A Bayesian Perspective on the Data-Driven LQR
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915929837797376 |
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| author | Schwaller, Thierry Zhao, Feiran Dörfler, Florian |
| author_facet | Schwaller, Thierry Zhao, Feiran Dörfler, Florian |
| contents | The data-driven linear quadratic regulator (ddLQR) is a widely studied control method for unknown dynamical systems with disturbance. Existing approaches, both indirect, i.e., those that identify a model followed by model-based design, and direct, which bypasses the identification step, often rely on the certainty-equivalence principle and therefore do not explicitly account for model uncertainty. In this paper, we propose a Bayesian formulation for both indirect and direct ddLQR that incorporates posterior uncertainty into the control design. The resulting expected cost decomposes into a certainty-equivalence term and a variance-dependent term, providing a principled interpretation of regularization. We further show that the indirect and direct formulations are equivalent under this perspective. The resulting direct method admits a tractable semidefinite program whose size is independent of the data length. Numerical simulations demonstrate improved optimality gap and closed-loop stability, particularly in low-data regimes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_09074 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Bayesian Perspective on the Data-Driven LQR Schwaller, Thierry Zhao, Feiran Dörfler, Florian Optimization and Control Systems and Control The data-driven linear quadratic regulator (ddLQR) is a widely studied control method for unknown dynamical systems with disturbance. Existing approaches, both indirect, i.e., those that identify a model followed by model-based design, and direct, which bypasses the identification step, often rely on the certainty-equivalence principle and therefore do not explicitly account for model uncertainty. In this paper, we propose a Bayesian formulation for both indirect and direct ddLQR that incorporates posterior uncertainty into the control design. The resulting expected cost decomposes into a certainty-equivalence term and a variance-dependent term, providing a principled interpretation of regularization. We further show that the indirect and direct formulations are equivalent under this perspective. The resulting direct method admits a tractable semidefinite program whose size is independent of the data length. Numerical simulations demonstrate improved optimality gap and closed-loop stability, particularly in low-data regimes. |
| title | A Bayesian Perspective on the Data-Driven LQR |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2604.09074 |