# From Finite to Countable-Armed Bandits

@article{Kalvit2021FromFT, title={From Finite to Countable-Armed Bandits}, author={Anand Kalvit and Assaf J. Zeevi}, journal={ArXiv}, year={2021}, volume={abs/2105.10721} }

We consider a stochastic bandit problem with countably many arms that belong to a finite set of types, each characterized by a unique mean reward. In addition, there is a fixed distribution over types which sets the proportion of each type in the population of arms. The decision maker is oblivious to the type of any arm and to the aforementioned distribution over types, but perfectly knows the total number of types occurring in the population of arms. We propose a fully adaptive online learning…

## 8 Citations

### Complexity Analysis of a Countable-armed Bandit Problem

- Computer Science
- 2023

While the order of regret and complexity of the problem suggests a great degree of similarity to the classical MAB problem, properties of the performance bounds and salient aspects of algorithm design are quite distinct from the latter, as are the key primitives that determine complexity along with the analysis tools needed to study them.

### The Countable-armed Bandit with Vanishing Arms

- Computer ScienceArXiv
- 2021

It is characterized necessary and sufficient conditions for achievability of sub-linear regret in terms of a critical vanishing rate of optimal arms, and two reservoir distribution-oblivious algorithms that are long-run-average optimal whenever sub- linear regret is statistically achievable are discussed.

### Stochastic bandits with groups of similar arms

- Computer ScienceNeurIPS
- 2021

A lowerbound inspired strategy involving a computationally efﬁcient relaxation that is based on a sorting mechanism achieves a lower bound close to the optimal one up to a controlled factor, and achieves an asymptotic regret q times smaller than the unstructured one.

### Non-stationary Bandits and Meta-Learning with a Small Set of Optimal Arms

- Computer ScienceArXiv
- 2022

An algorithm based on a reduction to bandit submodular maximization is designed, and it is shown that, for T rounds comprised of N tasks, in the regime of large number of tasks and small number of optimal arms M, its regret is smaller than the simple baseline of ˜ O ( √ KNT ) that can be obtained by using standard algorithms designed for non-stationary bandit problems.

### Bandits with Dynamic Arm-acquisition Costs*

- Computer Science2022 58th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- 2022

A UCB-inspired adaptive algorithm that is long-run-average optimal whenever said condition is satisfied, thereby establishing its tightness is discussed, and a necessary condition for achievability of sub-linear regret in the problem is characterized.

### Multi-Armed Bandits with Bounded Arm-Memory: Near-Optimal Guarantees for Best-Arm Identification and Regret Minimization

- Computer ScienceNeurIPS
- 2021

This work addresses the Stochastic Multi-armed Bandit problem from the perspective of two standard objectives: regret minimization, and best-arm identiﬁcation, and provides an algorithm with arm-memory size of O (log ∗ n ) and O ( nε 2 · log( 1 δ )) optimal sample complexity.

### A Closer Look at the Worst-case Behavior of Multi-armed Bandit Algorithms

- Computer ScienceNeurIPS
- 2021

It is shown that arm-sampling rates under UCB are asymptotically deterministic, regardless of the problem complexity, and the first complete process-level characterization of the MAB problem underUCB in the conventional diffusion scaling is provided.

### Max-Utility Based Arm Selection Strategy For Sequential Query Recommendations

- Computer ScienceArXiv
- 2021

It is shown that in tasks like online information gathering, where sequential query recommendations are employed, the sequences of queries are correlated and the number of potentially optimal queries can be reduced to a manageable size by selecting queries with maximum utility with respect to the currently executing query.

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