• Corpus ID: 227227752

Uncertainty Quantification in Deep Learning through Stochastic Maximum Principle

  title={Uncertainty Quantification in Deep Learning through Stochastic Maximum Principle},
  author={Richard Archibald and Feng Bao and Yanzhao Cao and He Zhang},
We develop a probabilistic machine learning method, which formulates a class of stochastic neural networks by a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced under the stochastic maximum principle framework. Convergence analysis for stochastic gradient descent optimization and numerical experiments for applications of stochastic neural networks are carried out to validate our methodology in both theory and performance. 



Bayesian Learning via Stochastic Gradient Langevin Dynamics

In this paper we propose a new framework for learning from large scale datasets based on iterative learning from small mini-batches. By adding the right amount of noise to a standard stochastic

A mean-field optimal control formulation of deep learning

This paper introduces the mathematical formulation of the population risk minimization problem in deep learning as a mean-field optimal control problem, and state and prove optimality conditions of both the Hamilton–Jacobi–Bellman type and the Pontryagin type.

Bayesian Optimization with Robust Bayesian Neural Networks

This work presents a general approach for using flexible parametric models (neural networks) for Bayesian optimization, staying as close to a truly Bayesian treatment as possible and obtaining scalability through stochastic gradient Hamiltonian Monte Carlo, whose robustness is improved via a scale adaptation.

An Efficient Gradient Projection Method for Stochastic Optimal Control Problems

This work first reduces the optimal control problem to an optimization problem for a convex functional by means of a projection operator, and proposes a convergent iterative scheme for the optimization problem.

SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimates

A new method for quantifying uncertainties of DNNs from a dynamical system perspective and introduces a Brownian motion term for capturing epistemic uncertainty, which can outperform existing uncertainty estimation methods across a series of tasks where uncertainty plays a fundamental role.

Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks

This work presents a novel scalable method for learning Bayesian neural networks, called probabilistic backpropagation (PBP), which works by computing a forward propagation of probabilities through the network and then doing a backward computation of gradients.

Stable Architectures for Deep Neural Networks

This paper relates the exploding and vanishing gradient phenomenon to the stability of the discrete ODE and presents several strategies for stabilizing deep learning for very deep networks.

SBEED: Convergent Reinforcement Learning with Nonlinear Function Approximation

This paper revisits the Bellman equation, and reformulate it into a novel primal-dual optimization problem using Nesterov’s smoothing technique and the Legendre-Fenchel transformation, and develops a new algorithm, called Smoothed Bellman Error Embedding, to solve this optimization problem where any differentiable function class may be used.

Neural Ordinary Differential Equations

This work shows how to scalably backpropagate through any ODE solver, without access to its internal operations, which allows end-to-end training of ODEs within larger models.

Solving high-dimensional partial differential equations using deep learning

A deep learning-based approach that can handle general high-dimensional parabolic PDEs using backward stochastic differential equations and the gradient of the unknown solution is approximated by neural networks, very much in the spirit of deep reinforcement learning with the gradient acting as the policy function.