Bayesoptimálás

Bayesoptimálás, also known as Bayesian optimization, is a powerful global optimization technique used to find the minimum or maximum of expensive black-box functions. These functions are often encountered in machine learning, hyperparameter tuning, experimental design, and engineering. The key characteristic of a black-box function is that its derivative is unknown or difficult to compute, and evaluating the function itself can be computationally expensive.

Bayesian optimization works by iteratively building a probabilistic model of the objective function, known as a surrogate model, and then using this model to decide where to sample next. Typically, a Gaussian process is used as the surrogate model due to its flexibility and ability to provide uncertainty estimates. The acquisition function, which quantifies the expected improvement at a given point, is then used to guide the selection of the next evaluation point. Popular acquisition functions include Expected Improvement (EI), Probability of Improvement (PI), and Upper Confidence Bound (UCB).

The process involves initializing the surrogate model with a few initial samples of the objective function. Then, in each iteration, the surrogate model is updated with the new evaluation result, and the acquisition function is optimized to find the point that offers the most promising trade-off between exploration (sampling in uncertain regions) and exploitation (sampling in regions known to be good). This iterative process continues until a predefined budget of function evaluations is exhausted or a satisfactory solution is found. Bayesian optimization is particularly effective when function evaluations are costly, as it aims to find good solutions with a minimal number of samples.