Distributed Event-Triggered Bandit Convex Optimization with Time-Varying Constraints

TL;DR

This paper introduces a distributed event-triggered bandit convex optimization algorithm for networks with time-varying constraints, reducing communication while maintaining competitive regret and constraint violation bounds.

Contribution

It proposes a novel distributed event-triggered primal-dual algorithm with two-point bandit feedback for constrained online optimization in networks.

Findings

Achieves regret and constraint violation bounds comparable to full-information algorithms.

Reduces communication by using event-triggered updates.

Validates theoretical results with numerical experiments.

Abstract

This paper considers the distributed bandit convex optimization problem with time-varying inequality constraints over a network of agents, where the goal is to minimize network regret and cumulative constraint violation. Existing distributed online algorithms require that each agent broadcasts its decision to its neighbors at each iteration. To better utilize the limited communication resources, we propose a distributed event-triggered online primal--dual algorithm with two-point bandit feedback. Under several classes of appropriately chosen decreasing parameter sequences and non-increasing event-triggered threshold sequences, we establish dynamic network regret and network cumulative constraint violation bounds. These bounds are comparable to the results achieved by distributed event-triggered online algorithms with full-information feedback. Finally, a numerical example is provided to verify the theoretical results.