Related papers: A comparison study of supervised learning techniqu…

High-dimensional reinforcement learning(RL) faces challenges with complex calculations and low sample efficiency in large state-action spaces. Q-learning algorithms struggle particularly with the curse of dimensionality, where the number of…

As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…

We revisit the classical kernel method of approximation/interpolation theory in a very specific context motivated by the desire to obtain a robust procedure to approximate discrete data sets by (super)level sets of functions that are merely…

A gradient-enhanced functional tensor train cross approximation method for the resolution of the Hamilton-Jacobi-Bellman (HJB) equations associated to optimal feedback control of nonlinear dynamics is presented. The procedure uses samples…

We explore unique considerations involved in fitting ML models to data with very high precision, as is often required for science applications. We empirically compare various function approximation methods and study how they scale with…

We present a method that allows efficient and safe approximation of model predictive controllers using kernel interpolation. Since the computational complexity of the approximating function scales linearly with the number of data points, we…

Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well-developed, the relative efficacy of different approaches in finite-sample…

Reinforcement learning (RL) algorithms have proven transformative in a range of domains. To tackle real-world domains, these systems often use neural networks to learn policies directly from pixels or other high-dimensional sensory input.…

High-dimensional representations, such as radial basis function networks or tile coding, are common choices for policy evaluation in reinforcement learning. Learning with such high-dimensional representations, however, can be expensive,…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

The State-Dependent Riccati Equation (SDRE) approach is extensively utilized in nonlinear optimal control as a reliable framework for designing robust feedback control strategies. This work provides an analysis of the SDRE approach,…

Computational models are quantitative representations of systems. By analyzing and comparing the outputs of such models, it is possible to gain a better understanding of the system itself. Though as the complexity of model outputs…

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective. The emphasis is put on discrete representations, where the description length can be measured in bits and…

Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…

The empirical success of deep convolutional networks on tasks involving high-dimensional data such as images or audio suggests that they can efficiently approximate certain functions that are well-suited for such tasks. In this paper, we…

Deep learning techniques have been widely applied, achieving state-of-the-art results in various fields of study. This survey focuses on deep learning solutions that target learning control policies for robotics applications. We carry out…

In this article, we review the literature on statistical theories of neural networks from three perspectives: approximation, training dynamics and generative models. In the first part, results on excess risks for neural networks are…

Model Predictive Controllers (MPC) are widely used for controlling cyber-physical systems. It is an iterative process of optimizing the prediction of the future states of a robot over a fixed time horizon. MPCs are effective in practice,…

Random feature approximation is arguably one of the most widely used techniques for kernel methods in large-scale learning algorithms. In this work, we analyze the generalization properties of random feature methods, extending previous…