Related papers: Uniformly bounded regret in the multi-secretary pr…
We consider the problem of repeatedly choosing policies to maximize social welfare. Welfare is a weighted sum of private utility and public revenue. Earlier outcomes inform later policies. Utility is not observed, but indirectly inferred.…
We study the repeated optimal stopping problem, in which the same optimal stopping instance with an unknown distribution is solved repeatedly over $T$ rounds. We aim to simultaneously achieve strong per-round performance guarantees relative…
While the importance of personalized policymaking is widely recognized, fully personalized implementation remains rare in practice, often due to legal, fairness or cost concerns. We study the problem of policy targeting for a regret-averse…
We consider generalizations of the classical secretary problem, also known as the problem of optimal choice, to posets where the only information we have is the size of the poset and the number of maximal elements. We show that, given this…
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…
We consider the classical problems of estimating the mean of an $n$-dimensional normally (with identity covariance matrix) or Poisson distributed vector under the squared loss. In a Bayesian setting the optimal estimator is given by the…
In learning theory, the performance of an online policy is commonly measured in terms of the static regret metric, which compares the cumulative loss of an online policy to that of an optimal benchmark in hindsight. In the definition of…
We consider a repeated newsvendor problem where the inventory manager has no prior information about the demand, and can access only censored/sales data. In analogy to multi-armed bandit problems, the manager needs to simultaneously…
We study online learning problems in which a decision maker has to take a sequence of decisions subject to $m$ long-term constraints. The goal of the decision maker is to maximize their total reward, while at the same time achieving small…
This paper introduces a heuristic framework for the Best Secretary Problem, where one item must be selected using rank information only. We develop five data-responsive rules extending classical fixed-cutoff methods: an expected-record…
The secretary problem has been a focus of extensive study with a variety of extensions that offer useful insights into the theory of optimal stopping. The original solution is to set one stopping threshold that gives rise to an immediately…
Street-level bureaucrats, such as caseworkers and border guards routinely face the dilemma of whether to follow rigid policy or exercise discretion based on professional judgement. However, frequent overrides threaten consistency and…
In many sequential decision problems, an agent performs a repeated task. He then suffers regret and obtains information that he may use in the following rounds. However, sometimes the agent may also obtain information and avoid suffering…
We consider distributed kernel bandits where $N$ agents aim to collaboratively maximize an unknown reward function that lies in a reproducing kernel Hilbert space. Each agent sequentially queries the function to obtain noisy observations at…
We consider the problem of online resource allocation with average budget constraints. At each time point the decision maker makes an irrevocable decision of whether to accept or reject a request before the next request arrives with the…
In the classical secretary problem, one attempts to find the maximum of an unknown and unlearnable distribution through sequential search. In many real-world searches, however, distributions are not entirely unknown and can be learned…
The secretary problem is one of the fundamental problems in online decision making; a tight competitive ratio for this problem of $1/\mathrm{e} \approx 0.368$ has been known since the 1960s. Much more recently, the study of algorithms with…
Performance of adaptive control policies is assessed through the regret with respect to the optimal regulator, which reflects the increase in the operating cost due to uncertainty about the dynamics parameters. However, available results in…
As a famous result, the ``37\% Law'' for Secretary Problem has widely influenced peoples' perception on online decision strategies about choice. However, using this strategy, too many attractive candidates may be rejected in the first 37\%,…
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…