Bayesian optimization

Bayesian Optimization is a black box algorithm used to optimize the objective function. It is suitable for non-convex, high-noise problems in many practical problems. This algorithm approximates the objective function by building a surrogate model (such as a Gaussian process or a random forest) and uses Bayesian inference to select the next sampling point to reduce the uncertainty of the surrogate model and the expectation of the objective function. Bayesian optimization usually only requires fewer sampling points to find the global optimal point, and can adaptively adjust the location and number of sampling points.

The basic idea of ​​Bayesian optimization is to select the next sampling point based on existing samples by calculating the posterior distribution of the objective function. This strategy balances exploration and exploitation, that is, exploring unknown areas and using known information to optimize.

Bayesian optimization has been widely used in fields such as hyperparameter tuning, model selection, and feature selection in practice, especially in deep learning. By using Bayesian optimization, we can effectively improve the performance and speed of the model, and be able to flexibly adapt to various objective functions and constraints. The uniqueness of the Bayesian optimization algorithm is that it can update the model based on existing sample data and use this information to select the next operation, thereby searching for the optimal solution more efficiently. Therefore, Bayesian optimization has become the preferred method in many optimization problems.

Bayesian Optimization Principle

The principle of Bayesian optimization can be divided into four steps:

Building a surrogate model: Construct a surrogate model of the objective function based on the sampled samples , models such as Gaussian process or random forest.

2. Select the sampling point: Based on the uncertainty of the agent model and the expectation of the objective function, some strategies are used to select the next sampling point. Common strategies include minimizing confidence intervals and expected improvement. These strategies can be adapted to specific circumstances and needs to achieve a more accurate and efficient sampling process.

3. Sampling objective function: After selecting the sampling point, sample the objective function and update the agent model.

Repeat steps 2 and 3 until a certain number of samples is reached or a certain stopping criterion is reached.

The core of Bayesian optimization includes the construction of surrogate models and the selection of sampling points. The surrogate model helps us understand the structure and characteristics of the objective function and guides the selection of the next sampling point. The selection of sampling points is based on Bayesian inference, which selects the most likely sampling points by calculating the posterior distribution. This method makes full use of existing information and avoids unnecessary sampling points.

In general, Bayesian optimization is an efficient and flexible black-box optimization algorithm that can be applied to non-convex and high-noise problems in various practical problems.

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