Optimization Landscape

Optimization landscape research investigates the shape of the objective function in optimization problems, aiming to understand how different algorithms navigate this landscape to find optimal solutions. Current research focuses on characterizing landscapes for various models, including neural networks (especially deep and narrow architectures), and algorithms like stochastic gradient descent (SGD) and policy gradient methods, analyzing their convergence properties and identifying factors like hyperparameter tuning and architecture choice that influence the landscape's shape and the optimization process. This research is crucial for improving the efficiency and effectiveness of optimization algorithms across diverse fields, from machine learning and reinforcement learning to engineering design and quantum computing, by providing insights into algorithm design and parameter selection.