Optimization with Zeroth-Order Oracles in Formation

TL;DR

This paper introduces a novel zeroth-order optimization method for multi-agent systems that estimates gradients using only neighbor information, ensuring convergence and collision avoidance.

Contribution

It proposes a new gradient estimation technique coupled with formation control for agents without gradient access, with proven convergence under certain conditions.

Findings

Algorithm converges for functions satisfying Polyak-Lojasiewicz inequality.

Simulation results validate theoretical convergence and collision avoidance.

Method effectively estimates gradients using only local neighbor information.

Abstract

In this paper, we consider the optimisation of time varying functions by a network of agents with no gradient information. The proposed a novel method to estimate the gradient at each agent's position using only neighbour information. The gradient estimation is coupled with a formation controller, to minimise gradient estimation error and prevent agent collisions. Convergence results for the algorithm are provided for functions which satisfy the Polyak-Lojasiewicz inequality. Simulations and numerical results are provided to support the theoretical results.