Projected Gradient Descent

Projected Gradient Descent (PGD) is an optimization algorithm used in constrained optimization problems, where the goal is to minimize a function subject to constraints on the solution space. It iteratively applies gradient descent steps to update the solution, followed by a projection step that maps the updated solution back onto the feasible set defined by the constraints. This ensures that all intermediate and final solutions satisfy the constraints, making it widely applicable in machine learning, signal processing, and engineering.

Also known as: PGD, Projected Gradient Method, Projected Gradient Algorithm, Gradient Projection Method, ProjGD

Why learn Projected Gradient Descent?

Developers should learn PGD when dealing with optimization problems where solutions must adhere to specific constraints, such as in machine learning for training models with bounded parameters (e.g., in adversarial robustness or regularization), or in engineering for resource allocation with limits. It is particularly useful in scenarios like convex optimization, where constraints are simple to project onto, and in adversarial machine learning to generate robust examples by projecting perturbations onto allowed bounds.

Learning Resources

• book: Stanford Convex Optimization - Projected Gradient Descent
• video: MIT OpenCourseWare - Projected Gradient Descent Lecture
• tutorial: Towards Data Science - PGD Tutorial for Adversarial Attacks
• docs: Scikit-learn Documentation - Optimization Algorithms
• course: Coursera - Optimization for Machine Learning