Optimization and Learning in Open Multi-Agent Systems

Diego Deplano

First

;Nicola Bastianello;Mauro Franceschelli;Karl H. Johansson

2026-01-01

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Abstract

Modern artificial intelligence relies on networks of agents that collect data, process information, and exchange it with neighbors to collaboratively solve optimization and learning problems. This article introduces a novel distributed algorithm to address a broad class of these problems in open networks, where the number of participating agents may vary due to several factors, such as autonomous decisions, heterogeneous resource availability, or DoS attacks. Extending the current literature, the convergence analysis of the proposed algorithm is based on the newly developed Theory of Open Operators, which characterizes an operator as open when the set of components to be updated changes over time, yielding time-varying operators acting on sequences of points of different dimensions and compositions. The mathematical tools and convergence results developed here provide a general framework for evaluating distributed algorithms in open networks, enabling characterization of their performance in terms of the punctual distance to the optimal solution, in contrast with regret-based metrics that assess cumulative performance over a finite-time horizon. As illustrative examples, the proposed algorithm is used to solve dynamic consensus and tracking problems on different metrics, such as average, median, and min/max, as well as classification problems with logistic loss functions.