相关论文: Approximation and Exactness in Finite State Optima…

The infinite horizon setting is widely adopted for problems of reinforcement learning (RL). These invariably result in stationary policies that are optimal. In many situations, finite horizon control problems are of interest and for such…

We demonstrate the use of a new, control-oriented notion of finite state approximation for a particular class of hybrid systems. Specifically, we consider the problem of designing a stabilizing binary output feedback switching controller…

We extend the convergence analysis of the Scholtes-type regularization method for cardinality-constrained optimization problems. Its behavior is clarified in the vicinity of saddle points, and not just of minimizers as it has been done in…

This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…

We investigate the problem of optimally approximating a desired state by the convex mixing of a set of available states. The problem is recasted as finding the optimal state with the minimum distance from target state in a convex set of…

A novel Policy Gradient (PG) algorithm, called $\textit{Matryoshka Policy Gradient}$ (MPG), is introduced and studied, in the context of fixed-horizon max-entropy reinforcement learning, where an agent aims at maximizing entropy bonuses…

LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…

The local Hamiltonian problem consists of estimating the ground-state energy (given by the minimum eigenvalue) of a local quantum Hamiltonian. First, we show the existence of a good product-state approximation for the ground-state energy of…

Entropy regularization is an efficient technique for encouraging exploration and preventing a premature convergence of (vanilla) policy gradient methods in reinforcement learning (RL). However, the theoretical understanding of…

This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…

We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…

The second part of our study is devoted to an analysis of the exactness of penalty functions for optimal control problems with terminal and pointwise state constraints. We demonstrate that with the use of the exact penalty function method…

This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…

Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian…

Bernstein polynomial approximation to a continuous function has a slower rate of convergence as compared to other approximation methods. "The fact seems to have precluded any numerical application of Bernstein polynomials from having been…

This paper is concerned with the discretization error analysis of semilinear Neumann boundary control problems in polygonal domains with pointwise inequality constraints on the control. The approximations of the control are piecewise…

An open question contributed by Yu. Orlov to a recently published volume "Unsolved Problems in Mathematical Systems and Control Theory", V.D. Blondel, A. Megretski (eds), Princeton Univ. Press, 2004, concerns regularization of optimal…

This paper presents a theoretical discussion on Ruttan's optimality conditions for rational minimax approximations in discrete and continuum settings, integrating analytical foundations with computational practice. We develop extended…

This paper studies equality-constrained composite minimization problems. This class of problems, capturing regularization terms and inequality constraints, naturally arises in a wide range of engineering and machine learning applications.…

We study a cardinality-constrained optimization problem with nonnegative variables in this paper. This problem is often encountered in practice. Firstly we study some properties on the optimal solutions of this optimization problem under…