Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Qixin Zhang, Zongqi Wan, Yu Yang, Li Shen, Dacheng Tao

TL;DR

The paper addresses online coordination of multiple agents with submodular objectives under uncertain dynamics. It introduces MA-OSMA and MA-OSEA, which leverage a multi-linear extension and a curvature-aware surrogate gradient to achieve the tight $\frac{1-e^{-c}}{c}$-approximation on connected networks while reducing the need for a fully connected communication graph. The authors establish dynamic regret bounds $\widetilde{O}(\sqrt{C_T T/(1-\beta)})$ against the corresponding surrogate-approximation benchmark and validate performance via simulations in multi-target tracking, highlighting improved efficiency and scalability. The work advances decentralized online submodular optimization by combining consensus-based updates, projection-free strategies, and surrogate-gradient techniques, with practical implications for real-world multi-agent systems requiring communication-efficient coordination.

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 $\textbf{MA-OSMA}$ 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, $\textbf{MA-OSMA}$ leverages a novel surrogate gradient to avoid sub-optimal stationary points. To eliminate the computationally intensive projection operations in $\textbf{MA-OSMA}$, we also introduce a projection-free $\textbf{MA-OSEA}$ algorithm, which effectively utilizes the KL divergence by mixing a uniform distribution. Theoretically, we confirm that both algorithms achieve a regret bound of $\widetilde{O}(\sqrt{\frac{C_{T}T}{1-β}})$ against a $(\frac{1-e^{-c}}{c})$-approximation to the best comparator in hindsight, where $C_{T}$ is the deviation of maximizer sequence, $β$ 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.

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

TL;DR

The paper addresses online coordination of multiple agents with submodular objectives under uncertain dynamics. It introduces MA-OSMA and MA-OSEA, which leverage a multi-linear extension and a curvature-aware surrogate gradient to achieve the tight -approximation on connected networks while reducing the need for a fully connected communication graph. The authors establish dynamic regret bounds against the corresponding surrogate-approximation benchmark and validate performance via simulations in multi-target tracking, highlighting improved efficiency and scalability. The work advances decentralized online submodular optimization by combining consensus-based updates, projection-free strategies, and surrogate-gradient techniques, with practical implications for real-world multi-agent systems requiring communication-efficient coordination.

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 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, leverages a novel surrogate gradient to avoid sub-optimal stationary points. To eliminate the computationally intensive projection operations in , we also introduce a projection-free algorithm, which effectively utilizes the KL divergence by mixing a uniform distribution. Theoretically, we confirm that both algorithms achieve a regret bound of against a -approximation to the best comparator in hindsight, where is the deviation of maximizer sequence, is the spectral gap of the network and is the joint curvature of submodular objectives. This result significantly improves the -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.

Paper Structure

This paper contains 21 sections, 27 theorems, 92 equations, 3 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Formulation
  3. Problem Formulation
  4. Multi-linear Extension and its Properties
  5. Characterizing stationary points
  6. Constructing an Unbiased Gradient for surrogate function
  7. Methodology
  8. Multi-Agent Online Surrogate Mirror Ascent
  9. Regret Analysis for Algorithm \ref{['alg:BDOMA']}
  10. Projection-free Multi-Agent Online Surrogate Entropic Ascent
  11. Numerical Experiments
  12. Conclusions and Future Work
  13. Additional Discussions
  14. More Details on Related Works
  15. More Discussions on Assumption \ref{['ass:4']}
  16. ...and 6 more sections

Key Result

Theorem 1

If $f:2^{\mathcal{V}}\rightarrow\mathbb{R}_{+}$ is a monotone submodular function with curvature $c$, then for any stationary point $\mathbf{x}$ of its multi-linear extension $F:[0,1]^{n}\rightarrow\mathbb{R}_{+}$ over domain $\mathcal{C}\subseteq[0,1]^{n}$, we have

Figures (3)

  • Figure 1: Left: Multi-target tracking with $4$ mobile sensors over a complete directed acyclic communication network. Right: Multi-target tracking with $4$ sensors over a connected undirected graph.
  • Figure 2: $\frac{1}{1+c}$ v.s. $\frac{1-e^{-c}}{c}$.
  • Figure 3: Comparison of average cumulative utility, average number of targets within 5 units, average distance of Top-5 nearest targets of MA-OSMA-c,MA-OSMA-r,MA-OSEA-c and MA-OSEA-c with OSG on different multi-target tracking scenarios(averaged over 5 runs).

Theorems & Definitions (55)

  • Definition 1
  • Definition 2
  • Theorem 1: Proof is deferred to \ref{['append:proof1']}
  • Remark 1
  • Theorem 2: Proof is deferred to \ref{['append:proof2']}
  • Remark 2
  • Remark 3
  • Definition 3: Bregman Divergence
  • Remark 4
  • Remark 5
  • ...and 45 more