On the Complexity of Best Arm Identification in Multi-Armed Bandit Models
The stochastic multi-armed bandit model is a simple abstraction that has proven useful in many different contexts in statistics and machine learning. Whereas the achievable limit in terms of regret minimization is now well known, our aim is to contribute to a better understanding of the performance in terms of identifying the m best arms. We introduce generic notions of complexity for the two dominant frameworks considered in the literature: fixed-budget and fixed-confidence settings. In the fixed-confidence setting, we provide the first known distribution-dependent lower bound on the complexity that involves information-theoretic quantities and holds when m is larger than 1 under general assumptions. In the specific case of two armed-bandits, we derive refined lower bounds in both the fixed-confidence and fixed-budget settings, along with matching algorithms for Gaussian and Bernoulli bandit models. These results show in particular that the complexity of the fixed-budget setting may be smaller than the complexity of the fixed-confidence setting, contradicting the familiar behavior observed when testing fully specified alternatives. In addition, we also provide improved sequential stopping rules that have guaranteed error probabilities and shorter average running times. The proofs rely on two technical results that are of independent interest : a deviation lemma for self-normalized sums (Lemma 19) and a novel change of measure inequality for bandit models (Lemma 1).
Code (0)
등록된 구현이 없습니다.
Tasks
LEMMASimilar Papers 제목 키워드 기반
Quantile Multi-Armed Bandits: Optimal Best-Arm Identification and a Differentially Private Scheme
We study the best-arm identification problem in multi-armed bandits with stochastic, potentially private rewards, when the goal is to identify the arm with the highest quantile at a fixed, prescribed level. First, we pro…
Multi-Armed BanditsBest Arm Identification in Linked Bandits
We consider the problem of best arm identification in a variant of multi-armed bandits called linked bandits. In a single interaction with linked bandits, multiple arms are played sequentially until one of them receives …
Multi-Armed BanditsOn Finding the Largest Mean Among Many
Sampling from distributions to find the one with the largest mean arises in a broad range of applications, and it can be mathematically modeled as a multi-armed bandit problem in which each distribution is associated wit…
Multi-Armed BanditsBandit algorithms to emulate human decision making using probabilistic distortions
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 probabili…
Decision MakingMulti-Armed BanditsIdentification of the Generalized Condorcet Winner in Multi-dueling Bandits
The reliable identification of the “best” arm while keeping the sample complexity as low as possible is a common task in the field of multi-armed bandits. In the multi-dueling variant of multi-armed bandits, where feedba…
Multi-Armed Bandits