Bayesian Optimization Stopping Criterion Using UCB-LCB Bounds
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Solution Overview
Problem
Existing Bayesian optimization techniques for black-box functions lack a robust stopping criterion, leading to excessive evaluations and increased costs due to lenient criteria and non-rigorous confidence intervals, resulting in suboptimal parameter sets.
Innovation Solution
A novel stopping criterion based on the difference between upper and lower confidence bounds (UCB and LCB) is introduced, evaluating the entire parameter space to determine when further exploration is unlikely to yield significantly better results, using surrogate models to approximate the target function and ensuring a high level of confidence in the optimality of the solution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Bayesian optimization is run for extended periods to improve parameter optimization accuracy, then optimization precision is improved, but evaluation costs and time consumption increase excessively
Solution Approach 1:
The patent applies preliminary action by pre-calculating and storing confidence intervals for all possible parameter combinations before the optimization process begins. This allows the system to quickly determine when optimization should stop without requiring extended evaluation periods, thus improving optimization precision while reducing evaluation time.
Solution Approach 2:
The patent implements feedback by continuously monitoring the confidence intervals during the Bayesian optimization process and using them to dynamically adjust the stopping criterion. When the confidence interval difference falls below a threshold, the system feedbacks that optimization should stop, preventing excessive evaluation time while maintaining high optimization precision.
2Loss of energy
If lenient stopping criteria are used to reduce evaluation costs, then evaluation costs are reduced, but optimization precision deteriorates due to suboptimal parameter sets
Solution Approach 1:
The patent applies preliminary action by pre-computing rigorous confidence intervals before optimization begins. These pre-calculated statistical bounds ensure that the stopping criterion is based on mathematically sound thresholds rather than lenient heuristics, thereby maintaining high optimization precision while still enabling cost-effective early stopping when the criterion is met.
Solution Approach 2:
The patent substitutes the mechanical trial-and-error approach of traditional stopping criteria with a statistical mechanism based on confidence intervals. This replacement allows for an objective, mathematically rigorous determination of when to stop, preventing both premature termination (which would reduce precision) and excessive continuation (which would increase costs).
3Ease of operation
If non-rigorous confidence intervals are used to simplify the stopping criterion, then ease of operation is improved, but reliability deteriorates due to lack of guarantees
Solution Approach 1:
The patent substitutes ad-hoc, non-rigorous confidence interval methods with statistically rigorous confidence interval calculations. This replacement maintains ease of operation through automated computation while ensuring reliability through mathematically proven guarantees that the stopping criterion will not terminate optimization prematurely.
Solution Approach 2:
The patent implements feedback by using the rigorous confidence intervals to continuously monitor optimization progress and provide statistically guaranteed stopping signals. This feedback mechanism ensures that when the stopping criterion is triggered, it is based on reliable statistical evidence rather than heuristic approximations, thereby maintaining both ease of operation and reliability.
4Measurement precision
If excessive evaluations are performed to ensure optimal parameters are found, then optimization precision is improved, but productivity decreases due to unnecessary evaluations
Solution Approach 1:
The patent applies preliminary action by pre-calculating confidence intervals for all parameter combinations before optimization begins. This allows the system to efficiently determine during the optimization process whether the stopping criterion is met, avoiding unnecessary evaluations while ensuring that optimization precision is maintained through rigorous statistical bounds.
Solution Approach 2:
The patent implements feedback by using the pre-calculated confidence intervals to continuously monitor whether the stopping criterion should be triggered. This feedback mechanism prevents excessive evaluations by automatically stopping optimization when statistical guarantees indicate that further evaluations are unlikely to improve results, thereby maintaining high precision while improving productivity.
Data Source
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Figure 4A~4C
AI summary
A system and method are provided for performing Bayesian optimization in respect of a set of parameters of a target function, such as a black-box function. The Bayesian optimization may be performed iteratively until a stopping criterion is reached. The stopping criterion may be based on an upper and lower confidence bound function and may be reached when a difference between an optimum of the upper confidence bound function and the optimum of the lower confidence bound function reaches or falls below an accuracy target. The stopping criterion may be evaluated by determining an optimum of a respective upper or lower confidence bound function over all of the parameter space. Thereby, it may be ensured that the stopping criterion is met not just based on the explored points but considering the parameter space's entire range.