Optimizer Comparison: SGD, Momentum, Adam, RMSprop, and When Each Shines

Optimizers are algorithms that update weights based on gradients. SGD is simple but slow. Momentum accelerates convergence. Adam adapts learning rates per parameter. Each optimizer has strengths: SGD generalizes well, Adam is fast, RMSprop for non-stationary problems.

SGD (Stochastic Gradient Descent)

# Update: w = w - lr * gradient
optimizer = torch.optim.SGD(model.parameters(), lr=0.01)

Pros: Simple, generalizes well. Cons: Slow convergence, sensitive to learning rate.

Momentum

# Momentum accumulates gradients: v = β*v + gradient
# Update: w = w - lr * v
optimizer = torch.optim.SGD(model.parameters(), lr=0.01, momentum=0.9)

Pros: Faster convergence, escapes local minima. Cons: Can overshoot.

Adam (Adaptive Moment Estimation)

# Adapts learning rate per parameter
# m = β1*m + (1-β1)*gradient
# v = β2*v + (1-β2)*gradient^2
# Update: w = w - (lr * m) / (sqrt(v) + ε)
optimizer = torch.optim.Adam(model.parameters(), lr=0.001)

Pros: Fast, automatic learning rate tuning. Cons: Can overfit, memory overhead.

When to Use

• SGD: Simple models, generalization matters
• Momentum: CNNs, need faster convergence
• Adam: LLMs, complex objectives, most practical choice
• RMSprop: Non-stationary data, sparse gradients

Conclusion

Choosing the right optimizer affects training speed and final performance. Adam is the practical default; SGD for maximum generalization. Understanding optimizer mechanics guides hyperparameter tuning and model development. Next: learning rate scheduling—how to adapt learning rate during training.