相关论文: Analysis and Optimisation of Bellman Residual Erro…

Previous theoretical work on deep learning and neural network optimization tend to focus on avoiding saddle points and local minima. However, the practical observation is that, at least in the case of the most successful Deep Convolutional…

We analyze a fixed-point algorithm for reinforcement learning (RL) of optimal portfolio mean-variance preferences in the setting of multivariate generalized autoregressive conditional-heteroskedasticity (MGARCH) with a small penalty on…

In spite of the accomplishments of deep learning based algorithms in numerous applications and very broad corresponding research interest, at the moment there is still no rigorous understanding of the reasons why such algorithms produce…

Offline Reinforcement Learning (RL) aims to learn a near-optimal policy from a fixed dataset of transitions collected by another policy. This problem has attracted a lot of attention recently, but most existing methods with strong…

Remote state estimation of large-scale distributed dynamic processes plays an important role in Industry 4.0 applications. In this paper, by leveraging the theoretical results of structural properties of optimal scheduling policies, we…

We study representation learning for Offline Reinforcement Learning (RL), focusing on the important task of Offline Policy Evaluation (OPE). Recent work shows that, in contrast to supervised learning, realizability of the Q-function is not…

We present practical Levenberg-Marquardt variants of Gauss-Newton and natural gradient methods for solving non-convex optimization problems that arise in training deep neural networks involving enormous numbers of variables and huge data…

This paper proposes a set of new error criteria and learning approaches, Adaptive Normalized Risk-Averting Training (ANRAT), to attack the non-convex optimization problem in training deep neural networks (DNNs). Theoretically, we…

First-order methods like stochastic gradient descent(SGD) are recently the popular optimization method to train deep neural networks (DNNs), but second-order methods are scarcely used because of the overpriced computing cost in getting the…

We propose a scalable preconditioned primal-dual hybrid gradient algorithm for solving partial differential equations (PDEs). We multiply the PDE with a dual test function to obtain an inf-sup problem whose loss functional involves…

In deep learning, fine-grained N:M sparsity reduces the data footprint and bandwidth of a General Matrix multiply (GEMM) up to x2, and doubles throughput by skipping computation of zero values. So far, it was mainly only used to prune…

The optimization foundations of deep linear networks have recently received significant attention. However, due to their inherent non-convexity and hierarchical structure, analyzing the loss functions of deep linear networks remains a…

In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…

In this paper, we consider approximating the parameter-to-solution maps of parametric partial differential equations (PPDEs) using deep neural networks (DNNs). We propose an efficient approach combining reduced collocation methods (RCMs)…

This paper develops fundamental limits of deep neural network learning by characterizing what is possible if no constraints are imposed on the learning algorithm and on the amount of training data. Concretely, we consider Kolmogorov-optimal…

Function approximation has been an indispensable component in modern reinforcement learning algorithms designed to tackle problems with large state spaces in high dimensions. This paper reviews recent results on error analysis for these…

We explore why many recently proposed robust estimation problems are efficiently solvable, even though the underlying optimization problems are non-convex. We study the loss landscape of these robust estimation problems, and identify the…

This paper aims to overcome a fundamental problem in the theory and application of deep neural networks (DNNs). We propose a method to solve the local minimum problem in training DNNs directly. Our method is based on the cross-entropy loss…

Verification of Neural Networks (NNs) that approximate the solution of Partial Differential Equations (PDEs) is a major milestone towards enhancing their trustworthiness and accelerating their deployment, especially for safety-critical…

Deep learning is mainly based on utilizing gradient-based optimization for training Deep Neural Network (DNN) models. Although robust and widely used, gradient-based optimization algorithms are prone to getting stuck in local minima. In…