What is gradient descent?

Gradient descent is an optimization algorithm used to minimize a function, typically a loss or cost function in machine learning. It works by iteratively adjusting the parameters of a model to find the values that result in the lowest possible error. The core idea is to calculate the gradient (slope) of the function at the current parameter values and then update the parameters in the opposite direction of the gradient, since the gradient points uphill. By repeating this process, the algorithm “descends” toward a local minimum of the function. For example, in linear regression, gradient descent adjusts the slope and intercept of a line to minimize the difference between predicted and actual values.

There are three main variants of gradient descent: batch, stochastic, and mini-batch. Batch gradient descent computes the gradient using the entire dataset, which is computationally expensive for large datasets but provides stable convergence. Stochastic gradient descent (SGD) uses a single randomly selected data point per iteration, making it faster per update but noisier, which can help escape local minima. Mini-batch gradient descent strikes a balance by using small random subsets of data, combining the efficiency of SGD with some stability from batch processing. For instance, training a neural network on a dataset with millions of images might use mini-batch (e.g., 64 samples per update) to leverage GPU parallelism while avoiding memory limits.

Practical implementation requires attention to the learning rate, which controls the size of parameter updates. A rate too high can cause overshooting the minimum, while one too low slows convergence. Techniques like learning rate schedules (gradually reducing the rate) or adaptive methods like Adam (which adjusts rates per parameter) help address this. Additionally, challenges like vanishing gradients in deep networks—where early layers train slowly due to small gradients—are mitigated using activation functions like ReLU or normalization layers. Developers often use libraries like TensorFlow or PyTorch, which handle automatic differentiation and optimization, allowing focus on model design rather than manual gradient calculations.