Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data

Dziugaite, Gintare Karolina; Roy, Daniel M.

doi:10.48550/arxiv.1703.11008

Cited by 64 publications

(113 citation statements)

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“…PAC generalization bounds have been used in robotics [40] and controls [41,42] for providing guarantees on learned models or controllers with low dimensionality. The PAC-Bayes framework [9] is a specific family of bounds in generalization theory that have recently been successful in providing generalization bounds for deep neural networks (DNNs) [43,44]. In our previous work, we developed the PAC-Bayes Control framework [45,3] for synthesizing control policies that provably generalize to novel environments.…”

Section: Related Workmentioning

confidence: 99%

Learning Provably Robust Motion Planners Using Funnel Libraries

Gurgen¹,

Majumdar²,

Veer³

2021

Preprint

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This paper presents an approach for learning motion planners that are accompanied with probabilistic guarantees of success on new environments that hold uniformly for any disturbance to the robot's dynamics within an admissible set. We achieve this by bringing together tools from generalization theory and robust control. First, we curate a library of motion primitives where the robustness of each primitive is characterized by an over-approximation of the forward reachable set, i.e., a "funnel". Then, we optimize probably approximately correct (PAC)-Bayes generalization bounds for training our planner to compose these primitives such that the entire funnels respect the problem specification. We demonstrate the ability of our approach to provide strong guarantees on two simulated examples: (i) navigation of an autonomous vehicle under external disturbances on a five-lane highway with multiple vehicles, and (ii) navigation of a drone across an obstacle field in the presence of wind disturbances.

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Section: Related Workmentioning

confidence: 99%

Learning Provably Robust Motion Planners Using Funnel Libraries

Gurgen¹,

Majumdar²,

Veer³

2021

Preprint

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“…Importantly, our goal in this work is to learn switching policies, which, given a dataset of environment instances, generalize with provable guarantees to novel environments. To achieve this, we will utilize PAC Bayes theory, which is known to provide strong generalization bounds in supervised learning [26], [27].…”

Section: Learning Provably Generalizable Switching Policiesmentioning

confidence: 99%

Interactive Dynamic Walking: Learning Gait Switching Policies with Generalization Guarantees

Chand¹,

Veer²,

Poulakakis³

2021

Preprint

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In this paper, we consider the problem of adapting a dynamically walking bipedal robot to follow a leading coworker while engaging in tasks that require physical interaction. Our approach relies on switching among a family of Dynamic Movement Primitives (DMPs) as governed by a supervisor. We train the supervisor to orchestrate the switching among the DMPs in order to adapt to the leader's intentions, which are only implicitly available in the form of interaction forces. The primary contribution of our approach is its ability to furnish certificates of generalization to novel leader intentions for the trained supervisor. This is achieved by leveraging the Probably Approximately Correct (PAC)-Bayes bounds from generalization theory. We demonstrate the efficacy of our approach by training a neural-network supervisor to adapt the gait of a dynamically walking biped to a leading collaborator whose intended trajectory is not known explicitly.

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“…Meanwhile, based on information-theoretic metrics, one can analyze general classes of updates and models, e.g., stochastic iterative algorithms for non-convex objectives, hence applicable to deep learning. It has been shown that the information theoretical bounds are non-vacuous and closely related with the real generalization error even in deep learning [14,26,9,39].…”

Section: Introductionmentioning

confidence: 99%

Optimizing Information-theoretical Generalization Bounds via Anisotropic Noise in SGLD

Wang¹,

Zhang²,

Zhang³

et al. 2021

Preprint

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Recently, the information-theoretical framework has been proven to be able to obtain non-vacuous generalization bounds for large models trained by Stochastic Gradient Langevin Dynamics (SGLD) with isotropic noise. In this paper, we optimize the information-theoretical generalization bound by manipulating the noise structure in SGLD. We prove that with constraint to guarantee low empirical risk, the optimal noise covariance is the square root of the expected gradient covariance if both the prior and the posterior are jointly optimized. This validates that the optimal noise is quite close to the empirical gradient covariance. Technically, we develop a new information-theoretical bound that enables such an optimization analysis. We then apply matrix analysis to derive the form of optimal noise covariance. Presented constraint and results are validated by the empirical observations.

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Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data

Cited by 64 publications

References 0 publications

Learning Provably Robust Motion Planners Using Funnel Libraries

Learning Provably Robust Motion Planners Using Funnel Libraries

Interactive Dynamic Walking: Learning Gait Switching Policies with Generalization Guarantees

Optimizing Information-theoretical Generalization Bounds via Anisotropic Noise in SGLD

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