Provably Data-driven Multiple Hyper-parameter Tuning with Structured Loss Function

2026-02-02

AI Summary

This work addresses the lack of provable generalization guarantees for multidimensional hyperparameter tuning in complex, non-smooth spaces. It proposes the first data-driven framework for such settings, establishing generalization bounds under mild assumptions by integrating structured loss with validation loss. Leveraging tools from real algebraic geometry, the analysis characterizes the complexity of semi-algebraic function classes, yielding tighter and more broadly applicable generalization bounds. The framework’s effectiveness and learnability are demonstrated on models such as weighted group Lasso and weighted fused Lasso, offering both theoretical foundations and practical methodologies for multidimensional hyperparameter optimization.

Technology Category

• Machine Learning: Auto ML and Hyperparameter Tuning
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Data-driven algorithm design automates hyperparameter tuning, but its statistical foundations remain limited because model performance can depend on hyperparameters in implicit and highly non-smooth ways. Existing guarantees focus on the simple case of a one-dimensional (scalar) hyperparameter. This leaves the practically important, multi-dimensional hyperparameter tuning setting unresolved. We address this open question by establishing the first general framework for establishing generalization guarantees for tuning multi-dimensional hyperparameters in data-driven settings. Our approach strengthens the generalization guarantee framework for semi-algebraic function classes by exploiting tools from real algebraic geometry, yielding sharper, more broadly applicable guarantees. We then extend the analysis to hyperparameter tuning using the validation loss under minimal assumptions, and derive improved bounds when additional structure is available. Finally, we demonstrate the scope of the framework with new learnability results, including data-driven weighted group lasso and weighted fused lasso.

Problem

• hyperparameter tuning
• multi-dimensional
• generalization guarantees
• data-driven
• structured loss

Innovation

• multi-dimensional hyperparameter tuning
• generalization guarantees
• real algebraic geometry
• structured loss function
• data-driven algorithm design