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Barnes Maze Testing Strategies with Small and Large Rodent Models
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A Fast Algorithm for the Real-Valued Combinatorial Pure Exploration of the Multi-Armed Bandit.

Shintaro Nakamura1,2, Masashi Sugiyama3,4

  • 1The University of Tokyo, Bunkyo-ku, Tokyo 113-8654, Japan.

Neural Computation
|December 2, 2024
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Summary
This summary is machine-generated.

We introduce the CombGapE algorithm for the real-valued combinatorial pure exploration problem in stochastic multi-armed bandits. This new method achieves optimal sample complexity and outperforms existing approaches in simulations and real-world tests.

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Area of Science:

  • Machine Learning
  • Optimization
  • Reinforcement Learning

Background:

  • The real-valued combinatorial pure exploration problem (R-CPE-MAB) is a key challenge in stochastic multi-armed bandit settings.
  • Existing methods struggle with large action sets, which are common in practical applications.

Purpose of the Study:

  • To develop an efficient algorithm for the R-CPE-MAB problem with polynomial action set sizes.
  • To establish theoretical performance guarantees for the proposed algorithm.
  • To demonstrate the practical superiority of the new algorithm over existing methods.

Main Methods:

  • Introducing the Combinatorial Gap-based Exploration (CombGapE) algorithm.
  • Analyzing the sample complexity of CombGapE, showing it matches the theoretical lower bound.
  • Conducting numerical experiments on synthetic and real-world datasets.

Main Results:

  • The CombGapE algorithm achieves an upper bound on sample complexity that matches the lower bound, up to a constant factor.
  • Numerical results demonstrate significant performance improvements of CombGapE compared to existing algorithms.
  • The algorithm's effectiveness is validated on both simulated and real-world data.

Conclusions:

  • CombGapE offers a theoretically grounded and practically effective solution for the R-CPE-MAB problem.
  • The algorithm provides a significant advancement in the field of stochastic multi-armed bandits, particularly for problems with large action sets.