Quadratic Cost

Quadratic cost functions are central to various optimization problems across diverse fields, with current research focusing on efficiently solving stochastic optimal transport and control problems where such costs are involved. Prominent approaches leverage Schr\"odinger bridges, often incorporating regularization techniques and employing algorithms like Sinkhorn iterations or novel two-timescale stochastic approximations to handle high-dimensional settings and unknown game structures. These advancements have implications for applications ranging from generative modeling and resource allocation to image processing and Bayesian inference, improving the efficiency and robustness of solutions in these areas.