The Learn to Optimize paradigm leverages machine learning to accelerate the discovery of new optimization methods. This method's core idea is to use a neural network to simulate the optimization process or provide critical decisions during the process to solve the optimization problem. This talk will introduce two recent research works in learning to optimization.

The first is a theoretical work discussing the application of graph neural networks (GNNs) to linear and mixed integer programming. We prove that well-trained GNNs can solve linear programs but not mixed integer programs without proper fixes. The other is constructing a fixed-point iterative neural network to solve inverse problems and game problems.