What optimization method uses past samples to influence where future sampling occurs in order to find the next optimal sample space?

Bayesian optimization is a sophisticated technique that utilizes probabilistic models to guide the search for optimal parameter values in an efficient manner. It operates by building a Gaussian process model of the objective function based on past evaluation results. This model not only provides a prediction of the function's value at untested points but also conveys uncertainty about those predictions.

By leveraging this uncertainty, Bayesian optimization systematically selects the next points to sample in a way that balances exploration (sampling in areas with high uncertainty) and exploitation (sampling in areas predicted to yield high values). This leads to a more informed sampling strategy compared to methods like grid search or random search, which do not incorporate prior results to influence future sampling decisions.

In contrast, grid search methodically explores a defined parameter space without consideration for previous results, while random search evaluates parameters randomly, potentially missing areas that might have been more fruitful. Simulated annealing is a different algorithm entirely, inspired by thermodynamic principles, focusing on finding a good approximation of the global minimum of a function, rather than adaptively selecting future samples based on past performance.

Thus, Bayesian optimization stands out as the method specifically designed to use past samples to influence future sampling strategies, effectively guiding the exploration of the sample space toward optimal solutions.