bayesian optimization

Bayesian optimization efficiently searches hyperparameters by building a probabilistic model of the objective function. **Core idea**: Maintain belief about how hyperparameters affect performance. Sample where uncertain or likely good. Update belief with results. **Components**: **Surrogate model**: Gaussian process or tree model approximating the objective. Gives mean prediction and uncertainty. **Acquisition function**: Balances exploration (uncertain regions) and exploitation (predicted good regions). Expected improvement common. **Process**: Fit surrogate on observed trials, maximize acquisition to select next trial, evaluate, repeat. **Advantages over random**: Fewer evaluations needed for same quality. Better for expensive objectives (neural network training). **When to use**: Expensive evaluations (full training runs), continuous hyperparameters, moderate dimensionality (under ~20). **Limitations**: Overhead of surrogate fitting, struggles with very high dimensions, discrete variables handled differently. **Tools**: Optuna, scikit-optimize, BoTorch, Ax, Spearmint. **Practical tips**: Good initialization matters, allow enough trials (20-50+ typical), handle crashes gracefully. **Multi-fidelity**: Early stopping or simpler evaluations to filter bad configurations quickly.