Optimization, sampling, and machine learning are essential components of data science. In this talk, I will cover my work on accelerated methods in these fields and highlight some connections between them.
In optimization, I will present optimization as a two-player zero-sum game, which is a modular approach for designing and analyzing convex optimization algorithms by pitting a pair of no-regret learning strategies against each other. This approach not only recovers several existing algorithms but also gives rise to new ones. I will also discuss the use of Heavy Ball in non-convex optimization, which is a popular momentum method in deep learning. Despite its success in practice, Heavy Ball currently lacks theoretical evidence for its acceleration in non-convex optimization. To bridge this gap, I will present some non-convex problems where Heavy Ball exhibits provable acceleration guarantees.
In sampling, I will describe how to accelerate a classical sampling method called Hamiltonian Monte Carlo by setting its integration time appropriately, which builds on a connection between sampling and optimization. In machine learning, I will talk about Gradient Descent with pseudo-labels for fast test-time adaptation under the context of tackling distribution shifts.