Batched Single-Index Global Multi-Armed Bandits with Covariates

2025-03-01 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, short

Summary

The paper "Batched Single-Index Global Multi-Armed Bandits with Covariates" by Sakshi Arya and Hyebin Song introduces a novel semi-parametric framework for batched multi-armed bandits (MAB) that incorporates contextual information and related arm rewards. This framework utilizes a shared parameter across arms and employs the single-index regression (SIR) model to capture reward relationships, balancing interpretability and flexibility. Their algorithm, Batched single-Index Dynamic binning and Successive arm elimination (BIDS), utilizes a batched successive arm elimination strategy with dynamic binning guided by the single-index direction. The authors derive theoretical regret bounds for two settings: one where a pilot direction is available and another where it is estimated from data. When an accurate pilot direction is available and the number of arms K is fixed, BIDS achieves minimax-optimal rates (with d = 1) for nonparametric batched bandits, circumventing the curse of dimensionality. Extensive experiments on simulated and real-world datasets confirm the algorithm's effectiveness compared to existing nonparametric batched bandit methods.

Key takeaway

For AI Scientists and Data Scientists developing sequential decision-making systems like personalized medicine or recommendation engines, the BIDS algorithm offers a robust solution for batched multi-armed bandits with covariates. You should consider this semi-parametric framework, which employs single-index regression, to achieve minimax-optimal rates and circumvent the curse of dimensionality when a pilot direction is available. This approach provides a balance of interpretability and flexibility, potentially improving long-term reward maximization in your applications.

Key insights

BIDS is a novel batched multi-armed bandit algorithm that uses single-index regression to efficiently manage covariates and related arm rewards.

Principles

• Shared parameters link MAB arm rewards.
• Single-index regression offers flexible interpretability.
• Dynamic binning guides successive arm elimination.

Method

BIDS algorithm uses batched successive arm elimination and dynamic binning, guided by a single-index direction. It operates with either a pilot direction or an estimated one, deriving theoretical regret bounds.

In practice

• Apply in personalized medicine systems.
• Use for recommendation system optimization.
• Achieve minimax-optimal rates in specific MAB.

Topics

• Multi-Armed Bandits
• Batched Bandits
• Single-Index Regression
• Covariates
• Sequential Decision Making
• Regret Bounds

Best for: AI Scientist, Data Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.