Taylor Representations for Model-Free RL in Networked MDPs

arXiv:2610.05456v1 Announce Type: cross 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 Theta(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.

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Source: arXiv cs.LG | 2026-10-06