Statistical Inference with M-Estimators on Adaptively Collected Data.

Area of Science:

• Machine Learning
• Statistics
• Data Science

Background:

• Bandit algorithms are widely used for sequential decision-making.
• Classical statistics struggle with valid inference on data from bandit algorithms.
• Existing methods are limited to simple models, lacking generality for complex scenarios.

Purpose of the Study:

• To develop general statistical inference methods for data collected with bandit algorithms.
• To enable valid confidence intervals for complex models, such as logistic regression.
• To address the limitations of current statistical approaches in adaptive data collection settings.

Main Methods:

• Developed theory for using M-estimators (e.g., empirical risk minimization, maximum likelihood) with adaptive data.
• Introduced modified M-estimators with specific adaptive weights.
• Established theoretical justification for these modified estimators.

Main Results:

• M-estimators, when appropriately weighted, can yield asymptotically valid confidence regions.
• The proposed methods extend valid statistical inference to complex models under bandit data.
• Demonstrated applicability to diverse inferential targets in adaptive learning.

Conclusions:

• The developed theory supports the use of weighted M-estimators for robust inference with bandit data.
• This work provides a general framework for statistical analysis of adaptive learning systems.
• Enables answering complex scientific questions using data from real-world bandit applications.