Hyperparameter Tuning via Spatial Partitioning for Stepwise Functions
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Solution Overview
Problem
Current machine learning methods face challenges in efficiently tuning hyperparameters for stepwise functions, particularly due to the constant and discontinuous nature of these functions, which renders gradient-based optimization ineffective and increases computational costs.
Innovation Solution
The implementation of a spatial-partitioning derivative-free optimization (DFO) method, specifically the StepDIRECT algorithm, which identifies potentially optimal hyper-rectangles using local variability and best function values, and employs a stochastic local search to optimize hyperparameters without relying on gradient estimates or surrogate models.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If gradient-based optimization is used for hyperparameter tuning, then the optimization process can leverage derivative information, but it becomes ineffective for stepwise functions due to their constant and discontinuous nature
Solution Approach 1:
The patent replaces gradient-based optimization (which relies on derivative information) with a derivative-free optimization approach that uses function evaluations and spatial partitioning. This substitution allows the optimization to work effectively with stepwise functions that have discontinuous gradients, resolving the contradiction between optimization effectiveness and adaptability to discontinuous functions.
2Ease of manufacture
If traditional hyperparameter tuning methods are used, then the process is simpler to implement, but computational costs increase due to the need for extensive function evaluations
Solution Approach 1:
The patent segments the hyperparameter search space into hyper-rectangles and systematically partitions them to identify potentially optimal regions. This segmentation approach reduces the number of function evaluations needed by focusing computations on promising areas rather than exhaustively searching the entire space, thereby reducing computational costs while maintaining implementation feasibility.
Solution Approach 2:
The patent performs preliminary actions by identifying and marking potentially optimal hyper-rectangles before conducting detailed local searches. This preliminary classification allows the algorithm to prioritize regions likely to contain optimal hyperparameters, reducing the overall computational burden while preserving implementation simplicity.
3Manufacturing precision
If the search space is exhaustively explored to ensure finding optimal hyperparameters, then solution quality improves, but convergence speed decreases
Solution Approach 1:
The patent applies local quality by performing detailed local searches only within potentially optimal hyper-rectangles identified through spatial partitioning. Instead of uniformly exploring the entire search space, the algorithm concentrates computational effort on regions with higher likelihood of containing optimal hyperparameters, thereby achieving high solution quality without sacrificing convergence speed.
Solution Approach 2:
The patent introduces potentially optimal hyper-rectangles as intermediaries between the global search space and local optimization. These intermediaries serve as a filtering mechanism that guides the optimization process toward promising regions, enabling the algorithm to achieve both high solution quality and fast convergence by avoiding exhaustive exploration of non-promising areas.
Data Source
AI summary
In an approach to hyperparameter optimization, one or more computer processors express a hyperparameter tuning process of a model based on a type of model, one or more dimensions of a training dataset, associated loss function of the model, and associated computational constraints of the model, comprising: identifying a set of optimal hyper-rectangles based a calculated local variability and a calculated best function value; calculating a point as a representative for each identified potentially optimal hyper-rectangle by locally searching over the identified set of potentially optimal hyper-rectangles; dividing one or more hyper-rectangles in the identified set of optimal hyper-rectangles into a plurality of smaller hyper-rectangles based on each calculated point; and calculating one or more optimal hyperparameters utilizing a globally converged hyper-rectangle from the plurality of smaller hyper-rectangles. The one or more computer processors classify one or more unknown datapoints utilizing the model associated with tuned hyperparameters.