Modern learning methods have proven promising for modeling complex physical phenomena and for designing controllers capable of executing intricate tasks, owing to their remarkable flexibility. However, they can be unreliable in deployment when faced with new scenarios not represented in their training data. This thesis develops data-driven frameworks that retain the expressiveness and scalability of state-of-the-art machine learning while providing formal reliability certificates along two complementary axes: stability of closed-loop dynamics and generalization beyond training scenarios. The contributions span two parts, namely reliable model learning and reliable controller design.
For model learning, we first study personalized federated learning, where the goal is to learn a shared model from private, decentralized client data and to adapt it to each client. We propose PAC-PFL, a probabilistic method that learns a shared hyper-posterior and performs client-level posterior inference for personalization. PAC-PFL formally addresses the generalization facet of reliability: the shared model generalizes to new clients, and each client's personalized model generalizes to unseen data. PAC-PFL mitigates overfitting and delivers accurate, well-calibrated predictions. Second, we propose a tractable approach for identifying a system using data obtained while the system operates in a stable closed loop with a given controller. We achieve this by building on a complete parameterization of systems stabilized by the given controller, extending the dual Youla parameterization beyond the linear case. Our method is consistent for linear systems and yields flexible, stability-preserving neural models for nonlinear plants.
For controller design, we study stochastic nonlinear optimal control with neural controllers learned from finite data. Reliability requires closed-loop stability and transfer of empirical performance to unseen disturbances. We address this by establishing PAC-Bayesian generalization bounds and using them to infer a posterior distribution over controllers. Additionally, we leverage expressive neural controller parameterizations that guarantee closed-loop stability. The resulting controllers are expressive, closed-loop stable, and generalize beyond their training data.
Finally, we study imitation learning, where policies are trained from expert demonstrations. This setting is prone to unreliable behavior in out-of-sample regions, so we target reliability as predictable recovery from unseen initial conditions and perturbations. We model policies as contractive dynamical systems that guarantee exponential convergence of all rollouts, enabling such recovery. Using recurrent equilibrium networks and coupling layers, the architecture is contractive for any parameter choice, permitting unconstrained training. We also derive upper bounds on worst-case and expected imitation loss, providing deployment-time guarantees.
Through simulations spanning regr
