Convex Cost

Convex cost optimization focuses on finding the minimum of a convex cost function, a problem arising frequently in machine learning, control theory, and operations research. Current research emphasizes developing efficient algorithms for online and federated settings, particularly addressing challenges posed by adversarial constraints, unbounded noise, and non-smooth or non-strongly convex functions. These advancements leverage techniques like online gradient descent, adaptive algorithms (e.g., AdaGrad), and duality-based methods to achieve optimal or near-optimal regret bounds, improving the performance and robustness of various applications. The resulting algorithms have significant implications for data-driven decision-making, resource allocation, and distributed learning systems.