Related papers: The Spend-It-All Region and Small Time Results for…
We study an infinite horizon optimal stopping problem which arises naturally in the optimal timing of a firm/project sale or in the valuation of natural resources: the functional to be maximised is a sum of a discounted running reward and a…
In the standard formulation of the occupancy problem one considers the distribution of r balls in n cells, with each ball assigned independently to a given cell with probability 1/n. Although closed form expressions can be given for the…
We consider a situation where an agent has $T$ ressources to be allocated to a larger number $N$ of actions. Each action can be completed at most once and results in a stochastic reward with unknown mean. The goal of the agent is to…
For a large number of random constraint satisfaction problems, such as random k-SAT and random graph and hypergraph coloring, there are very good estimates of the largest constraint density for which solutions exist. Yet, all known…
We consider the stochastic contextual bandit problem under the high dimensional linear model. We focus on the case where the action space is finite and random, with each action associated with a randomly generated contextual covariate. This…
We consider the problem of maximizing the expected average reward obtained over an infinite time horizon by $n$ weakly coupled Markov decision processes. Our setup is a substantial generalization of the multi-armed restless bandit problem…
In this paper we consider the contextual multi-armed bandit problem for linear payoffs under a risk-averse criterion. At each round, contexts are revealed for each arm, and the decision maker chooses one arm to pull and receives the…
In this paper we study a representation problem first considered in a simpler version by Bank and El Karoui [2004]. A key ingredient to this problem is a random measure $\mu$ on the time axis which in the present paper is allowed to have…
The general problem of robust optimization is this: one of several possible scenarios will appear tomorrow, but things are more expensive tomorrow than they are today. What should you anticipatorily buy today, so that the worst-case cost…
Continuity of the value of the martingale optimal transport problem on the real line w.r.t. its marginals was recently established in Backhoff-Veraguas and Pammer [2] and Wiesel [21]. We present a new perspective of this result using the…
We examine a multi-armed bandit problem with contextual information, where the objective is to ensure that each arm receives a minimum aggregated reward across contexts while simultaneously maximizing the total cumulative reward. This…
The question of the optimality of Thompson Sampling for solving the stochastic multi-armed bandit problem had been open since 1933. In this paper we answer it positively for the case of Bernoulli rewards by providing the first finite-time…
Assume that a target is known to be present at an unknown point among a finite set of locations in the plane. We search for it using a mobile robot that has imperfect sensing capabilities. It takes time for the robot to move between…
This paper introduces the first asymptotically optimal strategy for a multi armed bandit (MAB) model under side constraints. The side constraints model situations in which bandit activations are limited by the availability of certain…
We introduce a novel kind of robustness in linear programming. A solution x* is called robust optimal if for all realizations of objective functions coefficients and constraint matrix entries from given interval domains there are…
We consider an optimal control problem describing a laser-induced population transfer on a $n$-level quantum system. For a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists…
A continuous-time financial portfolio selection model with expected utility maximization typically boils down to solving a (static) convex stochastic optimization problem in terms of the terminal wealth, with a budget constraint. In…
Chance constraints are frequently used to limit the probability of constraint violations in real-world optimization problems where the constraints involve stochastic components. We study chance-constrained submodular optimization problems,…
We study the problem of optimizing the betting frequency in a dynamic game setting using Kelly's celebrated expected logarithmic growth criterion as the performance metric. The game is defined by a sequence of bets with independent and…
This work shows the existence of optimal control laws for persistent monitoring of mobile targets in a one-dimensional mission space and derives explicit solutions. The underlying performance metric consists of minimizing the total…