Related papers: Lookback Prophet Inequalities
We consider the problem in which n items arrive to a market sequentially over time, where two agents compete to choose the best possible item. When an agent selects an item, he leaves the market and obtains a payoff given by the value of…
Let X_1,X_2,... be a sequence of [0,1]-valued i.i.d. random variables, let c\geq 0 be a sampling cost for each observation and let Y_i=X_i-ic, i=1,2,.... For n=1,2,..., let M(Y_1,...,Y_n)=E(max_{1\leq i\leq n}Y_i) and…
We present pricing mechanisms for several online resource allocation problems which obtain tight or nearly tight approximations to social welfare. In our settings, buyers arrive online and purchase bundles of items; buyers' values for the…
Optimal stopping problems give rise to random distributions describing how many applicants the decision-maker will sample or interview before choosing one, a quantity sometimes referred to as the search time or process duration. This…
We present a new alternative theorems for sequences of functions. As applications, we extend recent results in the literature related to first-order necessary conditions for optimality problems. Our contributions involve extending…
We study the polynomial-time approximability of the optimal online stochastic bipartite matching algorithm, initiated by Papadimitriou et al. (EC'21). Here, nodes on one side of the graph are given upfront, while at each time $t$, an online…
Functions satisfying a defective renewal equation arise commonly in applied probability models. Usually these functions don't admit a explicit expression. In this work we consider to approximate them by means of a gamma-type operator given…
Motivated by fairness concerns, we study the `portfolio problem': given an optimization problem with set $D$ of feasible solutions, a class $\mathbf{C}$ of fairness objective functions on $D$, and an approximation factor $\alpha \ge 1$, a…
Influence maximization (IM) is a representative and classic problem that has been studied extensively before. The most important application derived from the IM problem is viral marketing. Take us as a promoter, we want to get benefits from…
The class of direct preference optimization (DPO) algorithms has emerged as a promising approach for solving the alignment problem in foundation models. These algorithms work with very limited feedback in the form of pairwise preferences…
In the classical Online Metric Matching problem, we are given a metric space with $k$ servers. A collection of clients arrive in an online fashion, and upon arrival, a client should irrevocably be matched to an as-yet-unmatched server. The…
A fundamental challenge in machine learning is the choice of a loss as it characterizes our learning task, is minimized in the training phase, and serves as an evaluation criterion for estimators. Proper losses are commonly chosen, ensuring…
A variant of the online knapsack problem is considered in the settings of trusted and untrusted predictions. In Unit Profit Knapsack, the items have unit profit, and it is easy to find an optimal solution offline: Pack as many of the…
We consider two variations of the classical secretary problem. * A variation of the returning secretary problem where each interviewee may appear a second time with a fixed probability p. The decision-maker observes interviewees…
We study metric learning from preference comparisons under the ideal point model, in which a user prefers an item over another if it is closer to their latent ideal item. These items are embedded into $\mathbb{R}^d$ equipped with an unknown…
The knapsack problem is one of the classical problems in combinatorial optimization: Given a set of items, each specified by its size and profit, the goal is to find a maximum profit packing into a knapsack of bounded capacity. In the…
Iterative preference optimization methods have recently been shown to perform well for general instruction tuning tasks, but typically make little improvement on reasoning tasks (Yuan et al., 2024, Chen et al., 2024). In this work we…
Recommendation systems capable of providing diverse sets of results are a focus of increasing importance, with motivations ranging from fairness to novelty and other aspects of optimizing user experience. One form of diversity of recent…
We study a fundamental problem in optimization under uncertainty. There are $n$ boxes; each box $i$ contains a hidden reward $x_i$. Rewards are drawn i.i.d. from an unknown distribution $\mathcal{D}$. For each box $i$, we see $y_i$, an…
In fair division of indivisible goods, using sequences of sincere choices (or picking sequences) is a natural way to allocate the objects. The idea is as follows: at each stage, a designated agent picks one object among those that remain.…