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In machine learning, a learning rule refers to a mathematical algorithm or procedure that adjusts the parameters of a machine learning model in response to the input data, with the goal of improving the model's performance on a specific task. Learning rules are a fundamental component of supervised learning, where a model learns from labeled training data, and they are typically used to update the model's parameters (e.g., weights in a neural network or coefficients in a linear regression model).

The learning rule is responsible for minimizing the difference between the model's predictions and the true target values in the training data. This difference is often expressed as a loss or cost function, and the learning rule's objective is to minimize this cost function by iteratively adjusting the model's parameters.

Common learning rules in machine learning include:

1. Gradient Descent: Gradient descent is a popular optimization algorithm used to minimize the loss function by iteratively updating the model parameters in the direction of the steepest gradient. There are different variants of gradient descent, such as stochastic gradient descent (SGD), mini-batch gradient descent, and more.

2. Backpropagation: Backpropagation is a learning rule specifically used in neural networks. It calculates the gradient of the loss function with respect to the network's weights and biases and then updates these parameters using gradient descent.

3. RMSprop, Adam, and other optimization algorithms: These are variants of gradient descent that incorporate adaptive learning rates and momentum to improve convergence speed and stability.

4. Lasso and Ridge Regression: These learning rules are used in linear regression to introduce regularization, which helps prevent overfitting by adding penalty terms to the loss function.

5. Decision Tree Learning Rules: Decision tree algorithms, like CART (Classification and Regression Trees), use learning rules to split data at each node based on a certain criterion, such as Gini impurity or information gain.

6. Reinforcement Learning Algorithms: In reinforcement learning, learning rules determine how an agent should update its policy or value function based on the rewards and experiences it encounters while interacting with an environment. Common algorithms include Q-learning, Policy Gradient methods, and more.

The choice of learning rule depends on the specific machine learning task, the type of model being used, and the available data. The goal is to find the optimal set of model parameters that minimize the difference between the predicted values and the true values for the training data, while avoiding overfitting to ensure good generalization to unseen data.

Table 3860. Examples of applications of learning rules.

Applications	Rule
GLM (Generalized Linear Model)

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