Optimization algorithms are the procedures that adjust model parameters to minimize a loss function during learning. They decide how far and in what direction each parameter moves based on gradients, step sizes, and optional second order signals. Good optimizers speed up convergence, stabilize training, and help models generalize by escaping poor local minima and plateaus. In practice, the choice of optimizer interacts with learning rate schedules, normalization, and model architecture. This guide surveys the Top 10 Optimization Algorithms for Training ML Models with concise explanations of when each shines, its main mechanics, and practical tips so beginners and advanced readers can choose confidently.
#1 Stochastic Gradient Descent (SGD)
Stochastic Gradient Descent updates parameters using gradients from mini batches, introducing noise that acts like a regularizer and can help escape shallow minima. Its simplicity, low memory footprint, and predictable behavior make it a baseline for many tasks. Performance depends strongly on learning rate and batch size; too large causes divergence, too small slows learning. Pair it with schedules like cosine decay or step decay, and with data shuffling each epoch. SGD is a strong choice for large scale vision and language models when combined with momentum, careful initialization, and normalization, delivering solid generalization with minimal overhead.
#2 Momentum
Momentum augments SGD by accumulating an exponential moving average of past gradients, which acts like velocity pushing parameters along consistent directions and damping oscillations across steep ravines. The momentum coefficient controls how much past information you retain; common values lie between 0.8 and 0.99. With the same learning rate, momentum often converges faster and more smoothly than vanilla SGD. It works especially well in deep networks with poorly conditioned loss surfaces. Combine momentum with learning rate warmup and decay schedules for stable ramps and precise finishes. Tune momentum jointly with learning rate, since higher momentum often tolerates slightly smaller steps.
#3 Nesterov Accelerated Gradient
Nesterov Accelerated Gradient modifies momentum by computing the gradient at a lookahead position, effectively peeking at where the current velocity will take you. This anticipatory step provides a corrective signal that reduces overshooting and improves responsiveness when loss curves bend. In practice, Nesterov momentum uses the same hyperparameters as classical momentum with a modest computational overhead. It is popular in image classification and other supervised tasks where sharp curvature changes slow plain momentum. Use it with batch normalization or layer normalization to keep gradients well scaled. When tuned, Nesterov frequently delivers faster convergence and slightly better validation accuracy than momentum.
#4 Adagrad
Adagrad adapts the learning rate per parameter based on the history of squared gradients, giving large updates to infrequent features and smaller updates to frequent ones. This makes it appealing for sparse problems such as text and recommendation systems. The key tradeoff is its monotonically decreasing effective learning rate, which can become extremely small and stall training. To mitigate, use initial learning rates on the higher side or switch optimizers once progress slows. Adagrad requires minimal tuning and stores one accumulator per parameter. It remains a practical choice when gradients are sparse and early rapid progress on rare parameters is desirable.
#5 RMSProp
RMSProp tackles the Adagrad issue of decaying rates by using an exponential moving average of squared gradients to normalize updates. This keeps learning rates responsive and prevents them from shrinking to zero. RMSProp is robust on nonstationary objectives and works well in recurrent networks and reinforcement learning. Typical hyperparameters include a decay factor around 0.9, epsilon for numerical stability, and a base learning rate similar to Adagrad. Combine with gradient clipping to control exploding gradients in sequence models. RMSProp provides reliable progress when gradients vary in scale over time, often outperforming Adagrad while maintaining per parameter adaptivity and modest memory requirements.
#6 Adam
Adam combines momentum on gradients with RMSProp style scaling, maintaining moving averages of first and second moments. It adapts step sizes per parameter while preserving directional memory, which delivers fast, stable training across many architectures. Default hyperparameters of beta1 0.9, beta2 0.999, and epsilon 1e-8 are strong starting points. Adam is less sensitive to learning rate than SGD, but still benefits from warmup and decay schedules. It can sometimes overfit or settle in sharp minima, so monitor validation metrics and consider weight decay. For many practitioners, Adam is the go to optimizer for quick, reliable convergence.
#7 AMSGrad
AMSGrad is a variant of Adam designed to address situations where the adaptive learning rate increases due to fluctuating second moment estimates. It enforces a non increasing schedule for the second moment by tracking the maximum of the past values, which leads to more conservative updates and improved theoretical convergence guarantees. In practice, AMSGrad behaves similarly to Adam but can be slightly more stable on noisy or adversarial objectives. It uses the same beta settings and learning rate, so swapping is straightforward. When training large transformers or GANs that exhibit training instabilities, AMSGrad can offer steadier training without major tuning.
#8 Nadam
Nadam blends Adam with Nesterov momentum, applying the lookahead idea to the first moment estimation. By anticipating the next position, Nadam often improves responsiveness and reduces overshoot compared with vanilla Adam. This can yield quicker convergence on tasks with rapidly changing curvature or when gradients are noisy. Hyperparameters mirror Adam, so beta values and epsilon typically remain unchanged, and learning rate tuning follows similar rules. Nadam pairs well with warmup, cosine decay, and gradient clipping. If Adam plateaus early or oscillates near minima, Nadam is a practical drop in alternative that preserves adaptivity while sharpening the momentum behavior.
#9 AdamW
AdamW decouples weight decay from the gradient based update, fixing an interaction in Adam where L2 regularization acts like scaled gradients rather than true parameter shrinkage. By applying weight decay directly to parameters, AdamW provides better control over regularization and often improves generalization, especially in transformer and vision models. Use the same betas and epsilon as Adam, and set weight decay in the range of 0.01 to 0.1 depending on dataset and model size. AdamW benefits from learning rate warmup and cosine schedules. When you need Adam like speed with clearer regularization, AdamW is a reliable default choice.
#10 L-BFGS
L-BFGS is a limited memory quasi Newton method that approximates second order curvature using a compact history of past gradients and parameter differences. It often reaches high accuracy in fewer iterations than first order methods on smooth problems and smaller networks. Because each step solves a line search subproblem, iterations are heavier than SGD, but progress per step can be significant. L-BFGS is effective for fine tuning smaller models, logistic regression, and some shallow networks. It is sensitive to batch noise, so use full batches or large mini batches. When you need precise convergence, L-BFGS is a compelling choice for deterministic, well conditioned objectives.