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LinearAPT: An Adaptive Algorithm for the Fixed-Budget Thresholding Linear Bandit Problem

Yun-Ang Wu, Yun-Da Tsai, Shou-De Lin

TL;DR

This study dives into the Thresholding Linear Bandit problem, a nuanced domain within stochastic Multi-Armed Bandit problems, focusing on maximizing decision accuracy against a linearly defined threshold under resource constraints, and presents LinearAPT, a novel algorithm designed for the fixed budget setting of TLB, providing an efficient solution to optimize sequential decision-making.

Abstract

In this study, we delve into the Thresholding Linear Bandit (TLB) problem, a nuanced domain within stochastic Multi-Armed Bandit (MAB) problems, focusing on maximizing decision accuracy against a linearly defined threshold under resource constraints. We present LinearAPT, a novel algorithm designed for the fixed budget setting of TLB, providing an efficient solution to optimize sequential decision-making. This algorithm not only offers a theoretical upper bound for estimated loss but also showcases robust performance on both synthetic and real-world datasets. Our contributions highlight the adaptability, simplicity, and computational efficiency of LinearAPT, making it a valuable addition to the toolkit for addressing complex sequential decision-making challenges.

LinearAPT: An Adaptive Algorithm for the Fixed-Budget Thresholding Linear Bandit Problem

TL;DR

This study dives into the Thresholding Linear Bandit problem, a nuanced domain within stochastic Multi-Armed Bandit problems, focusing on maximizing decision accuracy against a linearly defined threshold under resource constraints, and presents LinearAPT, a novel algorithm designed for the fixed budget setting of TLB, providing an efficient solution to optimize sequential decision-making.

Abstract

In this study, we delve into the Thresholding Linear Bandit (TLB) problem, a nuanced domain within stochastic Multi-Armed Bandit (MAB) problems, focusing on maximizing decision accuracy against a linearly defined threshold under resource constraints. We present LinearAPT, a novel algorithm designed for the fixed budget setting of TLB, providing an efficient solution to optimize sequential decision-making. This algorithm not only offers a theoretical upper bound for estimated loss but also showcases robust performance on both synthetic and real-world datasets. Our contributions highlight the adaptability, simplicity, and computational efficiency of LinearAPT, making it a valuable addition to the toolkit for addressing complex sequential decision-making challenges.
Paper Structure (25 sections, 4 theorems, 28 equations, 4 figures, 3 tables, 1 algorithm)

This paper contains 25 sections, 4 theorems, 28 equations, 4 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Unstructured Thresholding Bandit Problems
  4. Structured Thresholding Bandit Problems
  5. Level Set Estimation
  6. Problem Definition
  7. Linear Bandit
  8. Thresholding Bandit
  9. Algorithm
  10. LinearAPT
  11. Theoretical Bound
  12. Analysis
  13. Experiments
  14. Setup
  15. Dataset
  16. ...and 10 more sections

Key Result

Lemma 1

(NIPS2014_f387624d) For any $\delta > 0$, with probability at least $1-\delta$:

Figures (4)

  • Figure 1: (a) Uniform Box, $d = 5$
  • Figure 2: (b) Uniform Box, $d = 20$
  • Figure 4: (a) Modified version of iris dataset
  • Figure 5: (b) Modified version of wine dataset

Theorems & Definitions (10)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Theorem 1
  • proof
  • proof
  • proof