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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…

Motivated by the success of reinforcement learning (RL) for discrete-time tasks such as AlphaGo and Atari games, there has been a recent surge of interest in using RL for continuous-time control of physical systems (cf. many challenging…

Measure transport underpins several recent algorithms for posterior approximation in the Bayesian context, wherein a transport map is sought to minimise the Kullback--Leibler divergence (KLD) from the posterior to the approximation. The KLD…

We introduce a new variational approach to the stationary state of kinetic Ising-like models. The approach is based on the cluster expansion of the entropy term appearing in a functional which is minimized by the system history. We rederive…

Approximate Dynamic Programming (ADP) is a methodology to solve multi-stage stochastic optimization problems in multi-dimensional discrete or continuous spaces. ADP approximates the optimal value function by adaptively sampling both action…

Large-scale Markov decision processes (MDPs) require planning algorithms with runtime independent of the number of states of the MDP. We consider the planning problem in MDPs using linear value function approximation with only weak…

Dealing with massive data is a challenging task for machine learning. An important aspect of machine learning is function approximation. In the context of massive data, some of the commonly used tools for this purpose are sparsity,…

We consider the global minimization of smooth functions based solely on function evaluations. Algorithms that achieve the optimal number of function evaluations for a given precision level typically rely on explicitly constructing an…

A novel algorithm is proposed to solve the sample-based optimal transport problem. An adversarial formulation of the push-forward condition uses a test function built as a convolution between an adaptive kernel and an evolving probability…

Euclidean Markov decision processes are a powerful tool for modeling control problems under uncertainty over continuous domains. Finite state imprecise, Markov decision processes can be used to approximate the behavior of these infinite…

Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…

The lack of sufficient flexibility is the key bottleneck of kernel-based learning that relies on manually designed, pre-given, and non-trainable kernels. To enhance kernel flexibility, this paper introduces the concept of…

Calculating optimal policies is known to be computationally difficult for Markov decision processes (MDPs) with Borel state and action spaces. This paper studies finite-state approximations of discrete time Markov decision processes with…

Most commonly used \emph{adaptive} algorithms for univariate real-valued function approximation and global minimization lack theoretical guarantees. Our new locally adaptive algorithms are guaranteed to provide answers that satisfy a…

A data driven, kernel-based method for approximating the leading Koopman eigenvalues, eigenfunctions, and modes in problems with high dimensional state spaces is presented. This approach approximates the Koopman operator using a set of…

For many machine learning problem settings, particularly with structured inputs such as sequences or sets of objects, a distance measure between inputs can be specified more naturally than a feature representation. However, most standard…

Continuous-time reinforcement learning (CTRL) provides a principled framework for sequential decision-making in environments where interactions evolve continuously over time. Despite its empirical success, the theoretical understanding of…

Feedback particle filter (FPF) is a numerical algorithm to approximate the solution of the nonlinear filtering problem in continuous-time settings. In any numerical implementation of the FPF algorithm, the main challenge is to numerically…

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…

Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by…