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Warm-start or cold-start? A comparison of generalizability in gradient-based hyperparameter tuning.

Yubo Zhou1, Jun Shu2, Chengli Tan3

  • 1School of Mathematics and Statistics, Xi'an Jiaotong University, China; SGIT AI Lab, State Grid Corporation of China, China.

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Summary
This summary is machine-generated.

Warm-start strategies in bilevel optimization (BO) for hyperparameter tuning can lead to worse generalization and overfitting. This study reveals why and proposes methods, like random perturbation initialization, to improve performance.

Keywords:
Bilevel optimizationFeature learningGeneralization errorHyperparameter tuningWarm-start

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Area of Science:

  • Machine Learning
  • Optimization

Background:

  • Bilevel optimization (BO) is increasingly used for hyperparameter tuning.
  • Common inner-level strategies include cold-start (fixed initialization) and warm-start (reusing previous solutions).
  • Previous work suggested warm-start has better convergence, but its generalization was less understood.

Purpose of the Study:

  • To compare cold-start and warm-start strategies in BO for hyperparameter tuning from a generalization perspective.
  • To theoretically explain the generalization differences between the two strategies.
  • To propose methods for improving the generalization of warm-start strategies.

Main Methods:

  • Theoretical analysis establishing generalization bounds for cold-start and warm-start.
  • Empirical comparison of the two strategies on hyperparameter tuning tasks.
  • Development and testing of novel approaches to enhance warm-start generalization.

Main Results:

  • Warm-start strategy exhibits worse generalization performance and more severe overfitting compared to cold-start.
  • Theoretical bounds show warm-start's generalization upper bound is worse due to deeper interaction with inner-level dynamics.
  • Proposed methods, including random perturbation initialization, effectively enhance warm-start generalization.

Conclusions:

  • The choice of inner-level initialization strategy significantly impacts generalization in bilevel optimization for hyperparameter tuning.
  • Warm-start's poor generalization is theoretically explained by its reliance on inner-level dynamics.
  • Novel techniques can mitigate warm-start's generalization gap, making it more competitive with cold-start.