Bayesian Optimization Stopping Criterion Using Confidence Bounds
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Solution Overview
Problem
Conventional 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 upper and lower confidence bounds (UCB and LCB) is introduced, determining the difference between their optima over the entire parameter space, ensuring efficient termination by considering the entire range of uncertainty, using a surrogate model to approximate the target function.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If conventional Bayesian optimization with lenient stopping criteria is used, then the optimization process is simple to implement, but unnecessary evaluations are performed leading to increased costs and time consumption
Solution Approach 1:
The patent applies preliminary action by establishing a rigorous stopping criterion based on confidence bounds before the optimization process begins. The criterion uses pre-defined confidence levels (e.g., 95%) and accuracy thresholds to determine when to terminate, preventing unnecessary evaluations from the outset. This resolves the contradiction by maintaining ease of implementation through a clear rule-based approach while eliminating time waste through proactive termination conditions.
Solution Approach 2:
The patent implements feedback by continuously monitoring the difference between upper and lower confidence bounds during optimization iterations. When this difference falls below a predefined threshold, the system automatically terminates the process. This feedback mechanism resolves the contradiction by providing a simple-to-implement rule (monitor confidence bound difference) that actively prevents time consumption through automatic termination.
2Ease of operation
If conventional Bayesian optimization with adaptive accuracy targets is used, then the implementation is straightforward, but the stopping criterion is too lenient leading to excessive evaluations
Solution Approach 1:
The patent applies preliminary action by setting a fixed accuracy target and confidence level before optimization begins, rather than using adaptive targets. This preliminary configuration ensures a rigorous stopping criterion is in place from the start, preventing excessive evaluations while maintaining straightforward implementation through pre-defined parameters. The contradiction is resolved by establishing strict termination conditions upfront that balance ease of implementation with evaluation efficiency.
Solution Approach 2:
The patent changes the parameter of the stopping criterion from adaptive to fixed with rigorous confidence bounds. By setting a fixed accuracy threshold (e.g., 1e-6) and confidence level (e.g., 95%), the system achieves a more stringent stopping condition that improves evaluation efficiency. This parameter change resolves the contradiction by making the criterion both easy to implement (fixed parameters) and highly efficient (rigorous termination).
3Ease of operation
If non-rigorous confidence intervals are used, then the stopping rule is easier to apply, but guarantees for optimality are lost
Solution Approach 1:
The patent applies preliminary action by establishing rigorous confidence bounds with guaranteed statistical properties before optimization begins. The confidence intervals are constructed using proven statistical methods (e.g., Gaussian process confidence bounds) that provide theoretical guarantees. This preliminary setup resolves the contradiction by making rigorous reliability guarantees available from the start while maintaining ease of application through automated confidence bound calculations.
Solution Approach 2:
The patent replaces heuristic or empirical confidence interval methods with rigorously proven statistical methods. By using statistically guaranteed confidence bounds (e.g., based on Gaussian process theory), the system achieves optimality guarantees while maintaining ease of application. The substitution of rigorous statistical mechanics for heuristic approaches resolves the contradiction between ease of application and reliability guarantees.
4Measurement precision
If the optimization runs for extended periods to ensure optimality, then solution quality improves, but evaluation costs and time consumption increase
Solution Approach 1:
The patent applies preliminary action by setting a fixed accuracy target and confidence level before optimization begins. This preliminary configuration establishes a clear termination condition that guarantees solution quality within specified bounds without requiring extended optimization periods. The contradiction is resolved by proactively defining when sufficient quality is achieved, preventing unnecessary energy consumption from extended running.
Solution Approach 2:
The patent implements feedback by continuously evaluating whether the confidence bound difference meets the predefined accuracy target. When the target is met, the process terminates automatically. This feedback mechanism resolves the contradiction by providing a simple rule (check confidence bound difference) that ensures solution quality while preventing energy waste from unnecessary extended optimization.
Data Source
AI summary
A system and method 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.