This repository contains the slides behind my major presentations with a CC-BY license.

[2023] On optimal control and machine learning

This talk tours the optimal control and machine learning methodologies behind recent breakthroughs in the field. These are crucial components for building agents capable of computationally modeling and interacting with our world via planning and reasoning, e.g. for robotics, aircrafts, autonomous vehicles, games, economics, finance, and language, as well as agricultural, biomedical,chemical, industrial, and mechanical systems. We will start with 1) a lightweight introduction to optimal control, and then cover 2) machine learning for optimal control --- this includes reinforcement learning and overviews how the powerful abstractive and predictive capabilities of machine learning can drastically improve every part of a control system; and 3) optimal control for machine learning --- surprisingly in this opposite direction, some machine learning problems are able to be formulated as control problems and solved with optimal control methods, e.g. parts of diffusion models, optimal transport,and optimizing the parameters of models such as large language models with reinforcement learning.

[2023] Learning with differentiable and amortized optimization

Powerpoint | PDF

Optimization has been a transformative modeling and decision-making paradigm over the past century that computationally encodes non-trivial reasoning operations. Developments in optimization foundations alongside domain experts have resulted in breakthroughs for 1) controlling robotic, autonomous, mechanical, and multi-agent systems, 2) making operational decisions based on future predictions, 3) efficiently transporting or matching resources, information, and measures, 4) allocating budgets and portfolios, 5) designing materials, molecules, and other structures, 6) solving inverse problems to infer underlying hidden costs, incentives, geometries, terrains, and other structures, and 7) learning and meta-learning the parameters of predictive and statistical models. These settings often analytically specify the relevant models of the world along with an explicit objective to optimize for. Once these are specified, computational optimization solvers are able to search over the space of possible solutions or configurations and return the best one.

The magic of optimization stops when 1) the relevant models of the world are too difficult or impossible to specify, leading to inaccurate or incomplete representations of the true setting, and 2) solving the optimization problem is computationally challenging and takes too long to return a solution on today's hardware. Machine learning methods help overcome both of these by providing fast predictive models and powerful latent abstractions of the world. In this talk, I will cover two ways of tightly integrating optimization and machine learning methods:]

Differentiable optimization characterizes how the solution to an optimization problem changes as the inputs change. In machine learning settings, differentiable optimization provides an implicit layer that integrates optimization-based domain knowledge into the model and enables unknown parts of the optimization problem to be learned. I will cover the foundations of learning these layers with implicit differentiation and highlight applications in robotics and control settings.
Amortized optimization rapidly predicts approximate solutions to optimization problems and is useful when repeatedly solving optimization problems. Traditional optimization methods typically solve every new problem instance from scratch, ignoring shared structures and information when solving a new instance. In contrast, a solver augmented with amortized optimization learns the shared structure present in the solution mappings and better-searches the domain. I will cover the foundations of amortized optimization and highlight new applications in control and optimal transport.

[2023] Amortized optimization

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, exploiting the shared structure between similar problem instances. These methods have been crucial in variational inference and reinforcement learning and are capable of solving optimization problems many orders of magnitudes times faster than traditional optimization methods that do not use amortization. This talk presents an introduction to the amortized optimization foundations behind these advancements and overviews their applications in variational inference, sparse coding, gradient-based meta-learning, control, reinforcement learning, convex optimization, optimal transport, and deep equilibrium networks.

Powerpoint | PDF | paper

[2023] On amortizing convex conjugates for optimal transport

This paper focuses on computing the convex conjugate operation that arises when solving Euclidean Wasserstein-2 optimal transport problems. This conjugation, which is also referred to as the Legendre-Fenchel conjugate or c-transform,is considered difficult to compute and in practice,Wasserstein-2 methods are limited by not being able to exactly conjugate the dual potentials in continuous space. To overcome this, the computation of the conjugate can be approximated with amortized optimization, which learns a model to predict the conjugate. I show that combining amortized approximations to the conjugate with a solver for fine-tuning significantly improves the quality of transport maps learned for the Wasserstein-2 benchmark by Korotin et al. (2021a) and is able to model many 2-dimensional couplings and flows considered in the literature.

Powerpoint | PDF | paper