Bayesian Evaluation Point Selection Under Predictive Variance Limits
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Solution Overview
Problem
In control processes, selecting evaluation points for Bayesian optimization is challenging due to complex relationships between control parameters and output values, often requiring laborious and error-prone evaluations, especially in high-dimensional spaces.
Innovation Solution
A method for selecting evaluation points that involves determining a posterior model from previous evaluations and optimizing an acquisition function over a search space defined by a specified limit for predictive variance, allowing for efficient optimization and careful exploration of the control parameter space, using a Gaussian process to adapt the search space and ensure efficient sampling.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If a global approach is used to explore the control parameter space, then the coverage of the search space is improved, but the number of function evaluations required increases significantly
Solution Approach 1:
The patent applies local quality by defining a local search space around previously evaluated points rather than exploring the entire parameter space globally. The search space is constructed as a hypercube centered at previously evaluated points with side lengths determined by the predictive variance, focusing computational effort locally where it is most needed while maintaining adequate coverage through strategic placement of multiple local search spaces.
2Adaptability or versatility
If the search space is expanded to cover more areas, then the exploration capability is improved, but the risk of damage increases due to more extensive evaluations
Solution Approach 1:
The patent applies preliminary action by pre-defining the search space boundaries based on predictive variance calculations before actual evaluations are performed. The search space is constructed in advance as a hypercube with side lengths determined by the posterior predictive variance, allowing the system to plan evaluations carefully and avoid regions that would cause damage while still maintaining exploration capability within safe boundaries.
3Productivity
If a local approach is used to reduce the number of evaluations, then the efficiency is improved, but the coverage of the control parameter space decreases
Solution Approach 1:
The patent applies dimensionality change by transforming the search space definition from a fixed global boundary to a dynamic local hypercube structure centered at previously evaluated points. The side lengths of the hypercube are determined by the predictive variance in each dimension, allowing the search space to adapt its shape and coverage to the local characteristics of the objective function while maintaining computational efficiency through focused local exploration.
Data Source
AI summary
A method is described for selecting evaluation points for a Bayesian optimization method for optimizing a physical or chemical process that is modeled by a statistical model. The method includes the ascertainment of a posterior model of the statistical model in accordance with the results of one or multiple evaluations at previous evaluation points and the selection of a next evaluation point by optimizing an acquisition function over a search space, which is given by a specified limit for the predictive variance of the points in the search space given by the posterior model.