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The dynamic allocation problem, also known as the `multi-armed bandit' problem, simulates a situation in which an agent is faced with a tradeoff between actions that yield an immediate reward and actions whose benefits can only be perceived…
Motivated by applications such as online labor markets we consider a variant of the stochastic multi-armed bandit problem where we have a collection of arms representing strategic agents with different performance characteristics. The…
The restless multi-armed bandit problem is a paradigmatic modeling framework for optimal dynamic priority allocation in stochastic models of wide-ranging applications that has been widely investigated and applied since its inception in a…
In bandit with distribution shifts, one aims to automatically adapt to unknown changes in reward distribution, and restart exploration when necessary. While this problem has been studied for many years, a recent breakthrough of Auer et al.…
We study the fixed-confidence best-arm identification problem in unimodal bandits, in which the means of the arms increase with the index of the arm up to their maximum, then decrease. We derive two lower bounds on the stopping time of any…
Consider a Dirichlet process mixture model (DPM) with random precision parameter $\alpha$, inducing $K_n$ clusters over $n$ observations through its latent random partition. Our goal is to specify the prior distribution…
Most learning to rank research has assumed that the utility of different documents is independent, which results in learned ranking functions that return redundant results. The few approaches that avoid this have rather unsatisfyingly…
Traditionally, when recommender systems are formalized as multi-armed bandits, the policy of the recommender system influences the rewards accrued, but not the length of interaction. However, in real-world systems, dissatisfied users may…
Motivated by the study of asymptotic behaviour of the bandit problems, we obtain several strategy-driven limit theorems including the law of large numbers, the large deviation principle, and the central limit theorem. Different from the…
Motivated by models of human decision making proposed to explain commonly observed deviations from conventional expected value preferences, we formulate two stochastic multi-armed bandit problems with distorted probabilities on the reward…
We focus on the problem of best-arm identification in a stochastic multi-arm bandit with temporally decreasing variances for the arms' rewards. We model arm rewards as Gaussian random variables with fixed means and variances that decrease…
We consider a multi-hypothesis testing problem involving a K-armed bandit. Each arm's signal follows a distribution from a vector exponential family. The actual parameters of the arms are unknown to the decision maker. The decision maker…
We study the best-arm identification problem in linear bandit, where the rewards of the arms depend linearly on an unknown parameter $\theta^*$ and the objective is to return the arm with the largest reward. We characterize the complexity…
A key feature of sequential decision making under uncertainty is a need to balance between exploiting--choosing the best action according to the current knowledge, and exploring--obtaining information about values of other actions. The…
The multi-armed bandit (MAB) model is one of the most classical models to study decision-making in an uncertain environment. In this model, a player chooses one of $K$ possible arms of a bandit machine to play at each time step, where the…
We introduce a new stochastic multi-armed bandit setting where arms are grouped inside ``ordered'' categories. The motivating example comes from e-commerce, where a customer typically has a greater appetence for items of a specific…
We consider the problem of revenue-optimal dynamic mechanism design in settings where agents' types evolve over time as a function of their (both public and private) experience with items that are auctioned repeatedly over an infinite…
We study the recovering bandits problem, a variant of the stochastic multi-armed bandit problem where the expected reward of each arm varies according to some unknown function of the time since the arm was last played. While being a natural…
In restless bandits, a central agent is tasked with optimally distributing limited resources across several bandits (arms), with each arm being a Markov decision process. In this work, we generalize the traditional restless bandits problem…
Algorithms for hyperparameter optimization abound, all of which work well under different and often unverifiable assumptions. Motivated by the general challenge of sequentially choosing which algorithm to use, we study the more specific…