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Shallow Representation is Deep: Learning Uncertainty-aware and Worst-case Random Feature Dynamics

arXiv 2106.13066 ↗First posted 24 Jun 2021cs.LG cs.SY eess.SYcited by 0

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Abstract (arXiv)

Random features is a powerful universal function approximator that inherits the theoretical rigor of kernel methods and can scale up to modern learning tasks. This paper views uncertain system models as unknown or uncertain smooth functions in universal reproducing kernel Hilbert spaces. By directly approximating the one-step dynamics function using random features with uncertain parameters, which are equivalent to a shallow Bayesian neural network, we then view the whole dynamical system as a multi-layer neural network. Exploiting the structure of Hamiltonian dynamics, we show that finding worst-case dynamics realizations using Pontryagin's minimum principle is equivalent to performing the Frank-Wolfe algorithm on the deep net. Various numerical experiments on dynamics learning showcase the capacity of our modeling methodology.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 23 of its 40 references that are in the map. First posted on arXiv 24 Jun 2021.

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23 of 40 references.

References · 23

  1. 2018Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Modelscited by 774
  2. 2019Surprises in High-Dimensional Ridgeless Least Squares Interpolationcited by 513
  3. 2019The generalization error of random features regression: Precise asymptotics and double descent curvecited by 413
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  9. 2016Generalization Properties of Learning with Random Featurescited by 164
  10. 2020Efficiently Sampling Functions from Gaussian Process Posteriorscited by 127
  11. 2018Learning-based Model Predictive Control for Safe Explorationcited by 120
  12. 2020Random Features for Kernel Approximation: A Survey on Algorithms, Theory, and Beyondcited by 109
11 more
  1. 2017Cautious Model Predictive Control using Gaussian Process Regressioncited by 91
  2. 2017Maximum Principle Based Algorithms for Deep Learningcited by 78
  3. 2017Data-Efficient Reinforcement Learning with Probabilistic Model Predictive Controlcited by 53
  4. 2019Machine Learning from a Continuous Viewpointcited by 50
  5. 2014Scalable Kernel Methods via Doubly Stochastic Gradientscited by 36
  6. 2018Approximation beats concentration? An approximation view on inference with smooth radial kernelscited by 33
  7. 2018Learning with SGD and Random Featurescited by 33
  8. 2014Randomized Nonlinear Component Analysiscited by 18
  9. 2019On Simulation and Trajectory Prediction with Gaussian Process Dynamicscited by 11
  10. 2020Sampling-based Reachability Analysis: A Random Set Theory Approach with Adversarial Samplingcited by 11
  11. 2020Meta Learning MPC using Finite-Dimensional Gaussian Process Approximationscited by 8

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