with time-varying inequality constraints over a network of agents, where the nonconvex local loss and convex local constraint functions can vary arbitrarily across iterations. For a time-varying directed graph, we propose two distributed bandit online primal--dual algorithm with compressed communication to efficiently utilize communication resources in the one-point and two-point bandit feedback settings, respectively. To measure the performance of the proposed algorithms, we use a network regret metric grounded in the first-order optimality condition associated with the variational inequality. We show that the compressed algorithms establish sublinear network regret and cumulative constraint violation bounds. Moreover, the network cumulative constraint violation bounds are reduced under Slater's condition. Finally, a simulation example is presented to validate the theoretical results.