Related papers: The Stein hull
We propose a new risk-constrained formulation of the classical Linear Quadratic (LQ) stochastic control problem for general partially-observed systems. Our framework is motivated by the fact that the risk-neutral LQ controllers, although…
We introduce a hull operator on Poisson point processes, the easiest example being the convex hull of the support of a point process in Euclidean space. Assuming that the intensity measure of the process is known on the set generated by the…
The Wallace--Freeman estimator is a classical invariant point estimator whose large-sample properties have not been fully developed in a modern asymptotic framework. We show that the estimator can be formulated as a penalised M-estimator…
In this paper we develop a stochastic heavy ball method for solving ill-posed inverse problems. The method updates the iterate using only a randomly selected equation at each iteration step while incorporating a momentum term into the…
In this paper we consider the contextual multi-armed bandit problem for linear payoffs under a risk-averse criterion. At each round, contexts are revealed for each arm, and the decision maker chooses one arm to pull and receives the…
This paper focuses on stochastic optimal control problems with constraints in law, which are rewritten as optimization (minimization) of probability measures problem on the canonical space. We introduce a penalized version of this type of…
To recover a low rank structure from a noisy matrix, truncated singular value decomposition has been extensively used and studied. Recent studies suggested that the signal can be better estimated by shrinking the singular values. We pursue…
We consider a statistical inverse learning problem, where the task is to estimate a function $f$ based on noisy point evaluations of $Af$, where $A$ is a linear operator. The function $Af$ is evaluated at i.i.d. random design points $u_n$,…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
In this paper we present nonparametric estimators for coefficients in stochastic differential equation if the data are described by independent, identically distributed random variables. The problem is formulated as a nonlinear ill-posed…
We study stochastic linear optimization problem with bandit feedback. The set of arms take values in an $N$-dimensional space and belong to a bounded polyhedron described by finitely many linear inequalities. We provide a lower bound for…
We consider the problem of automatic variable selection in a linear model with asymmetric or heavy-tailed errors when the number of explanatory variables diverges with the sample size. For this high-dimensional model, the penalized least…
We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. Focusing on a stochastic query model that provides noisy evaluations of the operator, we analyze a variance-reduced stochastic…
Our focus is on robust recovery algorithms in statistical linear inverse problem. We consider two recovery routines - the much studied linear estimate originating from Kuks and Olman [42] and polyhedral estimate introduced in [37]. It was…
Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we apply this…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
Tuning parameters are parameters involved in an estimating procedure for the purpose of reducing the risk of some other estimator. Examples include the degree of penalization in penalized regression and likelihood problems, as well as the…
The safe linear bandit problem is a version of the classical stochastic linear bandit problem where the learner's actions must satisfy an uncertain constraint at all rounds. Due its applicability to many real-world settings, this problem…
We discuss a number of estimates of the hazard under the assumption that the hazard is monotone on an interval [0,a]. The usual isotonic least squares estimators of the hazard are inconsistent at the boundary points 0 and a. We use…
The Receding Horizon Control (RHC) strategy consists in replacing an infinite-horizon stabilization problem by a sequence of finite-horizon optimal control problems, which are numerically more tractable. The dynamic programming principle…