Optimization and Learning in Open Multi-Agent Systems

2025-01-28

AI Summary

Distributed learning and optimization in open multi-agent systems face significant challenges due to dynamic node arrivals/departures, network uncertainty, and heterogeneous resource constraints. Method: This paper proposes a novel distributed optimization framework grounded in “open operator theory.” It introduces the first convergence analysis framework for time-varying-dimensional operators, replacing conventional cumulative regret with pointwise error bounds to provide rigorous guarantees on proximity to the optimal solution. The method integrates dynamic consensus protocols, robust statistical estimation (e.g., mean, median, min-max), and logic-loss-based classification optimization, while supporting autonomous agent join/leave and resilience against DoS attacks. Results: Extensive evaluation across dynamic consensus, target tracking, and classification tasks demonstrates the algorithm’s provable convergence, robustness to topology changes and adversarial disruptions, and practical efficacy under realistic open-system conditions.

Technology Category

• Search and Optimization: Learning to Search
• Multiagent Systems: Adversarial Agents
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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 to 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, allowing to characterize their performance in terms of the punctual distance from 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 or tracking problems on different metrics of interest, such as average, median, and min/max value, as well as classification problems with logistic loss functions.

Problem

• Multi-Robot Systems
• Adaptive Learning
• Network Uncertainty

Innovation

• Distributed Learning
• Dynamic Optimization
• Adaptive Collaboration