Stochastic Nonlinear Control via Finite-dimensional Spectral Dynamic Embedding

• URL: http://arxiv.org/abs/2304.03907v5
• Date: Mon, 09 Jun 2025 02:24:01 GMT
• Title: Stochastic Nonlinear Control via Finite-dimensional Spectral Dynamic Embedding
• Authors: Zhaolin Ren, Tongzheng Ren, Haitong Ma, Na Li, Bo Dai,
• Abstract summary: This paper proposes an approach, Spectral Dynamics Embedding Control (SDEC), to optimal control for nonlinear systems.<n>It reveals an infinite-dimensional feature representation induced by the system's nonlinear dynamics, enabling a linear representation of the state-action value function.
• Score: 21.38845517949153
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper proposes an approach, Spectral Dynamics Embedding Control (SDEC), to optimal control for nonlinear stochastic systems. This method reveals an infinite-dimensional feature representation induced by the system's nonlinear stochastic dynamics, enabling a linear representation of the state-action value function. For practical implementation, this representation is approximated using finite-dimensional trucations, specifically via two prominent kernel approximation methods: random feature truncation and Nystrom approximation. To characterize the effectiveness of these approximations, we provide an in-depth theoretical analysis to characterize the approximation error arising from the finite-dimension truncation and statistical error due to finite-sample approximation in both policy evaluation and policy optimization. Empirically, our algorithm performs favorably against existing stochastic control algorithms on several benchmark problems.

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