Stochastic Nonconvex

Stochastic nonconvex optimization focuses on finding approximate solutions to optimization problems where the objective function is nonconvex and involves randomness, a common scenario in machine learning and other fields. Current research emphasizes developing efficient algorithms, such as variance-reduced methods and momentum-based approaches, to address challenges posed by stochasticity and nonconvexity, often within constrained settings or distributed environments. These advancements are crucial for improving the scalability and robustness of machine learning models, particularly in applications like low-rank matrix sensing, meta-learning, and federated learning, where large datasets and complex model architectures are prevalent. The development of algorithms with provable convergence guarantees and optimal complexity bounds is a major focus.