相关论文: Maximum a Posteriori State Path Estimation: Discre…

We study the $(\varepsilon, \delta)$-PAC policy identification problem in finite-horizon episodic Markov Decision Processes. Existing approaches provide finite-time guarantees for approximate settings ($\varepsilon>0$) but suffer from high…

In this paper, we propose a compositional approach for the construction of finite abstractions (a.k.a. finite Markov decision processes (MDPs)) for networks of discrete-time stochastic control subsystems that are not necessarily…

Sum-product networks (SPNs) are a class of probabilistic graphical models that allow tractable marginal inference. However, the maximum a posteriori (MAP) inference in SPNs is NP-hard. We investigate MAP inference in SPNs from both…

The framework of differential inclusions encompasses modern optimal control and the calculus of variations. Necessary optimality conditions in the literature identify potentially optimal paths, but do not show how to perturb paths to…

We consider the inverse problem of recovering an unknown functional parameter $u$ in a separable Banach space, from a noisy observation $y$ of its image through a known possibly non-linear ill-posed map ${\mathcal G}$. The data $y$ is…

The Dirichlet process mixture (DPM) is a ubiquitous, flexible Bayesian nonparametric statistical model. However, full probabilistic inference in this model is analytically intractable, so that computationally intensive techniques such as…

We propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…

We propose and analyze an a posteriori error estimator for a PDE-constrained optimization problem involving a nondifferentiable cost functional, fractional diffusion, and control-constraints. We realize fractional diffusion as the…

Maximum A Posteriori (MAP) estimation is a cornerstone framework for blind inverse problems, where an image and a forward operator are jointly estimated as the maximizers of a posterior distribution. In this paper, we analyze the recovery…

A classical problem in digital communications is to evaluate the symbol error probability (SEP) and bit error probability (BEP) of a multidimensional constellation over an additive white Gaussian noise channel. In this paper, we revisit…

We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…

Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…

In this paper, we consider a class of continuous-time, continuous-space stochastic optimal control problems. Building upon recent advances in Markov chain approximation methods and sampling-based algorithms for deterministic path planning,…

The minimization of operation costs for natural gas transport networks is studied. Based on a recently developed model hierarchy ranging from detailed models of instationary partial differential equations with temperature dependence to…

This paper addresses a new class of optimal control problems for perturbed sweeping processes with measurable controls in additive perturbations of the dynamics and smooth controls in polyhedral moving sets. We develop a constructive…

Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…

We consider the task of obtaining the maximum a posteriori estimate of discrete pairwise random fields with arbitrary unary potentials and semimetric pairwise potentials. For this problem, we propose an accurate hierarchical move making…

The present study proposes incorporating non-parametric knowledge into the diffusion least-mean-squares algorithm in the framework of a maximum a posteriori (MAP) estimation. The proposed algorithm leads to a robust estimation of an unknown…

Maximum entropy (maxEnt) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic dynamical systems, the effect of state space topology and path-dependent constraints on…

A class of linear parabolic equations are considered. We give a posteriori error estimates in the maximum norm for a method that comprises extrapolation applied to the backward Euler method in time and finite element discretisations in…