Asymptotically Optimal Contextual Bandit Algorithm Using Hierarchical Structures

Area of Science:

• Machine Learning
• Reinforcement Learning
• Online Learning

Background:

• Contextual multiarmed bandit (CMAB) problems are crucial for sequential decision-making under uncertainty.
• Existing methods often rely on statistical assumptions or struggle with scalability in large context spaces.

Purpose of the Study:

• To develop a robust and efficient online algorithm for the CMAB setting.
• To achieve near-optimal performance without relying on specific statistical assumptions about data distributions.
• To ensure computational scalability for practical applications.

Main Methods:

• Partitioning the context space into regions.
• Data-driven, optimal adaptive combination of mappings between partition regions and bandit arms.
• Utilizing hierarchical partitioning structures like binary trees (BTs) for efficient implementation.
• Theoretical analysis under mild Lipschitz conditions and adversarial environments.

Main Results:

• The proposed algorithm asymptotically achieves the performance of the best possible mapping and arm selection policy.
• Optimality is guaranteed even in adversarial environments, without statistical assumptions.
• Efficient implementation with log-linear computational complexity for BT partitioning.
• Demonstrated superior performance over state-of-the-art techniques in experiments.

Conclusions:

• The developed algorithm offers significant performance improvements and mathematical guarantees in CMAB.
• It provides a computationally scalable and robust solution for sequential learning tasks.
• The approach is versatile, showing effectiveness in both bandit settings and multiclass classification.