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We introduce and study a new class of stochastic bandit problems, referred to as predictive bandits. In each round, the decision maker first decides whether to gather information about the rewards of particular arms (so that their rewards…
We consider the combinatorial multi-armed bandit (CMAB) problem, where the reward function is nonlinear. In this setting, the agent chooses a batch of arms on each round and receives feedback from each arm of the batch. The reward that the…
Standard Multi-Armed Bandit (MAB) problems assume that the arms are independent. However, in many application scenarios, the information obtained by playing an arm provides information about the remainder of the arms. Hence, in such…
We study how to make decisions that minimize Bayesian regret in offline linear bandits. Prior work suggests that one must take actions with maximum lower confidence bound (LCB) on their reward. We argue that the reliance on LCB is…
Multi-armed bandit problems are the most basic examples of sequential decision problems with an exploration-exploitation trade-off. This is the balance between staying with the option that gave highest payoffs in the past and exploring new…
Multi-armed bandit problems are the predominant theoretical model of exploration-exploitation tradeoffs in learning, and they have countless applications ranging from medical trials, to communication networks, to Web search and advertising.…
This paper considers the use of a simple posterior sampling algorithm to balance between exploration and exploitation when learning to optimize actions such as in multi-armed bandit problems. The algorithm, also known as Thompson Sampling,…
In this paper, we study a family of conservative bandit problems (CBPs) with sample-path reward constraints, i.e., the learner's reward performance must be at least as well as a given baseline at any time. We propose a One-Size-Fits-All…
This paper studies bandit problems where an agent has access to offline data that might be utilized to potentially improve the estimation of each arm's reward distribution. A major obstacle in this setting is the existence of compound…
For traffic routing platforms, the choice of which route to recommend to a user depends on the congestion on these routes -- indeed, an individual's utility depends on the number of people using the recommended route at that instance.…
In $\mathcal{X}$-armed bandit problem an agent sequentially interacts with environment which yields a reward based on the vector input the agent provides. The agent's goal is to maximise the sum of these rewards across some number of time…
The causal bandit problem seeks to identify, through sequential experimentation, an intervention that maximizes the expected reward in a causal system modeled by a directed acyclic graph (DAG). Existing methods typically assume that the…
We consider a stochastic bandit problem with a possibly infinite number of arms. We write $p^*$ for the proportion of optimal arms and $\Delta$ for the minimal mean-gap between optimal and sub-optimal arms. We characterize the optimal…
In a multi-armed bandit (MAB) problem a gambler needs to choose at each round of play one of K arms, each characterized by an unknown reward distribution. Reward realizations are only observed when an arm is selected, and the gambler's…
We study contextual combinatorial bandits with probabilistically triggered arms (C$^2$MAB-T) under a variety of smoothness conditions that capture a wide range of applications, such as contextual cascading bandits and contextual influence…
We consider the stochastic combinatorial semi-bandit problem with adversarial corruptions. We provide a simple combinatorial algorithm that can achieve a regret of $\tilde{O}\left(C+d^2K/\Delta_{min}\right)$ where $C$ is the total amount of…
While classical formulations of multi-armed bandit problems assume that each arm's reward is independent and stationary, real-world applications often involve non-stationary environments and interdependencies between arms. In particular,…
In this study, we consider the infinitely many-armed bandit problems in a rested rotting setting, where the mean reward of an arm may decrease with each pull, while otherwise, it remains unchanged. We explore two scenarios regarding the…
We consider the Multi-Armed Bandit (MAB) problem, where an agent sequentially chooses actions and observes rewards for the actions it took. While the majority of algorithms try to minimize the regret, i.e., the cumulative difference between…
In the classic Bayesian restless multi-armed bandit (RMAB) problem, there are $N$ arms, with rewards on all arms evolving at each time as Markov chains with known parameters. A player seeks to activate $K \geq 1$ arms at each time in order…