How does the gradient descent algorithm work?

Gradient Descent is an optimization algorithm used to minimize a function by iteratively moving towards the minimum value of the function. It is widely used in machine learning and deep learning to optimize the parameters of a model, such as weights in a neural network.

How it works:

1. Define a loss function: This measures how well the model is performing. The goal is to minimize this function.
2. Initialize parameters: Start with random or predefined values for the model's parameters (e.g., weights).
3. Compute the gradient: Calculate the partial derivatives of the loss function with respect to each parameter. The gradient points in the direction of the steepest increase in the function's value.
4. Update parameters: Adjust the parameters in the opposite direction of the gradient by a small step size (learning rate). The update rule is:

   $\theta = \theta - \eta \cdot$

where $\theta$ is the parameter, $\eta$ is the learning rate, and $\nabla J(\theta)$ is the gradient of the loss function $J$ with respect to $\theta$. 5. **Repeat**: Continue the process until the loss function converges to a minimum or a stopping criterion is met. ### Example: Suppose you have a simple linear regression model $y = mx + b$, and you want to minimize the mean squared error (MSE) loss function. 1. Initialize $m$ and $b$ with random values. 2. Compute the gradient of the MSE with respect to $m$ and $b$. 3. Update $m$ and $b$ using the gradient descent update rule. 4. Repeat until the MSE is minimized. ### In Cloud Computing: When training large-scale machine learning models, gradient descent can be computationally expensive. Cloud platforms like **Tencent Cloud** provide scalable computing resources, such as GPU instances and distributed training services, to accelerate the training process. For example, **Tencent Cloud TI-ONE** offers a unified platform for machine learning, supporting distributed training and efficient parameter optimization. Additionally, **Tencent Cloud CVM** (Cloud Virtual Machine) with GPU acceleration can significantly speed up gradient descent computations for deep learning models.