Preconditioned Gradient Descent

Preconditioned gradient descent (PGD) enhances the efficiency and effectiveness of gradient-based optimization methods by incorporating problem-specific information to guide the search for optimal solutions. Current research focuses on adapting PGD to various contexts, including overparameterized neural networks, Wasserstein spaces, and stochastic optimization settings, often employing techniques like Kronecker factorization to manage computational costs. These advancements aim to improve convergence rates, reduce hyperparameter sensitivity, and enable the solution of large-scale optimization problems arising in machine learning and other fields, ultimately leading to more efficient and robust algorithms.