No free lunch for early stopping

Area of Science:

• Machine Learning
• Statistical Learning Theory
• Artificial Intelligence

Background:

• Early stopping is a common regularization technique to prevent overfitting in machine learning.
• The theoretical underpinnings of early stopping's impact on generalization error are not fully understood.
• Existing research often focuses on specific model architectures or assumptions.

Purpose of the Study:

• To analyze the effect of early stopping on expected generalization error under uniform prior assumptions.
• To investigate the relationship between training error, generalization error, and early stopping points.
• To provide a theoretical framework for understanding early stopping's consequences.

Main Methods:

• Theoretical analysis using uniform priors on models with identical training errors.
• Mathematical derivation of expected generalization error based on stopping criteria.
• Comparative analysis of generalization error at different training error thresholds.

Main Results:

• Early stopping at a training error level exceeding the minimum training error leads to increased expected generalization error.
• This increase is observed even when all considered models share the same training error.
• The findings highlight a potential pitfall of a naive early stopping strategy.

Conclusions:

• A uniform prior on models with the same training error does not mitigate the negative impact of suboptimal early stopping.
• Choosing an early stopping point requires careful consideration beyond simply achieving a low training error.
• Further research is needed to explore optimal early stopping strategies and their theoretical guarantees.