Stochastic Nonlinear Control via Finite-dimensional Spectral Dynamic Embedding

• URL: http://arxiv.org/abs/2304.03907v4
• Date: Fri, 15 Nov 2024 20:51:08 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 presents an approach, Spectral Dynamics Embedding Control (SDEC), to optimal control for nonlinear systems. We use an infinite-dimensional feature to linearly represent the state-action value function and exploits finite-dimensional truncation approximation for practical implementation.
• Score: 21.38845517949153
• License:
• Abstract: This paper presents an approach, Spectral Dynamics Embedding Control (SDEC), to optimal control for nonlinear stochastic systems. This method leverages an infinite-dimensional feature to linearly represent the state-action value function and exploits finite-dimensional truncation approximation for practical implementation. To characterize the effectiveness of these finite dimensional approximations, we provide an in-depth theoretical analysis to characterize the approximation error induced by the finite-dimension truncation and statistical error induced by finite-sample approximation in both policy evaluation and policy optimization. Our analysis includes two prominent kernel approximation methods: truncations onto random features and Nystrom features. We also empirically test the algorithm and compare the performance with Koopman-based, iLQR, and energy-based methods on a few benchmark problems.

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