Fixed-Budget Real-Valued Combinatorial Pure Exploration of Multi-Armed Bandit

• URL: http://arxiv.org/abs/2310.15681v2
• Date: Wed, 15 Nov 2023 11:10:12 GMT
• Title: Fixed-Budget Real-Valued Combinatorial Pure Exploration of Multi-Armed Bandit
• Authors: Shintaro Nakamura and Masashi Sugiyama
• Abstract summary: We first introduce the Combinatorial Successive Asign algorithm, which is the first algorithm that can identify the best action even when the size of the action class is exponentially large. We show that the upper bound of the probability of error of the CSA algorithm matches a lower bound up to a logarithmic factor in the exponent. We experimentally compare the algorithms with previous methods and show that our algorithm performs better.
• Score: 65.268245109828
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the real-valued combinatorial pure exploration of the multi-armed bandit in the fixed-budget setting. We first introduce the Combinatorial Successive Asign (CSA) algorithm, which is the first algorithm that can identify the best action even when the size of the action class is exponentially large with respect to the number of arms. We show that the upper bound of the probability of error of the CSA algorithm matches a lower bound up to a logarithmic factor in the exponent. Then, we introduce another algorithm named the Minimax Combinatorial Successive Accepts and Rejects (Minimax-CombSAR) algorithm for the case where the size of the action class is polynomial, and show that it is optimal, which matches a lower bound. Finally, we experimentally compare the algorithms with previous methods and show that our algorithm performs better.

Related papers

• On Universally Optimal Algorithms for A/B Testing [49.429419538826444]
  We study the problem of best-arm identification with fixed budget in multi-armed bandits with Bernoulli rewards. For the problem with two arms, also known as the A/B testing problem, we prove that there is no algorithm that performs as well as the algorithm sampling each arm equally.
  arXiv  Detail & Related papers  (2023-08-23T08:38:53Z)
• An Optimal Algorithm for the Real-Valued Combinatorial Pure Exploration of Multi-Armed Bandit [65.268245109828]
  We study the real-valued pure exploration problem in the multi-armed bandit (R-CPE-MAB) Existing methods in the R-CPE-MAB can be seen as a special case of the so-called transductive linear bandits. We propose an algorithm named the gap-based exploration (CombGapE) algorithm, whose sample complexity matches the lower bound.
  arXiv  Detail & Related papers  (2023-06-15T15:37:31Z)
• Practical, Provably-Correct Interactive Learning in the Realizable Setting: The Power of True Believers [12.09273192079783]
  We consider interactive learning in the realizable setting and develop a general framework to handle problems ranging from best arm identification to active classification. We design novel computationally efficient algorithms for the realizable setting that match the minimax lower bound up to logarithmic factors.
  arXiv  Detail & Related papers  (2021-11-09T02:33:36Z)
• 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)
• Upper Confidence Bounds for Combining Stochastic Bandits [52.10197476419621]
  We provide a simple method to combine bandit algorithms. Our approach is based on a "meta-UCB" procedure that treats each of $N$ individual bandit algorithms as arms in a higher-level $N$-armed bandit problem.
  arXiv  Detail & Related papers  (2020-12-24T05:36:29Z)
• On Regret with Multiple Best Arms [12.315392649501101]
  We study a regret problem with the existence of multiple best/near-optimal arms in a bandit setting. Our goal is to design algorithms that can automatically adapt to the unknown hardness of the problem.
  arXiv  Detail & Related papers  (2020-06-26T04:01:46Z)
• An Empirical Process Approach to the Union Bound: Practical Algorithms for Combinatorial and Linear Bandits [34.06611065493047]
  This paper proposes near-optimal algorithms for the pure-exploration linear bandit problem in the fixed confidence and fixed budget settings. We provide an algorithm whose sample complexity scales with the geometry of the instance and avoids an explicit union bound over the number of arms. We also propose the first algorithm for linear bandits in the the fixed budget setting.
  arXiv  Detail & Related papers  (2020-06-21T00:56:33Z)
• Corralling Stochastic Bandit Algorithms [54.10645564702416]
  We show that the regret of the corralling algorithms is no worse than that of the best algorithm containing the arm with the highest reward. We show that the gap between the highest reward and other rewards depends on the gap between the highest reward and other rewards.
  arXiv  Detail & Related papers  (2020-06-16T15:33:12Z)

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.