Related papers: Convex function approximations for Markov decision…

The self-concordant-like property of a smooth convex function is a new analytical structure that generalizes the self-concordant notion. While a wide variety of important applications feature the self-concordant-like property, this concept…

This paper studies the approximation of optimal control policies by quantized (discretized) policies for a very general class of Markov decision processes (MDPs). The problem is motivated by applications in networked control systems,…

This paper is devoted to the convergence analysis of stochastic approximation algorithms of the form $\theta\_{n+1} = \theta\_n + \gamma\_{n+1} H\_{\theta\_n}(X\_{n+1})$ where $\{\theta\_nn, n \geq 0\}$ is a $R^d$-valued sequence,…

Malleable scheduling is a model that captures the possibility of parallelization to expedite the completion of time-critical tasks. A malleable job can be allocated and processed simultaneously on multiple machines, occupying the same time…

We study the problem of learning optimal policies in finite-horizon Markov Decision Processes (MDPs) using low-rank reinforcement learning (RL) methods. In finite-horizon MDPs, the policies, and therefore the value functions (VFs) are not…

In this paper, we study darning of general symmetric Markov processes by shorting some parts of the state space into singletons. A natural way to construct such processes is via Dirichlet forms restricted to the function space whose members…

The present paper provides a generalization of the previous authors' work on Bellman functions for integral functionals on $\mathrm{BMO}$. Those Bellman functions are the minimal locally concave functions on parabolic strips in the plane.…

The formal verification and controller synthesis for Markov decision processes that evolve over uncountable state spaces are computationally hard and thus generally rely on the use of approximations. In this work, we consider the…

This paper proposes to decouple performance optimization and enforcement of asymptotic convergence in Model Predictive Control (MPC) so that convergence to a given terminal set is achieved independently of how much performance is optimized…

We are interested in risk constraints for infinite horizon discrete time Markov decision processes (MDPs). Starting with average reward MDPs, we show that increasing concave stochastic dominance constraints on the empirical distribution of…

We consider a discrete-time Markov decision process with Borel state and action spaces. The performance criterion is to maximize a total expected {utility determined by unbounded return function. It is shown the existence of optimal…

In this paper, we consider the gradual-impulse control problem of continuous-time Markov decision processes, where the system performance is measured by the expectation of the exponential utility of the total cost. We prove, under very…

We present convergence and error estimates of the time-discrete consensus-based optimization(CBO) algorithms proposed in [arXiv:1909.09249] for general nonconvex functions. In authors' recent work [arxiv: 1910.08239], rigorous error…

We provide a general framework to construct finite dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies. We give estimates…

In this work, we describe a generic approach to show convergence with high probability for stochastic convex optimization. In previous works, either the convergence is only in expectation or the bound depends on the diameter of the domain.…

In this paper we consider a broad class of infinite horizon discrete-time optimal control models that involve a nonnegative cost function and an affine mapping in their dynamic programming equation. They include as special cases classical…

The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method,…

We study time-changed Markov processes to speed up the convergence of Markov chain Monte Carlo (MCMC) algorithms. The time-changed process is defined by adjusting the speed of time of a base process via a user-chosen, state-dependent…

This paper deals with the optimal stopping problem under partial observation for piecewise-deterministic Markov processes. We first obtain a recursive formulation of the optimal filter process and derive the dynamic programming equation of…

This paper deals with control of partially observable discrete-time stochastic systems. It introduces and studies Markov Decision Processes with Incomplete Information and with semi-uniform Feller transition probabilities. The important…