Related papers: Solving Dynamic Discrete Choice Models Using Smoot…
We study the problem of estimating Dynamic Discrete Choice (DDC) models, also known as offline Maximum Entropy-Regularized Inverse Reinforcement Learning (offline MaxEnt-IRL) in machine learning. The objective is to recover reward or $Q^*$…
Randomized methods, such as the randomized SVD (singular value decomposition) and Nystr\"om approximation, are an effective way to compute low-rank approximations of large matrices. Motivated by applications to operator learning, Boull\'e…
In this paper, we analyse piecewise deterministic Markov processes, as introduced in Davis (1984). Many models in insurance mathematics can be formulated in terms of the general concept of piecewise deterministic Markov processes. In this…
In this paper we address the convergence of stochastic approximation when the functions to be minimized are not convex and nonsmooth. We show that the "mean-limit" approach to the convergence which leads, for smooth problems, to the ODE…
We present a de Bruijn type approximation for quantifying the content of m smooth numbers, derived from samples obtained through a probability measure over the set of integers less than or equal to n, with point mass function at k inversely…
This paper studies function approximation for finite horizon discrete time Markov decision processes under certain convexity assumptions. Uniform convergence of these approximations on compact sets is proved under several sampling schemes…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
We present the first finite-sample analysis of policy evaluation in robust average-reward Markov Decision Processes (MDPs). Prior work in this setting have established only asymptotic convergence guarantees, leaving open the question of…
Taylor's formula holds significant importance in function representation, such as solving differential difference equations, ordinary differential equations, partial differential equations, and further promotes applications in visual…
We analyze the performance of Dynamic Mode Decomposition (DMD)-based approximations of the stochastic Koopman operator for random dynamical systems where either the dynamics or observables are affected by noise. For many DMD algorithms, the…
In this paper, we introduce some adaptive methods for solving variational inequalities with relatively strongly monotone operators. Firstly, we focus on the modification of the recently proposed, in smooth case [1], adaptive numerical…
We describe an approximate dynamic programming approach to compute lower bounds on the optimal value function for a discrete time, continuous space, infinite horizon setting. The approach iteratively constructs a family of lower bounding…
The paper is devoted to the study of a new class of optimal control problems for nonsmooth dynamical systems governed by nonconvex discontinuous differential inclusions of the sweeping type with involving variable time into optimization. We…
We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…
We propose universal randomized function approximation-based empirical value iteration (EVI) algorithms for Markov decision processes. The `empirical' nature comes from each iteration being done empirically from samples available from…
This paper deals with convex nonsmooth optimization problems. We introduce a general smooth approximation framework for the original function and apply random (accelerated) coordinate descent methods for minimizing the corresponding smooth…
Dynamic discrete choice models often discretize the state vector and restrict its dimension in order to achieve valid inference. I propose a novel two-stage estimator for the set-identified structural parameter that incorporates a…
When approximating the expectations of a functional of a solution to a stochastic differential equation, the numerical performance of deterministic quadrature methods, such as sparse grid quadrature and quasi-Monte Carlo (QMC) methods, may…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…
The commonly used velocity discretization for simulating the radiative transport equation (RTE) is the discrete ordinates method (DOM). One of the long-standing drawbacks of DOM is the phenomenon known as the ray effect. Due to the high…