# PAC-Bayes Control: Learning Policies that Provably Generalize to Novel Environments

arXiv: https://arxiv.org/abs/1806.04225 · HTML: https://mlsanity.com/paper/1806.04225/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2018.

## Built on by (most cited first, 22 of 22)

- [Sim-to-Lab-to-Real: Safe Reinforcement Learning with Shielding and Generalization Guarantees](https://mlsanity.com/paper/2201.08355/) (2022)
- [Safe Perception-Based Control under Stochastic Sensor Uncertainty using Conformal Prediction](https://mlsanity.com/paper/2304.00194/) (2023)
- [Hamilton-Jacobi Reachability in Reinforcement Learning: A Survey](https://mlsanity.com/paper/2407.09645/) (2024)
- [Learning Differentiable Safety-Critical Control using Control Barrier Functions for Generalization to Novel Environments](https://mlsanity.com/paper/2201.01347/) (2022)
- [Human-AI Safety: A Descendant of Generative AI and Control Systems Safety](https://mlsanity.com/paper/2405.09794/) (2024)
- [Statistical Guarantees for Lifelong Reinforcement Learning using PAC-Bayes Theory](https://mlsanity.com/paper/2411.00401/) (2024)
- [PAC-Bayes Generalization Certificates for Learned Inductive Conformal Prediction](https://mlsanity.com/paper/2312.04658/) (2023)
- [Learning Latent Representations to Co-Adapt to Humans](https://mlsanity.com/paper/2212.09586/) (2022)
- [Data-Driven Performance Guarantees for Classical and Learned Optimizers](https://mlsanity.com/paper/2404.13831/) (2024)
- [Task-Driven Detection of Distribution Shifts with Statistical Guarantees for Robot Learning](https://mlsanity.com/paper/2106.13703/) (2021)
- [Deep FlexQP: Accelerated Nonlinear Programming via Deep Unfolding](https://mlsanity.com/paper/2512.01565/) (2025)
- [Generalization Guarantees for Imitation Learning](https://mlsanity.com/paper/2008.01913/) (2020)
- [Integrative Use of Computer Vision and Unmanned Aircraft Technologies in Public Inspection: Foreign Object Debris Image Collection](https://mlsanity.com/paper/2106.00161/) (2021)
- [Learning Provably Robust Motion Planners Using Funnel Libraries](https://mlsanity.com/paper/2111.08733/) (2021)
- [Stronger Generalization Guarantees for Robot Learning by Combining Generative Models and Real-World Data](https://mlsanity.com/paper/2111.08761/) (2021)
- [Model-Assisted Probabilistic Safe Adaptive Control With Meta-Bayesian Learning](https://mlsanity.com/paper/2307.00828/) (2023)
- [Interactive Dynamic Walking: Learning Gait Switching Policies with Generalization Guarantees](https://mlsanity.com/paper/2109.13417/) (2021)
- [Fundamental Tradeoffs in Learning with Prior Information](https://mlsanity.com/paper/2304.13479/) (2023)
- [PAC-Bayesian Certificates for Quadratic Closed-Loop Control](https://mlsanity.com/paper/2606.28281/) (2026)
- [Entanglement as a Structural Complexity Axis: A PAC-Bayesian View of Generalization in Quantum Policies and Value Functions](https://mlsanity.com/paper/2607.06230/) (2026)
- [PAC-DP: PAC-Bayesian Diffusion Policy Learning](https://mlsanity.com/paper/2607.24296/) (2026)
- [RL-Guided PAC-NMPC for Probabilistically-Safe Perception-Based Navigation in Unknown Environments](https://mlsanity.com/paper/2609.39854/) (2026)

## Abstract (arXiv)

Our goal is to learn control policies for robots that provably generalize well to novel environments given a dataset of example environments. The key technical idea behind our approach is to leverage tools from generalization theory in machine learning by exploiting a precise analogy (which we present in the form of a reduction) between generalization of control policies to novel environments and generalization of hypotheses in the supervised learning setting. In particular, we utilize the Probably Approximately Correct (PAC)-Bayes framework, which allows us to obtain upper bounds that hold with high probability on the expected cost of (stochastic) control policies across novel environments. We propose policy learning algorithms that explicitly seek to minimize this upper bound. The corresponding optimization problem can be solved using convex optimization (Relative Entropy Programming in particular) in the setting where we are optimizing over a finite policy space. In the more general setting of continuously parameterized policies (e.g., neural network policies), we minimize this upper bound using stochastic gradient descent. We present simulated results of our approach applied to learning (1) reactive obstacle avoidance policies and (2) neural network-based grasping policies. We also present hardware results for the Parrot Swing drone navigating through different obstacle environments. Our examples demonstrate the potential of our approach to provide strong generalization guarantees for robotic systems with continuous state and action spaces, complicated (e.g., nonlinear) dynamics, rich sensory inputs (e.g., depth images), and neural network-based policies.