Bayesoptimalizálás

Bayesoptimálás is a probabilistic approach to optimizing black-box functions. It is particularly useful when function evaluations are expensive or time-consuming, as it aims to find the global optimum with a minimal number of evaluations. The core idea is to build a probabilistic model of the objective function and then use this model to intelligently select the next point to evaluate.

The probabilistic model is typically a Gaussian process, which provides a distribution over possible functions that fit the observed data. This model allows for uncertainty quantification, meaning it can estimate not only the predicted value of the function at unobserved points but also the confidence in that prediction.

Bayesoptimálás uses an acquisition function to decide where to sample next. The acquisition function balances exploration (sampling in regions with high uncertainty) and exploitation (sampling in regions predicted to have high function values). Common acquisition functions include Expected Improvement, Probability of Improvement, and Upper Confidence Bound.

The algorithm proceeds iteratively. First, an initial set of points is evaluated. Then, a Gaussian process model is fitted to these evaluations. Next, the acquisition function is optimized to find the next point to evaluate. This new point is evaluated, and the Gaussian process model is updated with the new data. This process is repeated until a stopping criterion is met, such as a maximum number of iterations or a desired level of precision. Bayesoptimálás has found applications in hyperparameter tuning for machine learning models, experimental design, and robotics.