Best arm identification in rare events

• URL: http://arxiv.org/abs/2303.07627v1
• Date: Tue, 14 Mar 2023 04:51:24 GMT
• Title: Best arm identification in rare events
• Authors: Anirban Bhattacharjee, Sushant Vijayan and Sandeep K Juneja
• Abstract summary: A key application of this framework is in online advertising where click rates of advertisements could be a fraction of a single percent and final conversion to sales, while highly profitable, may again be a small fraction of the click rates. Lately, algorithms for BAI problems have been developed that minimise sample complexity while providing statistical guarantees on the correct arm selection. We exploit the fact that the reward process for each arm is well approximated by a Compound Poisson process to arrive at algorithms that are faster, with a small increase in sample complexity.
• Score: 0.43012765978447565
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: We consider the best arm identification problem in the stochastic multi-armed bandit framework where each arm has a tiny probability of realizing large rewards while with overwhelming probability the reward is zero. A key application of this framework is in online advertising where click rates of advertisements could be a fraction of a single percent and final conversion to sales, while highly profitable, may again be a small fraction of the click rates. Lately, algorithms for BAI problems have been developed that minimise sample complexity while providing statistical guarantees on the correct arm selection. As we observe, these algorithms can be computationally prohibitive. We exploit the fact that the reward process for each arm is well approximated by a Compound Poisson process to arrive at algorithms that are faster, with a small increase in sample complexity. We analyze the problem in an asymptotic regime as rarity of reward occurrence reduces to zero, and reward amounts increase to infinity. This helps illustrate the benefits of the proposed algorithm. It also sheds light on the underlying structure of the optimal BAI algorithms in the rare event setting.

Related papers

• An Algorithm for Fixed Budget Best Arm Identification with Combinatorial Exploration [3.9901365062418312]
  We consider the best arm identification problem in the $K-$armed bandit framework. Agent is allowed to play a subset of arms at each time slot instead of one arm. We propose an algorithm that constructs $log K$ groups and performs a likelihood ratio test to detect the presence of the best arm.
  arXiv  Detail & Related papers  (2025-02-03T15:10:08Z)
• Breaking the $\log(1/Δ_2)$ Barrier: Better Batched Best Arm Identification with Adaptive Grids [28.547030766096956]
  We introduce an algorithm that achieves near-optimal sample complexity and features an instance-sensitive batch complexity. We extend this framework to the problem of batched best arm identification in linear bandits and achieve similar improvements.
  arXiv  Detail & Related papers  (2025-01-29T01:40:36Z)
• Optimal Multi-Objective Best Arm Identification with Fixed Confidence [62.36929749450298]
  We consider a multi-armed bandit setting in which each arm yields an $M$-dimensional vector reward upon selection. The end goal is to identify the best arm of em every objective in the shortest (expected) time subject to an upper bound on the probability of error. We propose an algorithm that uses the novel idea of em surrogate proportions to sample the arms at each time step, eliminating the need to solve the max-min optimisation problem at each step.
  arXiv  Detail & Related papers  (2025-01-23T12:28:09Z)
• A General Framework for Clustering and Distribution Matching with Bandit Feedback [81.50716021326194]
  We develop a general framework for clustering and distribution matching problems with bandit feedback. We derive a non-asymptotic lower bound on the average number of arm pulls for any online algorithm with an error probability not exceeding $delta$. Our refined analysis uncovers a novel bound on the speed at which the average number of arm pulls of our algorithm converges to the fundamental limit as $delta$ vanishes.
  arXiv  Detail & Related papers  (2024-09-08T12:19:12Z)
• Optimal Multi-Fidelity Best-Arm Identification [65.23078799972188]
  In bandit best-arm identification, an algorithm is tasked with finding the arm with highest mean reward with a specified accuracy as fast as possible. We study multi-fidelity best-arm identification, in which the can choose to sample an arm at a lower fidelity (less accurate mean estimate) for a lower cost. Several methods have been proposed for tackling this problem, but their optimality remain elusive, notably due to loose lower bounds on the total cost needed to identify the best arm.
  arXiv  Detail & Related papers  (2024-06-05T08:02:40Z)
• lil'HDoC: An Algorithm for Good Arm Identification under Small Threshold Gap [4.666048091337632]
  Good arm identification (GAI) is a pure-exploration bandit problem in which a single learner outputs an arm as soon as it is identified as a good arm. This paper focuses on the GAI problem under a small threshold gap, which refers to the distance between the expected rewards of arms and the given threshold. We propose a new algorithm called lil'HDoC to significantly improve the total sample complexity of the HDoC algorithm.
  arXiv  Detail & Related papers  (2024-01-29T04:21:47Z)
• Best Arm Identification with Fixed Budget: A Large Deviation Perspective [54.305323903582845]
  We present sred, a truly adaptive algorithm that can reject arms in it any round based on the observed empirical gaps between the rewards of various arms. In particular, we present sred, a truly adaptive algorithm that can reject arms in it any round based on the observed empirical gaps between the rewards of various arms.
  arXiv  Detail & Related papers  (2023-12-19T13:17:43Z)
• Mean-based Best Arm Identification in Stochastic Bandits under Reward Contamination [80.53485617514707]
  This paper proposes two algorithms, a gap-based algorithm and one based on the successive elimination, for best arm identification in sub-Gaussian bandits. Specifically, for the gap-based algorithm, the sample complexity is optimal up to constant factors, while for the successive elimination, it is optimal up to logarithmic factors.
  arXiv  Detail & Related papers  (2021-11-14T21:49:58Z)
• Optimal Best-arm Identification in Linear Bandits [79.3239137440876]
  We devise a simple algorithm whose sampling complexity matches known instance-specific lower bounds. Unlike existing best-arm identification strategies, our algorithm uses a stopping rule that does not depend on the number of arms.
  arXiv  Detail & Related papers  (2020-06-29T14:25:51Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.