Taylor Representations for Model-Free RL in Networked MDPs
Abstract
In Networked Markov Decision Processes, transition dynamics are often unknown and the state--action space grows rapidly with the number of agents. In this setting, Taylor representations naturally approximate Q-functions, but a naive order-n expansion over N agents requires Θ(Nn) coefficients. We justify these expansions under smooth expected future local rewards with controlled derivatives. Under this condition, finite-speed information propagation and discounting imply that local-critic Taylor coefficients decay exponentially with the graph distance to the farthest agent involved. Discarding distant-agent coefficients and marginalizing then yield scalable local Taylor representations with a bound controlled by graph locality. Building on these representations, we propose a scalable model-free actor--critic algorithm, establishing finite-sample critic and near-stationarity guarantees for a linear LSTD critic. We then introduce a more expressive neural TD parameterization. Unlike prior constructive spectral methods, our approach covers settings without access to a known local dynamics map, such as hidden switched linear--quadratic regulation. Across three control benchmarks, our method matches or outperforms spectral baselines while scaling efficiently to large graphs.
Related
- Reducibility of linear representations, free ideals, and Kippenhahn's conjecture
- Symmetric spaces and skew multiplicity free representations
- Sharp Convergence and Sample Complexity of Policy Mirror Descent for Average-Reward MDPs
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- Closing the Horizon Gap in Policy Optimization for Adversarial MDPs
BibTeX
@misc{chikhi2026taylor,
title = {{Taylor Representations for Model-Free RL in Networked MDPs}},
author = {Salah Chikhi and Abdelhaq Chaoui and Asuman Ozdaglar and Saurabh Amin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05456},
eprint = {2610.05456},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05456},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Taylor Representations for Model-Free RL in Networked MDPs
AU - Salah Chikhi
AU - Abdelhaq Chaoui
AU - Asuman Ozdaglar
AU - Saurabh Amin
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05456
UR - https://arxiv.org/abs/2610.05456
AB - In Networked Markov Decision Processes, transition dynamics are often unknown and the state--action space grows rapidly with the number of agents. In this setting, Taylor representations naturally approximate Q-functions, but a naive order-n expansion over N agents requires Θ(N^n) coefficients. We justify these expansions under smooth expected future local rewards with controlled derivatives. Under this condition, finite-speed information propagation and discounting imply that local-critic Taylor coefficients decay exponentially with the graph distance to the farthest agent involved. Discarding distant-agent coefficients and marginalizing then yield scalable local Taylor representations with a bound controlled by graph locality. Building on these representations, we propose a scalable model-free actor--critic algorithm, establishing finite-sample critic and near-stationarity guarantees for a linear LSTD critic. We then introduce a more expressive neural TD parameterization. Unlike prior constructive spectral methods, our approach covers settings without access to a known local dynamics map, such as hidden switched linear--quadratic regulation. Across three control benchmarks, our method matches or outperforms spectral baselines while scaling efficiently to large graphs.
ER -