Approximation Error

Approximation error, the discrepancy between a simplified model and the true underlying function or process, is a central challenge across numerous scientific fields. Current research focuses on bounding and minimizing this error in various contexts, including reinforcement learning (using algorithms like optimistic value function elimination), neural network approximation (exploring ReLU networks and tensor decompositions), and kernel methods (such as Bayesian quadrature). Understanding and controlling approximation error is crucial for improving the accuracy and efficiency of machine learning models, numerical methods for solving differential equations, and other computational techniques, ultimately leading to more reliable and robust scientific inferences and technological applications.