Distributionally Robust PAC-Bayesian Control

• URL: http://arxiv.org/abs/2604.10588v1
• Date: Sun, 12 Apr 2026 11:17:20 GMT
• Title: Distributionally Robust PAC-Bayesian Control
• Abstract summary: We present a distributionally robust PAC-Bayesian framework for certifying the performance of learning-based finite-horizon controllers.<n>We achieve this by drawing on two modern lines of research, namely the PAC-Bayes generalization theory and distributionally robust optimization via the type-1 Wasserstein distance.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a distributionally robust PAC-Bayesian framework for certifying the performance of learning-based finite-horizon controllers. While existing PAC-Bayes control literature typically assumes bounded losses and matching training and deployment distributions, we explicitly address unbounded losses and environmental distribution shifts (the sim-to-real gap). We achieve this by drawing on two modern lines of research, namely the PAC-Bayes generalization theory and distributionally robust optimization via the type-1 Wasserstein distance. By leveraging the System Level Synthesis (SLS) reparametrization, we derive a sub-Gaussian loss proxy and a bound on the performance loss due to distribution shift. Both are tied directly to the operator norm of the closed-loop map. For linear time-invariant systems, this yields a computationally tractable optimization-based framework together with high-probability safety certificates for deployment in real-world environments that differ from those used in training.

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