Bayesian optimization is a powerful method for optimizing complex systems with many tunable parameters. It is particularly useful in scenarios where evaluations are costly, derivatives are unavailable, and the objective function is non-convex and multimodal. The method involves building a probabilistic model of the objective function and using it to guide the search for optimal parameters. The key components of Bayesian optimization include a probabilistic surrogate model and an acquisition function that balances exploration and exploitation. The paper reviews Bayesian optimization, highlighting its applications in various domains such as A/B testing, recommender systems, robotics, environmental monitoring, and automatic machine learning. It discusses different models, including parametric and non-parametric approaches, and explores various acquisition functions used to guide the optimization process. The paper also covers the use of Gaussian processes, which are non-parametric models that provide a flexible framework for Bayesian optimization. Common kernels, such as Matérn and squared exponential kernels, are discussed, along with their properties and applications. The paper emphasizes the importance of selecting appropriate models and acquisition functions to achieve efficient and effective optimization in complex scenarios.Bayesian optimization is a powerful method for optimizing complex systems with many tunable parameters. It is particularly useful in scenarios where evaluations are costly, derivatives are unavailable, and the objective function is non-convex and multimodal. The method involves building a probabilistic model of the objective function and using it to guide the search for optimal parameters. The key components of Bayesian optimization include a probabilistic surrogate model and an acquisition function that balances exploration and exploitation. The paper reviews Bayesian optimization, highlighting its applications in various domains such as A/B testing, recommender systems, robotics, environmental monitoring, and automatic machine learning. It discusses different models, including parametric and non-parametric approaches, and explores various acquisition functions used to guide the optimization process. The paper also covers the use of Gaussian processes, which are non-parametric models that provide a flexible framework for Bayesian optimization. Common kernels, such as Matérn and squared exponential kernels, are discussed, along with their properties and applications. The paper emphasizes the importance of selecting appropriate models and acquisition functions to achieve efficient and effective optimization in complex scenarios.