相关论文: The secretary problem with non-uniform arrivals vi…

We solve the secretary problem in the case that the ranked items arrive in a statistically biased order rather than in uniformly random order. The bias is given by a Mallows distribution with parameter $q\in(0,1)$, so that higher ranked…

In the classical secretary problem, $n$ ranked items arrive one by one, and each item's rank relative to its predecessors is noted. The observer must select or reject each item as it arrives, with the object of selecting the item of highest…

For $2\le k\in\mathbb{N}$, consider the following adaptation of the classical secretary problem. There are $k$ items at each of $n$ linearly ordered ranks. The $kn$ items are revealed, one item at a time, in a uniformly random order, to an…

We analyze the secretary problem in the case that the $n$ ranked items arrive not in uniformly random order but rather according to a certain type of Luce distribution or according to a Mallows distribution on the set $S_n$ of permutations…

In this paper, we investigate two variants of the secretary problem. In these variants, we are presented with a sequence of numbers $X_i$ that come from distributions $\mathcal{D}_i$, and that arrive in either random or adversarial order.…

We revisit the problem of selecting an item from $n$ choices that appear before us in random sequential order so as to minimize the expected rank of the item selected. In particular, we examine the stopping rule where we reject the first…

We study a twist on the classic secretary problem, which we term the secretary ranking problem: elements from an ordered set arrive in random order and instead of picking the maximum element, the algorithm is asked to assign a rank, or…

Suppose that $n$ items arrive online in random order and the goal is to select $k$ of them such that the expected sum of the selected items is maximized. The decision for any item is irrevocable and must be made on arrival without knowing…

In the online random-arrival model, an algorithm receives a sequence of n requests that arrive in a random order. The algorithm is expected to make an irrevocable decision with regard to each request based only on the observed history. We…

For many online problems, it is known that the uniform arrival order enables the design of algorithms with much better performance guarantees than under worst-case. The quintessential example is the secretary problem. If the sequence of…

Optimal stopping theory is a powerful tool for analyzing scenarios such as online auctions in which we generally require optimizing an objective function over the space of stopping rules for an allocation process under uncertainty. Perhaps…

We take a unifying approach to single selection optimal stopping problems with random arrival order and independent sampling of items. In the problem we consider, a decision maker (DM) initially gets to sample each of $N$ items…

We study variants of the secretary problem, where $N$, the number of candidates, is a random variable, and the decision maker wants to maximize the probability of success -- picking the largest number among the $N$ candidates -- using only…

A version of the classical secretary problem is studied, in which one is interested in selecting one of the b best out of a group of n differently ranked persons who are presented one by one in a random order. It is assumed that b is a…

Suppose a customer is faced with a sequence of fluctuating prices, such as for airfare or a product sold by a large online retailer. Given distributional information about what price they might face each day, how should they choose when to…

The value maximization version of the secretary problem is the problem of hiring a candidate with the largest value from a randomly ordered sequence of candidates. In this work, we consider a setting where predictions of candidate values…

We study a learning-augmented variant of the secretary problem, recently introduced by Fujii and Yoshida (2023), in which the decision-maker has access to machine-learned predictions of candidate values. The central challenge is to balance…

The secretary problem is probably the purest model of decision making under uncertainty. In this paper we ask which advice can we give the algorithm to improve its success probability? We propose a general model that unifies a broad range…

In learning-augmented online algorithms, predictions are usually valued for what they say: a value estimate, a solution, or an algorithmic recommendation. This paper shows that predictions can also be valuable solely due to their arrival…

Candidates arrive sequentially for an interview process which results in them being ranked relative to their predecessors. Based on the ranks available at each time, one must develop a decision mechanism that selects or dismisses the…