Tutorial on amortized optimization for learning to optimize over continuous domains

Optimization is a ubiquitous modeling tool and is often deployed in settings which repeatedly solve similar instances of the same problem. Amortized optimization methods use learning to predict the solutions to problems in these settings. This leverages the shared structure between similar problem instances. In this tutorial, we will discuss the key design choices behind amortized optimization, roughly categorizing 1) models into fully-amortized and semi-amortized approaches, and 2) learning methods into regression-based and objective-based. We then view existing applications through these foundations to draw connections between them, including for manifold optimization, variational inference, sparse coding, meta-learning, control, reinforcement learning, convex optimization, and deep equilibrium networks. This framing enables us easily see, for example, that the amortized inference in variational autoencoders is conceptually identical to value gradients in control and reinforcement learning as they both use fully-amortized models with an objective-based loss. The source code for this tutorial is available at https://www.github.com/facebookresearch/amortized-optimization-tutorial