Related papers: A comparison study of supervised learning techniqu…

In a regression setting we propose algorithms that reduce the dimensionality of the features while simultaneously maximizing a statistical measure of dependence known as distance correlation between the low-dimensional features and a…

In this work we establish the relation between optimal control and training deep Convolution Neural Networks (CNNs). We show that the forward propagation in CNNs can be interpreted as a time-dependent nonlinear differential equation and…

Accurate Monte Carlo (MC) modelling in high-energy physics is challenging, particularly in complex scenarios where simulations fail to reproduce observed data. In practice, experimental information is often limited to one-dimensional (1D)…

Optimal control of diffusion processes is intimately connected to the problem of solving certain Hamilton-Jacobi-Bellman equations. Building on recent machine learning inspired approaches towards high-dimensional PDEs, we investigate the…

Policy gradient methods are among the most effective methods in challenging reinforcement learning problems with large state and/or action spaces. However, little is known about even their most basic theoretical convergence properties,…

We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…

Semisupervised methods inevitably invoke some assumption that links the marginal distribution of the features to the regression function of the label. Most commonly, the cluster or manifold assumptions are used which imply that the…

Reinforcement learning (RL) aims to estimate the action to take given a (time-varying) state, with the goal of maximizing a cumulative reward function. Predominantly, there are two families of algorithms to solve RL problems: value-based…

Machine learning is at the heart of managing the real-world problems associated with massive data. With the success of neural networks on such large-scale problems, more research in machine learning is being conducted now than ever before.…

We focus on developing efficient and reliable policy optimization strategies for robot learning with real-world data. In recent years, policy gradient methods have emerged as a promising paradigm for training control policies in simulation.…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

Complex systems in science and engineering sometimes exhibit behavior that changes across different regimes. Traditional global models struggle to capture the full range of this complex behavior, limiting their ability to accurately…

Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…

This thesis reviews numerical optimization methods with machine learning problems in mind. Since machine learning models are highly parametrized, we focus on methods suited for high dimensional optimization. We build intuition on quadratic…

We provide performance guarantees for a variant of simulation-based policy iteration for controlling Markov decision processes that involves the use of stochastic approximation algorithms along with state-of-the-art techniques that are…

We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural…

Deep neural networks have achieved strong performance in image classification tasks due to their ability to learn complex patterns from high-dimensional data. However, their large computational and memory requirements often limit deployment…

We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…

This paper deals with a class of neural SDEs and studies the limiting behavior of the associated sampled optimal control problems as the sample size grows to infinity. The neural SDEs with $N$ samples can be linked to the $N$-particle…

In general, approximating classes of functions defined over high-dimensional input spaces by linear combinations of a fixed set of basis functions or ``features'' is known to be hard. Typically, the worst-case error of the best basis set…