Gradient-based optimization algorithms play an essential role in training machine learning models, especially deep neural networks, by efficiently minimizing loss functions to improve model performance.
These algorithms iteratively adjust model parameters based on gradient information, navigating the complex shape of loss surfaces to find optimal or near-optimal values.
Among these, Adam and its variants have become popular choices due to their adaptive learning rates and robust convergence.
Complementing optimizer choice, learning rate schedulers dynamically adjust the learning rate during training to enhance convergence speed and stability.
Introduction to Gradient-Based Optimization
Gradient-based optimization methods rely on computing the gradient (or approximate gradient) of the loss function with respect to model parameters and updating those parameters iteratively to minimize loss.
Parameters θ are updated as: 
Where, 
Proper choice of optimizer and learning rate is critical to training efficiency and model quality.
Adam Optimizer and Its Variants
Adam (Adaptive Moment Estimation) combines ideas from two classical methods, Momentum and RMSProp, to adapt learning rates for each parameter individually, improving convergence on noisy and sparse gradients.
1. Maintains decaying averages of past gradients 
and squared gradients 
to adapt step sizes.
2. Updates parameters using bias-corrected estimates:
Common Adam variants include:
1. AdamW: Separates weight decay from the gradient update for more effective regularization.
2. AMSGrad: Addresses convergence issues by enforcing non-increasing learning rates.
3. AdaBound: Combines Adam’s adaptive method with learning rate clipping for stable convergence.
Learning Rate Schedulers
Learning rate schedulers modulate the learning rate during training to avoid issues like overshooting minima or slow convergence.
Popular Scheduler Types:
Schedulers help avoid plateaus, promote better minima discovery, and prevent training instability.
Practical Guidelines
1. Start with Adam or AdamW optimizers as default choices in deep learning tasks.
2. Use learning rate warmup in large-scale or transformer-based training for stable beginnings.
3. Implement step decay or cosine annealing to dynamically adjust the learning rate over epochs.
4. Monitor training and validation losses to adjust the learning rate manually if necessary.
5. Combine weight decay with AdamW to improve generalization by reducing overfitting.