Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Distributed Multi-Agent Reinforcement Learning Based on Graph-Induced Local Value Functions

Gangshan Jing, He Bai, Jemin George, Aranya Chakrabortty, Piyush K. Sharma

TL;DR

The paper tackles scalable distributed MARL by modeling three intrinsic inter-agent couplings with graphs $\mathcal{G}_S$, $\mathcal{G}_O$, $\mathcal{G}_R$ and deriving a learning graph $\mathcal{G}_L$ to guide information exchange. It introduces local value functions (LVFs) that replicate the GVF gradients within local agent subsets, enabling policy updates via black-box zeroth-order methods; two distributed approaches are proposed: (i) LVF-based learning with local consensus and (ii) TLVF-based learning for dense couplings, along with convergence analyses and variance-reduction techniques using two-point zeroth-order oracles. The key contributions include a graph-theoretic LVF design that preserves gradient information, a TLVF framework with a tunable truncation index $\kappa$, and rigorous convergence and variance bounds demonstrating improved scalability on large-scale MASs. Simulations on warehouse-resource transfer scenarios show faster convergence and lower variance for LVF-based methods compared with GVF-based baselines, and TLVF with small $\kappa$ plus two-point OOs further reduces sample complexity in large networks. Overall, the work provides a practical, graph-informed methodology to achieve scalable, distributed MARL in networks with multiple couplings, with significant implications for large-scale multi-agent control and coordination.

Abstract

Achieving distributed reinforcement learning (RL) for large-scale cooperative multi-agent systems (MASs) is challenging because: (i) each agent has access to only limited information; (ii) issues on convergence or computational complexity emerge due to the curse of dimensionality. In this paper, we propose a general computationally efficient distributed framework for cooperative multi-agent reinforcement learning (MARL) by utilizing the structures of graphs involved in this problem. We introduce three coupling graphs describing three types of inter-agent couplings in MARL, namely, the state graph, the observation graph and the reward graph. By further considering a communication graph, we propose two distributed RL approaches based on local value-functions derived from the coupling graphs. The first approach is able to reduce sample complexity significantly under specific conditions on the aforementioned four graphs. The second approach provides an approximate solution and can be efficient even for problems with dense coupling graphs. Here there is a trade-off between minimizing the approximation error and reducing the computational complexity. Simulations show that our RL algorithms have a significantly improved scalability to large-scale MASs compared with centralized and consensus-based distributed RL algorithms.

Distributed Multi-Agent Reinforcement Learning Based on Graph-Induced Local Value Functions

TL;DR

The paper tackles scalable distributed MARL by modeling three intrinsic inter-agent couplings with graphs , , and deriving a learning graph to guide information exchange. It introduces local value functions (LVFs) that replicate the GVF gradients within local agent subsets, enabling policy updates via black-box zeroth-order methods; two distributed approaches are proposed: (i) LVF-based learning with local consensus and (ii) TLVF-based learning for dense couplings, along with convergence analyses and variance-reduction techniques using two-point zeroth-order oracles. The key contributions include a graph-theoretic LVF design that preserves gradient information, a TLVF framework with a tunable truncation index , and rigorous convergence and variance bounds demonstrating improved scalability on large-scale MASs. Simulations on warehouse-resource transfer scenarios show faster convergence and lower variance for LVF-based methods compared with GVF-based baselines, and TLVF with small plus two-point OOs further reduces sample complexity in large networks. Overall, the work provides a practical, graph-informed methodology to achieve scalable, distributed MARL in networks with multiple couplings, with significant implications for large-scale multi-agent control and coordination.

Abstract

Achieving distributed reinforcement learning (RL) for large-scale cooperative multi-agent systems (MASs) is challenging because: (i) each agent has access to only limited information; (ii) issues on convergence or computational complexity emerge due to the curse of dimensionality. In this paper, we propose a general computationally efficient distributed framework for cooperative multi-agent reinforcement learning (MARL) by utilizing the structures of graphs involved in this problem. We introduce three coupling graphs describing three types of inter-agent couplings in MARL, namely, the state graph, the observation graph and the reward graph. By further considering a communication graph, we propose two distributed RL approaches based on local value-functions derived from the coupling graphs. The first approach is able to reduce sample complexity significantly under specific conditions on the aforementioned four graphs. The second approach provides an approximate solution and can be efficient even for problems with dense coupling graphs. Here there is a trade-off between minimizing the approximation error and reducing the computational complexity. Simulations show that our RL algorithms have a significantly improved scalability to large-scale MASs compared with centralized and consensus-based distributed RL algorithms.
Paper Structure (16 sections, 15 theorems, 69 equations, 8 figures, 1 algorithm)

This paper contains 16 sections, 15 theorems, 69 equations, 8 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Multi-Agent Reinforcement Learning
  3. Local Value Function and Learning Graph
  4. Local Value Function Design
  5. Learning Graph
  6. Distributed RL Based on Local Consensus
  7. Communication Weights and Distributed RL Design
  8. Convergence Analysis
  9. Distributed RL via Truncated Local Value Functions
  10. Truncated Local Value Function Design
  11. Distributed RL with Convergence Analysis
  12. Variance Reduction by Two-Point Zeroth-Order Oracles
  13. Simulation Results
  14. Conclusions
  15. Appendix A: Proofs of Lemmas and Theorems
  16. ...and 1 more sections

Key Result

Lemma 1

The following statements are true: (i). Assumption as weakly connected holds if graph $\mathcal{G}_{SOR}$ has $n>1$ SCCs. (ii). Assumption as weakly connected holds only if graph $\mathcal{G}_{SO}$ has $n>1$ SCCs.

Figures (8)

  • Figure 1: The state graph $\mathcal{G}_S=(\mathcal{V},\mathcal{E}_S)$ and the observation graph $\mathcal{G}_O=(\mathcal{V},\mathcal{E}_O)$. The black and red lines correspond to edges in $\mathcal{E}_S$ and $\mathcal{E}_O$, respectively.
  • Figure 2: The reward graph $\mathcal{G}_R=(\mathcal{V},\mathcal{E}_R)$.
  • Figure 3: A counter-example for the converse of Lemma \ref{['le GCOR']} (i). Graphs (a), (b), (c), and (d) denote graphs $\mathcal{G}_{SO}$, $\mathcal{G}_R$, $\mathcal{G}_{SOR}$, and the learning graph $\mathcal{G}_L$, respectively.
  • Figure 4: The learning graph $\mathcal{G}_L$ corresponding to $\mathcal{G}_{SO}$ in Fig. \ref{['fig GCO']} and $\mathcal{G}_R$ in Fig. \ref{['fig GR']}.
  • Figure 5: (Left) Comparison of different algorithms for 9 warehouses; (Middle) centralized and distributed algorithms under zeroth-order oracles with one-point feedback; (Right) centralized and distributed algorithms under zeroth-order oracles with two-point feedback. The observed GVF value $W(\theta^k,\xi^*)=\sum_{i\in\mathcal{V}}W_i(\theta^k,\xi_i^*)$ is employed as the performance metric. The boundaries of the shaded area are obtained by running each RL algorithm for 10 times and taking the upper bound and lower bound of $W(\theta^k,\xi^*)$ in each learning episode.
  • ...and 3 more figures

Theorems & Definitions (25)

  • Example 1
  • Remark 1
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Remark 2
  • Lemma 5
  • Lemma 6
  • Lemma 7
  • ...and 15 more