Related papers: Optimal single threshold stopping rules and sharp …
In this work, solution of the finite horizon hybrid optimal control problem as the central element of the receding horizon optimal control (model predictive control) is investigated based on the indirect approach. The response of a hybrid…
Due to numerous applications in retail and (online) advertising the problem of assortment selection has been widely studied under many combinations of discrete choice models and feasibility constraints. In many situations, however, an…
Due to their numerous applications, in particular in Mechanism Design, Prophet Inequalities have experienced a surge of interest. They describe competitive ratios for basic stopping time problems where random variables get revealed…
Many decision problems in economics, information technology, and industry can be transformed to an optimal stopping of adapted random vectors with some utility function over the set of Markov times with respect to filtration build by the…
Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…
Infinite horizon optimization problems accompany two perplexities. First, the infinite series of utility sequences may diverge. Second, boundary conditions at the infinite terminal time may not be rigorously expressed. In this paper, we…
Raghavendra (STOC 2008) gave an elegant and surprising result: if Khot's Unique Games Conjecture (STOC 2002) is true, then for every constraint satisfaction problem (CSP), the best approximation ratio is attained by a certain simple…
We investigate prophet inequalities with competitive ratios approaching $1$, seeking to generalize $k$-uniform matroids. We first show that large girth does not suffice: for all $k$, there exists a matroid of girth $\geq k$ and a prophet…
We optimize the running time of the primal-dual algorithms by optimizing their stopping criteria for solving convex optimization problems under affine equality constraints, which means terminating the algorithm earlier with fewer…
We consider a general formulation of the random horizon Principal-Agent problem with a continuous payment and a lump-sum payment at termination. In the European version of the problem, the random horizon is chosen solely by the principal…
We consider concurrent games played on graphs. At every round of a game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety…
In this paper, we consider the social optimal problem of discrete time finite state space mean field games (referred to as finite mean field games [1]). Unlike the individual optimization of their own cost function in competitive models, in…
We aim to construct the optimal solutions to the undiscounted continuous-time infinite horizon optimization problems, the objective functionals of which may be unbounded. We identify the condition under which the limit of the solutions to…
This paper concerns rollout and certainty-equivalent rollout policies for stochastic shortest path problems with absorbing terminal states. The main result provides a direct non-asymptotic performance certificate for a fixed rollout policy:…
We study the prophet inequality when the gambler has an access only to a single sample from each distribution. Rubinstein, Wang and Weinberg showed that an optimal guarantee of 1/2 can be achieved when the underlying matroid has rank 1,…
Online contention resolution schemes (OCRSs) were proposed by Feldman, Svensson, and Zenklusen as a generic technique to round a fractional solution in the matroid polytope in an online fashion. It has found applications in several…
The study of the prophet inequality problem in the limited information regime was initiated by Azar et al. [SODA'14] in the pursuit of prior-independent posted-price mechanisms. As they show, $O(1)$-competitive policies are achievable using…
This work introduces \emph{sharding} and \emph{Poissonization} as a unified framework for analyzing prophet inequalities. Sharding involves splitting a random variable into several independent random variables, shards, that collectively…
The secretary problem or the game of Googol are classic models for online selection problems that have received significant attention in the last five decades. We consider a variant of the problem and explore its connections to data-driven…
An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an $\alpha$-maxmin nonlinear…