The main idea behind the grid search approach is to create a grid of the most reasonable hyperparameter values. The grid is used to generate a reasonable number of distinct parameter sets quickly. We should have some prior knowledge about the task domain to initialize the minimum and maximum values for grid generation, or we can initialize the grid with some reasonable broad ranges. However, if the chosen ranges are too broad, the process of searching for parameters can take a long time and will require a significant amount of computational resources.

At each step, the grid search algorithm chooses a set of hyperparameter values and trains a model. After that, the training step algorithm uses the K-fold cross-validation technique to estimate model performance. We should also define a single model performance estimation metric for model comparison that the algorithm will calculate at each training step for every model. After completing the model training process with each set of parameters from every grid cell, the algorithm chooses the best set of hyperparameter values by comparing the metric's values and selecting the best one. Usually, the set with the smallest value is the best one.

Consider an implementation of this algorithm in different libraries. Our task is to select the best set of hyperparameters for the polynomial regression model, which gives us the best curve that fits the given data. The data in this example is some cosine function values with some random noise.