Related papers: Optimal single threshold stopping rules and sharp …
We study matroid prophet inequalities when distributions are unknown and accessible only through samples. While single-sample prophet inequalities for special matroids are known, no constant-factor competitive algorithm with even a…
We study the ergodicity of deterministic two-person zero-sum differential games. This property is defined by the uniform convergence to a constant of either the infinite-horizon discounted value as the discount factor tends to zero, or…
While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the properties that optimal solutions need to have, and devised a…
We present a method to solve optimal stopping problems in infinite horizon for a L\'evy process when the reward function can be non-monotone. To solve the problem we introduce two new objects. Firstly, we define a random variable $\eta(x)$…
We study a class of infinite horizon impulse control problems with execution delay when the dynamics of the system is described by a general adapted stochastic process. The problem is solved by means of probabilistic tools relying on the…
We study a zero-sum stochastic differential switching game in infinite horizon. We prove the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities…
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…
In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed…
We consider the optimal multi-agent persistent monitoring problem defined by a team of cooperating agents visiting a set of nodes (targets) on a graph with the objective of minimizing a measure of overall node state uncertainty. The…
In this research we study a finite horizon optimal purchasing problem for items with a mean reverting price process. Under this model a fixed amount of identical items are bought under a given deadline, with the objective of minimizing the…
The secretary and the prophet inequality problems are central to the field of Stopping Theory. Recently, there has been a lot of work in generalizing these models to multiple items because of their applications in mechanism design. The most…
Consider a set of discounted optimal stopping problems for a one-parameter family of objective functions and a fixed diffusion process, started at a fixed point. A standard problem in stochastic control/optimal stopping is to solve for the…
Optimal stopping is the problem of determining when to stop a stochastic system in order to maximize reward, which is of practical importance in domains such as finance, operations management and healthcare. Existing methods for…
To estimate the optimal constant in Hardy-type inequalities, some variational formulas and approximating procedures are introduced. The known basic estimates are improved considerably. The results are illustrated by typical examples. It is…
In this paper we present the Warm-starting Dynamic Thresholding algorithm, developed using dynamic programming, for a variant of the standard online selection problem. The problem allows job positions to be either free or already occupied…
This paper considers a variation of the full-information secretary problem where the random variables to be observed are independent but not necessary identically distributed. The main result is a sharp lower bound for the optimal win…
We study two-player zero-sum concurrent stochastic games with finite state and action space played for an infinite number of steps. In every step, the two players simultaneously and independently choose an action. Given the current state…
In this work we study the problem of single-shot discrimination of von Neumann measurements, which we associate with measure-and-prepare channels. There are two possible approaches to this problem. The first one is simple and does not…
In this paper we provide optimal bounds for fully discrete approximations to finite horizon problems via dynamic programming. We adapt the error analysis in \cite{nos} for the infinite horizon case to the finite horizon case. We prove an a…
For an infinite-horizon continuous-time optimal stopping problem under non-exponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the…