arXiv subjects

Riccardo Brumali

Publications and source records attributed to Riccardo Brumali.

3 recordsLinked to original sources

arXiv2026

A Distributed Bilevel Framework for the Macroscopic Optimization of Multi-Agent Systems

In this paper, we propose a novel distributed algorithm to optimize the emergent macroscopic behavior of large-scale multi-agent systems via microscopic actions. We cast this task as a bilevel optimization problem, where the upper level formalizes the desired macroscopic target behavior through a suitable performance criterion, which is shaped in the lower level by leveraging a compressed aggregate representation estimating the macroscopic state. More precisely, the macroscopic state is parametrized by an exponential-family of distributions and constructed from the multi-agent microscopic configuration. The proposed algorithm integrates a distributed estimation mechanism, through which each agent reconstructs the macroscopic state locally, with a hypergradient-based update of the microscopic states aimed at improving the collective macroscopic behavior. We prove convergence to the set of stationary points of the bilevel problem via timescale separation arguments. Numerical simulations validate the effectiveness of the proposed method.

math.OC↗

arXiv2026

Model-Free Aggregative Cooperative Optimization via Randomized Gradient-Free Minimization and Exploration Momentum

Aggregative cooperative optimization problems arise in distributed decision-making settings where each agent's objective depends on its own decision as well as on an aggregate variable capturing global system behavior. Motivated by practical scenarios where gradient information is unavailable, this paper introduces a randomized gradient-free algorithm, named ARGFree, for solving such problems. ARGFree combines finite-difference gradient approximations with a set of tracking variables, emulating the behavior of a gradient-based method. We prove that ARGFree converges in expectation to an approximate optimizer, with the approximation error stemming from the use of a randomized gradient estimator. To enhance performance in high-dimensional settings, we further propose an improved variant, ARGFree-EM, which incorporates momentum in the exploration signals to smooth sudden fluctuations in the gradient exploration signals and thereby improve the accuracy of the underlying distributed tracking mechanism. To the best of our knowledge, the class of ARGFree methods is the first in the literature capable of solving aggregating cooperative optimization problems without gradient information.

math.OC↗

arXiv2025

Data-Driven Distributed Optimization via Aggregative Tracking and Deep-Learning

In this paper, we propose a novel distributed data-driven optimization scheme. In detail, we focus on the so-called aggregative framework, a scenario in which a set of agents aim to cooperatively minimize the sum of local costs, each depending on both local decision variables and an aggregation of all of them. We consider a data-driven setup where each objective function is unknown and can be sampled at a single point per iteration (thanks to, e.g., feedback from users or sensors). We address this scenario through a distributed algorithm combining three components: (i) a learning part leveraging neural networks to learn the local costs descent direction, (ii) an optimization routine steering the estimates according to the learned direction to minimize the global cost, and (iii) a tracking mechanism locally reconstructing the unavailable global quantities. Using tools from system theory, i.e., timescale separation and averaging theory, we formally prove that in strongly convex setups, the distributed scheme linearly converges to a neighborhood of the optimum, whose radius depends on the accuracy of the neural networks. Finally, numerical simulations validate the theoretical results.

math.OC↗