Bregman Information

Bregman information, a measure of divergence based on convex functions, is central to various optimization and machine learning problems. Current research focuses on leveraging Bregman divergences within algorithms like mirror descent and Bregman proximal gradient methods for tasks such as image restoration, phase retrieval, and training neural networks, including unfolded proximal neural networks and gradient boosting machines. This framework offers advantages in handling non-convex objectives and constraints, leading to improved efficiency and robustness in diverse applications, from computational imaging to dimensionality reduction of PDE solutions. The resulting algorithms demonstrate improved convergence properties and reduced computational costs compared to traditional methods.