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Learning Optimal Interaction Weights in Multi-Agents Systems

Sara Honarvar, Yancy Diaz-Mercado

TL;DR

This paper employs a graph representation approach and model the dynamics of interactions between agents as state-dependent edge weights in a consensus algorithm, incorporating both spatial and temporal dynamics, to derive necessary and sufficient conditions for the optimality of these interaction weights.

Abstract

This paper presents a spatio-temporal inverse optimal control framework for understanding interactions in multi-agent systems (MAS). We employ a graph representation approach and model the dynamics of interactions between agents as state-dependent edge weights in a consensus algorithm, incorporating both spatial and temporal dynamics. Our method learns these edge weights from trajectory observations, such as provided by expert demonstrations, which allows us to capture the complexity of nonlinear, distributed interaction behaviors. We derive necessary and sufficient conditions for the optimality of these interaction weights, explaining how the network topology affects MAS coordination. The proposed method is demonstrated on a multi-agent formation control problem, where we show its effectiveness in recovering the interaction weights and coordination patterns from sample trajectory data.

Learning Optimal Interaction Weights in Multi-Agents Systems

TL;DR

This paper employs a graph representation approach and model the dynamics of interactions between agents as state-dependent edge weights in a consensus algorithm, incorporating both spatial and temporal dynamics, to derive necessary and sufficient conditions for the optimality of these interaction weights.

Abstract

This paper presents a spatio-temporal inverse optimal control framework for understanding interactions in multi-agent systems (MAS). We employ a graph representation approach and model the dynamics of interactions between agents as state-dependent edge weights in a consensus algorithm, incorporating both spatial and temporal dynamics. Our method learns these edge weights from trajectory observations, such as provided by expert demonstrations, which allows us to capture the complexity of nonlinear, distributed interaction behaviors. We derive necessary and sufficient conditions for the optimality of these interaction weights, explaining how the network topology affects MAS coordination. The proposed method is demonstrated on a multi-agent formation control problem, where we show its effectiveness in recovering the interaction weights and coordination patterns from sample trajectory data.

Paper Structure

This paper contains 16 sections, 5 theorems, 54 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notation
  4. Multi-Agent Dynamics and Interaction Representation
  5. Inverse Optimal Control Problem
  6. Learning Multi-agent Interaction Dynamics
  7. Optimality Conditions
  8. Learning Interaction Weight Algorithm
  9. Simulation Example
  10. Generating Demonstrations
  11. Case Study
  12. Reconstructing Interaction Weights
  13. Simulation Results
  14. Conclusion and Future Work
  15. Derivation of Optimality Conditions
  16. ...and 1 more sections

Key Result

Lemma 1

The Hadamard product (i.e., element-wise multiplication) of two compatible vectors $a\in\mathbb{R}^d$ and $b\in\mathbb{R}^d$ can be expressed as the matrix multiplication of the corresponding diagonal matrix of one vector by the other vector liu2008hadamard: where $\mathbf{1}_d$ is a vector of all ones and $I_d$ is the identity matrix.

Figures (4)

  • Figure 1: A network of agents in a MAS. The topology of interactions evolves dynamically as agents move and share information, with interaction strengths represented by edge weights. The goal is to learn the edge weight policy from observed trajectories.
  • Figure 2: Total cost across iterations
  • Figure 3: Comparing learned (red) vs. true (blue) policy, $u(s)$, over $s$
  • Figure 4: Comparing the simulated trajectories (red) vs. the ground truth trajectories (blue

Theorems & Definitions (6)

  • Lemma 1
  • Lemma 2
  • Corollary 1
  • Theorem 1
  • Corollary 2
  • Remark 1