Related papers: Bicausal Optimal Transport for Markov Chains via D…
This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex…
Important pricing problems in centralized matching markets -- such as carpooling, food delivery and freight shipping platforms -- often exhibit a bi-level structure. At the upper level, the platform sets prices for heterogeneous demand…
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…
A new pairwise cost function is proposed for the optimal transport barycenter problem, adopting the form of the minimal action between two points, with a Lagrangian that takes into account an underlying probability distribution. Under this…
We study optimal control problems in infinite horizon when the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (inspired by traffic models). We adapt the results in [H. M.…
We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…
We consider the problem of finding optimal strategies that maximize the average growth-rate of multiplicative stochastic processes. For a geometric Brownian motion the problem is solved through the so-called Kelly criterion, according to…
Couplings play a central role in contemporary Markov chain Monte Carlo methods and in the analysis of their convergence to stationarity. In most cases, a coupling must induce relatively fast meeting between chains to ensure good…
Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted…
In this paper, we consider the classic stochastic (dynamic) knapsack problem, a fundamental mathematical model in revenue management, with general time-varying random demand. Our main goal is to study the optimal policies, which can be…
As the automotive industry is developing autonomous driving systems and vehicular networks, attention to truck platooning has increased as a way to reduce costs (fuel consumption) and improve efficiency in the highway. Recent research in…
Optimal transport aims to learn a mapping of sources to targets by minimizing the cost, which is typically defined as a function of distance. The solution to this problem consists of straight line segments optimally connecting sources to…
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 here a general framework and a specific algorithm for predicting the destination, route, or more generally a pattern, of an ongoing journey, building on the recent work of [Y. Lassoued, J. Monteil, Y. Gu, G. Russo, R. Shorten,…
This paper considers the relaxed version of the transport problem for general nonlinear control systems, where the objective is to design time-varying feedback laws that transport a given initial probability measure to a target probability…
A new approach for optimal estimation of Markov chains with sparse transition matrices is presented.
In this paper we revisit a class of optimal transport problems associated to non-autonomous linear control systems. Building on properties of the cost functions on $\mathbb{R}^{d}\times\mathbb{R}^{d}$ derived from suitable variational…
Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold. In…
In this paper, we introduce a class of indicators that enable to compute efficiently optimal transport plans associated to arbitrary distributions of N demands and M supplies in R in the case where the cost function is concave. The…
This paper presents a new condition for the existence of optimal stationary policies in average-cost continuous-time Markov decision processes with unbounded cost and transition rates, arising from controlled queueing systems. This…