Data-Driven Optimal Feedback Laws via Kernel Mean Embeddings

• URL: http://arxiv.org/abs/2407.16407v1
• Date: Tue, 23 Jul 2024 11:53:03 GMT
• Title: Data-Driven Optimal Feedback Laws via Kernel Mean Embeddings
• Authors: Petar Bevanda, Nicolas Hoischen, Stefan Sosnowski, Sandra Hirche, Boris Houska,
• Abstract summary: We introduce kernel mean embeddings (KMEs) to identify the Markov transition operators associated with controlled diffusion processes. Unlike traditional dynamic programming methods, our approach exploits the Kernel trick'' to break the curse of dimensionality. We demonstrate the effectiveness of our method through numerical examples, highlighting its ability to solve a large class of nonlinear optimal control problems.
• Score: 3.007066256364399
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper proposes a fully data-driven approach for optimal control of nonlinear control-affine systems represented by a stochastic diffusion. The focus is on the scenario where both the nonlinear dynamics and stage cost functions are unknown, while only control penalty function and constraints are provided. Leveraging the theory of reproducing kernel Hilbert spaces, we introduce novel kernel mean embeddings (KMEs) to identify the Markov transition operators associated with controlled diffusion processes. The KME learning approach seamlessly integrates with modern convex operator-theoretic Hamilton-Jacobi-Bellman recursions. Thus, unlike traditional dynamic programming methods, our approach exploits the ``kernel trick'' to break the curse of dimensionality. We demonstrate the effectiveness of our method through numerical examples, highlighting its ability to solve a large class of nonlinear optimal control problems.

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