Penalty Method

Penalty methods are optimization techniques that transform constrained problems into unconstrained ones by adding penalty terms to the objective function, aiming to balance performance and constraint satisfaction. Current research focuses on developing adaptive penalty functions, often integrated within reinforcement learning algorithms (e.g., Proximal Policy Optimization) or neural network architectures (e.g., Neural ODEs), to improve efficiency and robustness, particularly in complex scenarios like bilevel optimization and decentralized settings. These advancements are significant for various applications, including safe reinforcement learning, robust machine learning, and efficient solutions to large-scale optimization problems in diverse fields.