Adaptive Learn-then-Test: Statistically Valid and Efficient Hyperparameter Selection

TL;DR

The paper presents a new adaptive hyperparameter selection method, aLTT, that offers statistically valid, efficient testing with fewer rounds, suitable for costly or risky testing scenarios.

Contribution

aLTT extends learn-then-test by incorporating sequential, data-dependent hypothesis testing with early stopping, improving efficiency while maintaining statistical guarantees.

Findings

aLTT reduces testing rounds significantly compared to traditional methods.

aLTT maintains statistical validity in hyperparameter selection.

aLTT performs comparably to existing methods in practical applications.

Abstract

We introduce adaptive learn-then-test (aLTT), an efficient hyperparameter selection procedure that provides finite-sample statistical guarantees on the population risk of AI models. Unlike the existing learn-then-test (LTT) technique, which relies on conventional p-value-based multiple hypothesis testing (MHT), aLTT implements sequential data-dependent MHT with early termination by leveraging e-processes. As a result, aLTT can reduce the number of testing rounds, making it particularly well-suited for scenarios in which testing is costly or presents safety risks. Apart from maintaining statistical validity, in applications such as online policy selection for offline reinforcement learning and prompt engineering, aLTT is shown to achieve the same performance as LTT while requiring only a fraction of the testing rounds.