Personalized Multi-Agent Average Reward TD-Learning via Joint Linear Approximation
arXiv:2603.02426v1 Announce Type: new Abstract: We study personalized multi-agent average reward TD learning, in which a collection of agents interacts with different environments and jointly learns their respective value functions. We focus on the setting where there exists a shared linear representation, and the agents' optimal weights collectively lie in an unknown linear subspace. Inspired by the recent success of personalized federated learning (PFL), we study the convergence of cooperative single-timescale TD learning in which agents iteratively estimate the common subspace and local heads. We showed that this decomposition can filter out conflicting signals, effectively mitigating the negative impacts of ``misaligned'' signals, and achieving linear speedup. The main technical challenges lie in the heterogeneity, the Markovian sampling, and their intricate interplay in shaping error evolutions. Specifically, not only are the error dynamics of multiple variables closely interconn
arXiv:2603.02426v1 Announce Type: new Abstract: We study personalized multi-agent average reward TD learning, in which a collection of agents interacts with different environments and jointly learns their respective value functions. We focus on the setting where there exists a shared linear representation, and the agents' optimal weights collectively lie in an unknown linear subspace. Inspired by the recent success of personalized federated learning (PFL), we study the convergence of cooperative single-timescale TD learning in which agents iteratively estimate the common subspace and local heads. We showed that this decomposition can filter out conflicting signals, effectively mitigating the negative impacts of ``misaligned'' signals, and achieving linear speedup. The main technical challenges lie in the heterogeneity, the Markovian sampling, and their intricate interplay in shaping error evolutions. Specifically, not only are the error dynamics of multiple variables closely interconnected, but there is also no direct contraction for the principal angle distance between the optimal subspace and the estimated subspace. We hope our analytical techniques can be useful to inspire research on deeper exploration into leveraging common structures. Experiments are provided to show the benefits of learning via a shared structure to the more general control problem.
Executive Summary
This article presents a novel approach to personalized multi-agent average reward TD-learning, focusing on the setting where agents share a linear representation. The authors propose a cooperative single-timescale TD-learning method that enables agents to iteratively estimate a common subspace and local heads. The method effectively mitigates the negative impacts of 'misaligned' signals, achieving a linear speedup. The contributions of this work include a convergence analysis of the proposed method, addressing the challenges posed by heterogeneity and Markovian sampling. Experiments demonstrate the benefits of learning via a shared structure in the general control problem. This work has the potential to inspire research on leveraging common structures in multi-agent systems.
Key Points
- ▸ Proposes a cooperative single-timescale TD-learning method for personalized multi-agent average reward TD-learning
- ▸ Introduces a shared linear representation to mitigate the negative impacts of 'misaligned' signals
- ▸ Achieves a linear speedup through the iterative estimation of a common subspace and local heads
Merits
Strength
The work provides a comprehensive convergence analysis of the proposed method, addressing the challenges of heterogeneity and Markovian sampling.
Strength
The experimental results demonstrate the benefits of learning via a shared structure in the general control problem.
Demerits
Limitation
The work assumes a shared linear representation, which may not be applicable to all multi-agent systems.
Limitation
The convergence analysis is focused on the specific setting of cooperative single-timescale TD-learning, limiting the generalizability of the results.
Expert Commentary
This article presents a significant contribution to the field of multi-agent systems, highlighting the potential benefits of shared structures in cooperation and coordination. The proposed method is well-motivated and provides a comprehensive convergence analysis, addressing the challenges of heterogeneity and Markovian sampling. While the work assumes a shared linear representation, which may not be applicable to all multi-agent systems, the experimental results demonstrate the benefits of learning via a shared structure in the general control problem. The implications of this work are far-reaching, with potential applications in autonomous vehicles, smart grids, and other real-world multi-agent systems.
Recommendations
- ✓ Future work should explore the extension of the proposed method to more general settings, such as non-linear representations or non-cooperative agents.
- ✓ The authors should provide more detailed experimental results, including a comparison with other state-of-the-art methods, to further demonstrate the benefits of the proposed approach.