Decentralized Online Convex Optimization in Networked Systems

TL;DR

This paper introduces a novel decentralized predictive control algorithm for networked online convex optimization, providing near-optimal competitive ratio bounds that account for temporal and spatial interactions among agents.

Contribution

The work presents the first competitive ratio bound for decentralized predictive control in networked online convex optimization, extending predictive control to multi-agent systems with provable guarantees.

Findings

LPC achieves a competitive ratio of 1 + O( ho_T^k) + O( ho_S^r) in adversarial settings.

The dependence on prediction horizon k and neighborhood r is near optimal.

This is the first bound of its kind for decentralized online convex optimization with predictive control.

Abstract

We study the problem of networked online convex optimization, where each agent individually decides on an action at every time step and agents cooperatively seek to minimize the total global cost over a finite horizon. The global cost is made up of three types of local costs: convex node costs, temporal interaction costs, and spatial interaction costs. In deciding their individual action at each time, an agent has access to predictions of local cost functions for the next $k$ time steps in an $r$-hop neighborhood. Our work proposes a novel online algorithm, Localized Predictive Control (LPC), which generalizes predictive control to multi-agent systems. We show that LPC achieves a competitive ratio of $1 + \tilde{O}(\rho_T^k) + \tilde{O}(\rho_S^r)$ in an adversarial setting, where $\rho_T$ and $\rho_S$ are constants in $(0, 1)$ that increase with the relative strength of temporal and spatial interaction costs, respectively. This is the first competitive ratio bound on decentralized predictive control for networked online convex optimization. Further, we show that the dependence on $k$ and $r$ in our results is near optimal by lower bounding the competitive ratio of any decentralized online algorithm.