Compositional Optimization

Compositional optimization focuses on efficiently solving optimization problems where the objective function is a nested composition of other functions, often involving expectations. Current research emphasizes developing variance-reduction techniques and adaptive algorithms, such as those based on STORM and FedAvg, to improve convergence rates and handle stochasticity, particularly in multi-level and federated settings. These advancements are crucial for tackling complex machine learning problems like distributionally robust optimization, meta-learning, and material design, enabling more efficient and scalable solutions. The resulting algorithms are finding applications in diverse fields, including reinforcement learning, deep learning, and scientific modeling.