Online decentralized decision making with inequality constraints: an ADMM approach

TL;DR

This paper presents an ADMM-based approach for online decentralized decision making under inequality constraints, analyzing convergence, optimality gaps, and proposing a warm-start scheme to improve efficiency in dynamic multi-agent control scenarios.

Contribution

It introduces a novel online ADMM framework with convergence analysis, optimality gap assessment, and a warm-start scheme for accelerated convergence in dynamic decentralized decision problems.

Findings

ADMM converges under online decision-making constraints.

Warm-start significantly improves convergence speed.

Method effectively applied to multi-agent control with simulation results.

Abstract

We discuss an online decentralized decision making problem where the agents are coupled with affine inequality constraints. Alternating Direction Method of Multipliers (ADMM) is used as the computation engine and we discuss the convergence of the algorithm in an online setting. To be specific, when decisions have to be made sequentially with a fixed time step, there might not be enough time for the ADMM to converge before the scenario changes and the decision needs to be updated. In this case, a suboptimal solution is employed and we analyze the optimality gap given the convergence condition. Moreover, in many cases, the decision making problem changes gradually over time. We propose a warm-start scheme to accelerate the convergence of ADMM and analyze the benefit of the warm-start. The proposed method is demonstrated in a decentralized multiagent control barrier function problem with simulation.