PAC-Bayes Control: Synthesizing Controllers that Provably Generalize to Novel Environments

Anirudha Majumdar, Maxwell Goldstein
Proceedings of The 2nd Conference on Robot Learning, PMLR 87:293-305, 2018.

Abstract

Our goal is to synthesize controllers 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 robustness of controllers to novel environments and generalization of hypotheses in supervised learning. 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) controllers across novel environments. We propose control synthesis algorithms that explicitly seek to minimize this upper bound. The corresponding optimization problem can be solved efficiently using convex optimization (Relative Entropy Programming in particular) in the setting where we are optimizing over a finite control policy space. In the more general setting of continuously parameterized controllers, we minimize this upper bound using stochastic gradient descent. We present examples of our approach in the context of obstacle avoidance control with depth measurements. Our simulated examples demonstrate the potential of our approach to provide strong generalization guarantees on controllers for robotic systems with continuous state and action spaces, nonlinear dynamics, and partially observable state via sensor measurements.

Cite this Paper

BibTeX
@InProceedings{pmlr-v87-majumdar18a, title = {PAC-Bayes Control: Synthesizing Controllers that Provably Generalize to Novel Environments}, author = {Majumdar, Anirudha and Goldstein, Maxwell}, booktitle = {Proceedings of The 2nd Conference on Robot Learning}, pages = {293--305}, year = {2018}, editor = {Billard, Aude and Dragan, Anca and Peters, Jan and Morimoto, Jun}, volume = {87}, series = {Proceedings of Machine Learning Research}, month = {29--31 Oct}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v87/majumdar18a/majumdar18a.pdf}, url = {https://proceedings.mlr.press/v87/majumdar18a.html}, abstract = {Our goal is to synthesize controllers 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 robustness of controllers to novel environments and generalization of hypotheses in supervised learning. 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) controllers across novel environments. We propose control synthesis algorithms that explicitly seek to minimize this upper bound. The corresponding optimization problem can be solved efficiently using convex optimization (Relative Entropy Programming in particular) in the setting where we are optimizing over a finite control policy space. In the more general setting of continuously parameterized controllers, we minimize this upper bound using stochastic gradient descent. We present examples of our approach in the context of obstacle avoidance control with depth measurements. Our simulated examples demonstrate the potential of our approach to provide strong generalization guarantees on controllers for robotic systems with continuous state and action spaces, nonlinear dynamics, and partially observable state via sensor measurements.} }
Endnote
%0 Conference Paper %T PAC-Bayes Control: Synthesizing Controllers that Provably Generalize to Novel Environments %A Anirudha Majumdar %A Maxwell Goldstein %B Proceedings of The 2nd Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2018 %E Aude Billard %E Anca Dragan %E Jan Peters %E Jun Morimoto %F pmlr-v87-majumdar18a %I PMLR %P 293--305 %U https://proceedings.mlr.press/v87/majumdar18a.html %V 87 %X Our goal is to synthesize controllers 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 robustness of controllers to novel environments and generalization of hypotheses in supervised learning. 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) controllers across novel environments. We propose control synthesis algorithms that explicitly seek to minimize this upper bound. The corresponding optimization problem can be solved efficiently using convex optimization (Relative Entropy Programming in particular) in the setting where we are optimizing over a finite control policy space. In the more general setting of continuously parameterized controllers, we minimize this upper bound using stochastic gradient descent. We present examples of our approach in the context of obstacle avoidance control with depth measurements. Our simulated examples demonstrate the potential of our approach to provide strong generalization guarantees on controllers for robotic systems with continuous state and action spaces, nonlinear dynamics, and partially observable state via sensor measurements.
APA
Majumdar, A. & Goldstein, M.. (2018). PAC-Bayes Control: Synthesizing Controllers that Provably Generalize to Novel Environments. Proceedings of The 2nd Conference on Robot Learning, in Proceedings of Machine Learning Research 87:293-305 Available from https://proceedings.mlr.press/v87/majumdar18a.html.

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