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Stochastic Nonlinear Control via Finite-dimensional Spectral Dynamic Embedding
- Publication Year :
- 2023
-
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.<br />Comment: Compared to v1, added analysis of Nystrom features, more streamlined proofs, and more extensive numerical studies; compared to v2, corrected a small error in ordering of author list
Details
- Database :
- OAIster
- Publication Type :
- Electronic Resource
- Accession number :
- edsoai.on1381616081
- Document Type :
- Electronic Resource