Distributionally Robust PAC-Bayesian Control
It provides a theoretical and practical certification method for control systems under distribution shift, which is important for safe deployment of learning-based controllers in real-world environments.
This paper presents a distributionally robust PAC-Bayesian framework for certifying the performance of learning-based finite-horizon controllers, addressing unbounded losses and environmental distribution shifts (sim-to-real gap). The framework yields computationally tractable optimization and high-probability safety certificates for linear time-invariant systems.
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.