Diving into Optimization.

2026-07-19 · Source: AI on Medium · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Intermediate, long

Summary

The article discusses machine learning optimization algorithms, explaining their purpose, types (first-order and second-order), and practical trade-offs. It details Gradient Descent, Stochastic Gradient Descent (SGD), Adam, Newton's Method, and Gauss-Newton, including their mathematical principles and update rules. A benchmark analysis compared these algorithms on Breast Cancer, Diabetes, Synthetic, and Adult Income datasets. Results showed second-order methods like Newton's and Gauss-Newton converged in 3-50 iterations for smaller datasets, achieving low loss but not always highest accuracy (e.g., Gradient Descent hit 98.25% on Breast Cancer). For larger datasets like Adult Income, Adam converged in 151 iterations (under 1 second) versus Gradient Descent's 6,916 iterations (36 seconds), both reaching 82.47% accuracy. The analysis concludes that second-order methods excel on small datasets due to faster convergence, while first-order methods, especially Adam, are more practical for large-scale problems due to lower computational cost and better scalability.

Key takeaway

For Machine Learning Engineers selecting an optimizer, you should prioritize first-order methods like Adam for large datasets, as they offer superior scalability and faster training times, as seen with the Adult Income dataset. Conversely, for smaller datasets, consider second-order methods such as Newton's Method or Gauss-Newton for their rapid convergence, noting that lowest loss doesn't always yield the highest predictive accuracy. Always benchmark optimizers against your specific data and model.

Key insights

First-order optimizers scale better for large datasets, while second-order methods offer faster convergence on smaller problems.

Principles

• Gradient Descent moves opposite the gradient to minimize loss.
• Hessian matrix describes loss surface curvature for more accurate updates.
• Lower loss does not always equate to higher prediction accuracy.

Method

Optimization involves iteratively adjusting model parameters using gradients (first-order) or gradients plus curvature information (second-order) to minimize a loss function.

In practice

• Use Adam for large datasets due to faster convergence and scalability.
• Apply Newton's Method or Gauss-Newton for small datasets for rapid convergence.
• Consider that lowest loss does not guarantee best predictive accuracy.

Topics

• Optimization Algorithms
• Gradient Descent
• Adam Optimizer
• Newton's Method
• Hessian Matrix
• Machine Learning Benchmarking

Code references

• ayushzzzz/Optimization-comparison

Best for: Machine Learning Engineer, AI Scientist, AI Student

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Editorial summary, takeaway, and curation by AIssential. Original article published by AI on Medium.