PAC-Bayes Control: Learning Policies that Provably Generalize to Novel Environments (1806.04225v5)

Abstract: 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.

• The paper introduces a PAC-Bayes framework to derive probabilistic generalization bounds for robotic control policies across unseen environments.
• It employs convex optimization and stochastic gradient descent to minimize PAC-Bayes bounds in both finite and continuously parameterized policy spaces.
• Empirical results in simulation and hardware demonstrate high collision-free traversal and grasping success, highlighting robust transfer learning potential.

Summary of "PAC-Bayes Control: Learning Policies that Provably Generalize to Novel Environments"

The paper "PAC-Bayes Control: Learning Policies that Provably Generalize to Novel Environments" by Anirudha Majumdar, Alec Farid, and Anoopkumar Sonar explores the development of control policies for robotic systems that not only perform well in observed environments but also generalize effectively to previously unseen ones. This research addresses a significant challenge in robotics: the ability to transfer learned behaviors to new scenarios without additional training. The authors leverage the Probably Approximately Correct (PAC)-Bayes framework to derive upper bounds on the expected cost of control policies across novel environments, with these bounds holding with high probability.

Techniques and Methodology

The core approach of this paper involves drawing an analogy between the generalization problem in control and supervised learning. The authors employ the PAC-Bayes framework, traditionally used in supervised learning to obtain guarantees on generalization, to control policy learning. By framing policy learning in this probabilistic setting, it becomes possible to derive generalization bounds that apply not just to the training environments but to new, unseen ones.

For computational aspects, the paper describes methods to minimize the derived PAC-Bayes bound, offering examples using convex optimization techniques such as Relative Entropy Programming for finite policy spaces. When dealing with continuously parameterized policies (e.g., neural networks), the authors adapt to optimization using stochastic gradient descent. They construct their models to evaluate results on two main applications: reactive obstacle avoidance and neural network-based grasping policies in simulation environments. The achieved performance guarantees are supported by simulations, where collision-free traversal and grasping success rates achieved were high, even with relatively small training sets.

Empirical Results

The empirical evidence provided in the paper demonstrates strong generalization guarantees, which are quantitatively assessed. For instance, the paper reports an impressive collision-free traversal rate of $87.9\%$ with a set of 1000 training environments for obstacle avoidance, and a $70.6\%$ success rate in grasping using 2000 training objects. Furthermore, hardware results utilizing a Parrot Swing drone showed a guaranteed expected success rate, underscoring that the framework retains its efficacy beyond simulations.

Implications

From a theoretical standpoint, the approach paves the way for applying PAC-Bayes bounds in domains traditionally restricted to supervised learning, opening avenues for transferring robust learning concepts to dynamic and uncertain robotic environments. Practically, this framework could significantly reduce the need for large-scale real-world data or exhaustive retraining on robotic platforms, thereby pushing the boundaries of autonomy in robotics.

The paper also introduces a direction for creating distributionally robust policies capable of adapting to changes in the environment. This extension ensures robustness where training and testing environments might differ, which is essential for practical deployment in varied conditions.

Future Developments

Looking ahead, this research suggests several potential advancements. One key area is the adaptation of deterministic policies, which are highly desirable in critical safety applications. Furthermore, a focus on choosing or learning priors that better match the robotic task might improve the PAC-Bayes bounds. Moreover, integrating this approach with meta-learning strategies could enhance overall data efficiency. Broadening the framework by including more sophisticated or varied forms of regularization could also be beneficial—especially where deterministic policies need to be realized.

In conclusion, this paper makes a substantial contribution by advancing how we understand and implement transfer learning and generalization in robotics, providing not just immediate practical techniques but also rich areas for future exploration.