The Batch Complexity of Bandit Pure Exploration

• URL: http://arxiv.org/abs/2502.01425v1
• Date: Mon, 03 Feb 2025 15:03:45 GMT
• Title: The Batch Complexity of Bandit Pure Exploration
• Authors: Adrienne Tuynman, Rémy Degenne,
• Abstract summary: In a pure exploration problem in multi-armed bandits, an algorithm iteratively samples arms and should stop as early as possible and return the correct answer to a query about the arms distributions. We are interested in batched methods, which change their sampling behaviour only a few times, between batches of observations. We give an instance-dependent lower bound on the number of batches used by any sample efficient algorithm for any pure exploration task.
• Score: 10.036727981085223
• License:
• Abstract: In a fixed-confidence pure exploration problem in stochastic multi-armed bandits, an algorithm iteratively samples arms and should stop as early as possible and return the correct answer to a query about the arms distributions. We are interested in batched methods, which change their sampling behaviour only a few times, between batches of observations. We give an instance-dependent lower bound on the number of batches used by any sample efficient algorithm for any pure exploration task. We then give a general batched algorithm and prove upper bounds on its expected sample complexity and batch complexity. We illustrate both lower and upper bounds on best-arm identification and thresholding bandits.

Related papers

• 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)
• A Fast Algorithm for the Real-Valued Combinatorial Pure Exploration of Multi-Armed Bandit [55.2480439325792]
  We study the real-valued pure exploration problem in the multi-armed bandit (R-CPE-MAB) We introduce an algorithm named the gap-based exploration (CombGapE) algorithm, whose sample complexity upper bound matches the lower bound up to a problem-dependent constant factor. We numerically show that the CombGapE algorithm outperforms existing methods significantly in both synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2023-06-15T15:37:31Z)
• Some performance considerations when using multi-armed bandit algorithms in the presence of missing data [1.0499611180329804]
  When using multi-armed bandit algorithms, the potential impact of missing data is often overlooked. We investigate the impact of missing data on several bandit algorithms via a simulation study assuming the rewards are missing at random.
  arXiv  Detail & Related papers  (2022-05-08T09:20:10Z)
• Optimal Clustering with Bandit Feedback [57.672609011609886]
  This paper considers the problem of online clustering with bandit feedback. It includes a novel stopping rule for sequential testing that circumvents the need to solve any NP-hard weighted clustering problem as its subroutines. We show through extensive simulations on synthetic and real-world datasets that BOC's performance matches the lower boundally, and significantly outperforms a non-adaptive baseline algorithm.
  arXiv  Detail & Related papers  (2022-02-09T06:05:05Z)
• From Optimality to Robustness: Dirichlet Sampling Strategies in Stochastic Bandits [0.0]
  We study a generic Dirichlet Sampling (DS) algorithm, based on pairwise comparisons of empirical indices computed with re-sampling of the arms' observations. We show that different variants of this strategy achieve provably optimal regret guarantees when the distributions are bounded and logarithmic regret for semi-bounded distributions with a mild quantile condition.
  arXiv  Detail & Related papers  (2021-11-18T14:34:21Z)
• 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)
• Efficient Pure Exploration for Combinatorial Bandits with Semi-Bandit Feedback [51.21673420940346]
  Combinatorial bandits generalize multi-armed bandits, where the agent chooses sets of arms and observes a noisy reward for each arm contained in the chosen set. We focus on the pure-exploration problem of identifying the best arm with fixed confidence, as well as a more general setting, where the structure of the answer set differs from the one of the action set. Based on a projection-free online learning algorithm for finite polytopes, it is the first computationally efficient algorithm which is convexally optimal and has competitive empirical performance.
  arXiv  Detail & Related papers  (2021-01-21T10:35:09Z)
• The Price of Incentivizing Exploration: A Characterization via Thompson Sampling and Sample Complexity [83.81297078039836]
  We consider incentivized exploration: a version of multi-armed bandits where the choice of arms is controlled by self-interested agents. We focus on the price of incentives: the loss in performance, broadly construed, incurred for the sake of incentive-compatibility.
  arXiv  Detail & Related papers  (2020-02-03T04:58:51Z)
• The Simulator: Understanding Adaptive Sampling in the Moderate-Confidence Regime [52.38455827779212]
  We propose a novel technique for analyzing adaptive sampling called the em Simulator. We prove the first instance-based lower bounds the top-k problem which incorporate the appropriate log-factors. Our new analysis inspires a simple and near-optimal for the best-arm and top-k identification, the first em practical of its kind for the latter problem.
  arXiv  Detail & Related papers  (2017-02-16T23:42:02Z)

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.