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This paper introduces and addresses a wide class of stochastic bandit problems where the function mapping the arm to the corresponding reward exhibits some known structural properties. Most existing structures (e.g. linear, Lipschitz,…
We study Thompson Sampling-based algorithms for stochastic bandits with bounded rewards. As the existing problem-dependent regret bound for Thompson Sampling with Gaussian priors [Agrawal and Goyal, 2017] is vacuous when $T \le 288 e^{64}$,…
This paper investigates the fusion of absolute (reward) and relative (dueling) feedback in stochastic bandits, where both feedback types are gathered in each decision round. We derive a regret lower bound, demonstrating that an efficient…
We consider a replicable stochastic multi-armed bandit algorithm that ensures, with high probability, that the algorithm's sequence of actions is not affected by the randomness inherent in the dataset. Replicability allows third parties to…
Under the uncoupled learning setup, the last-iterate convergence guarantee towards Nash equilibrium is shown to be impossible in many games. This work studies the last-iterate convergence guarantee in general games toward rationalizability,…
In many applications, e.g. in healthcare and e-commerce, the goal of a contextual bandit may be to learn an optimal treatment assignment policy at the end of the experiment. That is, to minimize simple regret. However, this objective…
We study fairness within the stochastic, \emph{multi-armed bandit} (MAB) decision making framework. We adapt the fairness framework of "treating similar individuals similarly" to this setting. Here, an `individual' corresponds to an arm and…
Thompson sampling is one of the earliest randomized algorithms for multi-armed bandits (MAB). In this paper, we extend the Thompson sampling to Budgeted MAB, where there is random cost for pulling an arm and the total cost is constrained by…
The empirically successful Thompson Sampling algorithm for stochastic bandits has drawn much interest in understanding its theoretical properties. One important benefit of the algorithm is that it allows domain knowledge to be conveniently…
One of the key drivers of complexity in the classical (stochastic) multi-armed bandit (MAB) problem is the difference between mean rewards in the top two arms, also known as the instance gap. The celebrated Upper Confidence Bound (UCB)…
We investigate a natural but surprisingly unstudied approach to the multi-armed bandit problem under safety risk constraints. Each arm is associated with an unknown law on safety risks and rewards, and the learner's goal is to maximise…
In sequential decision-making scenarios i.e., mobile health recommendation systems revenue management contextual multi-armed bandit algorithms have garnered attention for their performance. But most of the existing algorithms are built on…
This paper considers a multi-armed bandit game where the number of arms is much larger than the maximum budget and is effectively infinite. We characterize necessary and sufficient conditions on the total budget for an algorithm to return…
Motivated by the concept of satisficing in decision-making, we consider the problem of satisficing regret minimization in bandit optimization. In this setting, the learner aims at selecting satisficing arms (arms with mean reward exceeding…
We study a distributed multi-armed bandit (MAB) problem over arm erasure channels, motivated by the increasing adoption of MAB algorithms over communication-constrained networks. In this setup, the learner communicates the chosen arm to…
We develop a meta-learning framework for simple regret minimization in bandits. In this framework, a learning agent interacts with a sequence of bandit tasks, which are sampled i.i.d.\ from an unknown prior distribution, and learns its…
We consider bandit problems involving a large (possibly infinite) collection of arms, in which the expected reward of each arm is a linear function of an $r$-dimensional random vector $\mathbf{Z} \in \mathbb{R}^r$, where $r \geq 2$. The…
We study the stochastic multi-armed bandit problem in the case when the arm samples are dependent over time and generated from so-called weak $\cC$-mixing processes. We establish a $\cC-$Mix Improved UCB agorithm and provide both…
We consider a stochastic multi-armed bandit setting where reward must be actively queried for it to be observed. We provide tight lower and upper problem-dependent guarantees on both the regret and the number of queries. Interestingly, we…
We study the problem of designing replication-proof bandit mechanisms when agents strategically register or replicate their own arms to maximize their payoff. Specifically, we consider Bayesian agents who only know the distribution from…