Parameter Optimization Using Lower-Dimensional Affine Subspaces
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Solution Overview
Problem
In high-dimensional parameter optimization, existing methods like Bayesian optimization face inefficiencies due to increased computational costs and complexity, particularly when determining optimal parameter values that maximize or minimize objective functions in large search spaces.
Innovation Solution
A parameter optimization system that restricts data sets used for surrogate modeling to those within a predetermined distance from a search space, employing a search space determination unit to select a lower-dimensional affine subspace and a parameter search unit that uses Bayesian optimization to iteratively find optimal parameter values, thereby reducing computational load and maintaining search efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Bayesian optimization is iterated in high-dimensional parameter search, then the search for optimal parameter values can be performed, but the computational cost and complexity increase significantly
Solution Approach 1:
The patent segments the high-dimensional parameter space by identifying and focusing on a subset of critical parameters that have the most significant impact on the objective function. This segmentation allows the optimization process to divide the complex high-dimensional search into manageable lower-dimensional subspaces, reducing computational complexity while maintaining optimization accuracy for the most influential parameters.
Solution Approach 2:
The patent extracts and isolates the most influential parameters from the high-dimensional parameter space by analyzing parameter sensitivity and impact. By taking out only the critical parameters that significantly affect the objective function and excluding less influential ones, the method reduces the dimensionality of the optimization problem and decreases computational burden while preserving optimization effectiveness.
2Adaptability or versatility
If the number of parameters to be adjusted increases, then the comprehensiveness of optimization improves, but the search space becomes larger and optimization becomes more complicated
Solution Approach 1:
The patent applies local quality by treating different parameters differently based on their influence on the objective function. Instead of uniformly optimizing all parameters, the method identifies regions of the parameter space with higher impact and concentrates optimization efforts there, while applying coarser or no optimization to less influential parameters. This localized approach maintains comprehensiveness where needed while improving overall efficiency.
Solution Approach 2:
The patent transforms the high-dimensional parameter optimization problem into a lower-dimensional problem by projecting the parameter space onto a subspace spanned by the most influential parameters. This dimensionality change reduces the search space from D dimensions to a smaller subset, making the optimization process more efficient while maintaining comprehensiveness through subsequent refinement steps.
3Measurement precision
If all data sets are used for surrogate modeling, then the model accuracy improves, but the computational load increases
Solution Approach 1:
The patent performs preliminary action by pre-selecting and filtering data sets before they are used for surrogate modeling. The method预先 identifies and selects only the most relevant and influential data sets based on parameter importance and data quality metrics, discarding or de-emphasizing less useful data. This preliminary filtering reduces the amount of data that needs to be processed for model training, decreasing computational load while maintaining model accuracy through selective use of high-value data.
Data Source
AI summary
According to one embodiment, a parameter optimization apparatus stores data sets which each include a first parameter value of a first number of dimensions and an observed value of an objective function corresponding to the first parameter value. The apparatus determines a search space of a second number of dimensions smaller than the first number of dimensions. The apparatus acquires one or more data sets each having a first parameter value present within a predetermined distance from the search space. The apparatus searches the search space for a first parameter value that may optimize the objective function, using a surrogate model of an objective function based on one or more data sets acquired.