Near-Optimal Online Learning for Multi-Agent Submodular Coordination: Tight Approximation and Communication Efficiency

2025-02-07

AI Summary

This paper addresses the problem of online submodular function maximization in dynamic multi-agent systems, overcoming key limitations of existing methods—such as reliance on fully connected communication graphs and weak approximation ratios (e.g., only $1/(1+c)$ for OSG). We propose two distributed algorithms, MA-OSMA and MA-OSEA, which achieve the first tight approximation ratio of $(1-e^{-c})/c$—strictly improving upon the state-of-the-art. Both algorithms exhibit robustness to arbitrary time-varying communication topologies and attain a tight regret bound of $ ilde{O}ig(sqrt{C_T T/(1-eta)}ig)$. Key technical innovations include multilinear extension modeling, a consensus-based optimization framework, KL-divergence-driven projection-free updates, and joint curvature analysis. Extensive simulations on multi-target tracking demonstrate significant improvements in coordination efficiency and convergence speed.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Coordinating multiple agents to collaboratively maximize submodular functions in unpredictable environments is a critical task with numerous applications in machine learning, robot planning and control. The existing approaches, such as the OSG algorithm, are often hindered by their poor approximation guarantees and the rigid requirement for a fully connected communication graph. To address these challenges, we firstly present a $ extbf{MA-OSMA}$ algorithm, which employs the multi-linear extension to transfer the discrete submodular maximization problem into a continuous optimization, thereby allowing us to reduce the strict dependence on a complete graph through consensus techniques. Moreover, $ extbf{MA-OSMA}$ leverages a novel surrogate gradient to avoid sub-optimal stationary points. To eliminate the computationally intensive projection operations in $ extbf{MA-OSMA}$, we also introduce a projection-free $ extbf{MA-OSEA}$ algorithm, which effectively utilizes the KL divergence by mixing a uniform distribution. Theoretically, we confirm that both algorithms achieve a regret bound of $widetilde{O}(sqrt{frac{C_{T}T}{1-eta}})$ against a $(frac{1-e^{-c}}{c})$-approximation to the best comparator in hindsight, where $C_{T}$ is the deviation of maximizer sequence, $eta$ is the spectral gap of the network and $c$ is the joint curvature of submodular objectives. This result significantly improves the $(frac{1}{1+c})$-approximation provided by the state-of-the-art OSG algorithm. Finally, we demonstrate the effectiveness of our proposed algorithms through simulation-based multi-target tracking.

Problem

• Improves approximation in multi-agent coordination.
• Reduces communication graph dependency effectively.
• Enhances efficiency in submodular function maximization.

Innovation

• Multi-linear extension for optimization
• Surrogate gradient avoids sub-optimal points
• Projection-free algorithm uses KL divergence