Gradient-based optimization has been critical to the success of machine learning, updating a single set of parameters to minimize a single loss. A growing number of applications rely on a generalization of this, where we have a bilevel or nested optimization of which subsets of parameters update on different objectives nested inside each other. We focus on motivating examples of hyperparameter optimization and generative adversarial networks. However, naively applying classical methods often fails when we look at solving these nested problems on a large scale. In this thesis, we build tools for nested optimization that scale to deep learning setups.

What are your thoughts on the topic? How likely do you think that a neural network model will eventually learn to reason and prove theorems like humans? The success of AlphaZero shows that it's possible for artificial neural network based agents to derive their own knowledge from a simple set of rules. However, they suffer from challenges in reinforcement learning: they are not very sample-efficient, and an RL agent that is capable of understanding mathematics has yet to be seen. After looking around many papers I think that there exists a general lack of ability to understand logic in ML models.