Related papers: Impulse control maximising average cost per unit t…

We consider the problem of estimating the possibly non-convex cost of an agent by observing its interactions with a nonlinear, non-stationary and stochastic environment. For this inverse problem, we give a result that allows to estimate the…

We consider partially observable Markov decision processes (POMDPs) with a set of target states and every transition is associated with an integer cost. The optimization objective we study asks to minimize the expected total cost till the…

To profit from price oscillations, investors frequently use threshold-type strategies where changes in the portfolio position are triggered by some indicators reaching prescribed levels. In this paper, we investigate threshold-type…

In this paper, we propose a novel solution for the distributed unconstrained optimization problem where the total cost is the summation of time-varying local cost functions of a group networked agents. The objective is to track the optimal…

Equidistant and non-equidistant single pulse "bang-bang" dynamical controls are investigated in the context of mean ergodic theorems. We show the requirements in which the limit of infinite pulse control for both the equidistant and the…

Let $a_n$ be the random increasing sequence of natural numbers which takes each value independently with decreasing probability of order $n^{-\alpha}$, $0 < \alpha < 1/2$. We prove that, almost surely, for every measure-preserving system…

Using the tools of the Markov Decision Processes, we justify the dynamic programming approach to the optimal impulse control of deterministic dynamical systems. We prove the equivalence of the integral and differential forms of the…

Let $X:=(X_t)_{t\geq 0}$ be an ergodic Markov process on $\real^d$, and $p>0$. We derive upper bounds of the $p$-Wasserstein distance between the invariant measure and the empirical measures of the Markov process $X$. For this we assume,…

This paper solves a Bayes sequential impulse control problem for a diffusion, whose drift has an unobservable parameter with a change point. The partially-observed problem is reformulated into one with full observations, via a change of…

Inverse Optimal Control (IOC) is a powerful framework for learning a behaviour from observations of experts. The framework aims to identify the underlying cost function that the observed optimal trajectories (the experts' behaviour) are…

For a Markov decision process with countably infinite states, the optimal value may not be achievable in the set of stationary policies. In this paper, we study the existence conditions of an optimal stationary policy in a countable-state…

We study the optimization of ergodic averages for multi-valued dynamical systems, i.e. where points may have multiple different forward orbits. Under upper semi-continuity assumptions, we show that the maximum space average with respect to…

This paper addresses the inverse optimal control problem of finding the state weighting function that leads to a quadratic value function when the cost on the input is fixed to be quadratic. The paper focuses on a class of infinite horizon…

As is well known, average-cost optimality inequalities imply the existence of stationary optimal policies for Markov Decision Processes with average costs per unit time, and these inequalities hold under broad natural conditions. This paper…

Dynamic capacity allocation control for resource sharing networks (RSN) is studied when the networks are in heavy traffic. The goal is to minimize an ergodic cost with a linear holding cost function. Our main result shows that the optimal…

This paper presents a numerical method to calculate the value function for a general discounted impulse control problem for piecewise deterministic Markov processes. Our approach is based on a quantization technique for the underlying…

This paper is concerned with ergodic properties of inhomogeneous Markov processes. Since the transition probabilities depend on initial times, the existing methods to obtain invariant measures for homogeneous Markov processes are not…

Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. For a wide class of intrinsically ergodic subshifts over a finite alphabet, we show that the space of…

Motivated by applications in natural resource management, risk management, and finance, this paper is focused on an ergodic two-sided singular control problem for a general one-dimensional diffusion process. The control is given by a…

The classical Birkhoff ergodic theorem states that for an ergodic Markov process the limiting behaviour of the time average of a function (having finite $p$-th moment, $p\ge1$, with respect to the invariant measure) along the trajectories…