Gradient Descent
Gradient Descent is one of the most widely used optimization algorithms in machine learning. Its purpose is to minimize the loss function by iteratively updating the model’s parameters in the opposite direction of the gradient of the loss with respect to those parameters.
Background
Although the idea dates back to 1847 (Cauchy), gradient descent became central in AI with the development of backpropagation for training neural networks in the 1980s. Today, it remains the backbone of deep learning optimization.
Variants
- Batch Gradient Descent: computes updates using the entire dataset.
- Stochastic Gradient Descent (SGD): updates after each data point, introducing randomness that can help escape local minima.
- Mini-Batch Gradient Descent: balances efficiency and stability.
Applications
- Deep learning models for computer vision and NLP.
- Training regression models for forecasting tasks.
- Reinforcement learning policy optimization.
Strengths and challenges
- ✅ Simple, intuitive, and widely applicable.
- ✅ Scales well with the right variant.
- ❌ Sensitive to learning rate choice.
- ❌ May converge slowly or oscillate on poorly conditioned functions.
Gradient Descent is often compared to walking downhill in a foggy valley: you can’t see the global landscape, but by feeling the slope under your feet (the gradient), you take small steps downward until you (hopefully) reach the bottom. This analogy helps explain both its strength—simplicity—and its challenge: it may get stuck in valleys that are not the absolute lowest point (local minima).
Modern practice extends the basic algorithm with refinements. Momentum methods smooth updates by accumulating past gradients, helping the optimizer roll past small bumps. Adaptive algorithms like Adam, RMSProp, or Adagrad adjust learning rates automatically for each parameter, which accelerates convergence and improves robustness.
Despite being a workhorse of deep learning, gradient descent still requires careful tuning. Too large a learning rate can make training unstable, while too small a rate can make it painfully slow. Researchers increasingly explore second-order methods or hybrid techniques to combine the efficiency of gradient descent with better curvature awareness.
📚 Further Reading
- Bishop, C. (2006). Pattern Recognition and Machine Learning.
- Optimization by gradient descent in AI, Innovatiana
