# Deep Learning Meets Optimal Control - How Optimal Control Enables Faster and Better Training

## Abstract

Deep learning has shown great promise for a variety of machine learning applications. However, many challenges associated with very deep networks remain to be solved, such as for example the scalability barrier created by serial forward and backward propagation where training runtimes increase linearly with the number of layers, the high dimensionality of the resulting learning problem, as well as the question of initialization of the network weights. In this talk, we leverage recent advances in optimal control to address these challenges. In particular, a class of layer-parallel training methodologies is presented that enable concurrency across the network model. The approach is based on a continuous interpretation of deep residual learning as a problem of optimally controlling a continuous dynamical system, which will be summarized in the first part of the talk. Then, a parallel multigrid scheme is proposed that replaces the serial network propagation such that runtimes remain bounded when increasing network depth along with computational resources. The multigrid scheme further allows for coarse-grid representations of the training problem enabling effective initialization strategies. Advanced learning strategies such as simultaneous optimization algorithms and decoupled state and control discretization approaches drawn from optimal control will be discussed.

## Speaker Bio

- 2012 – Diploma (equiv. to masters degree) in Applied Mathematics and Computer Sciences, focus on numerical optimization, University of Trier, Germany
- 2017 – PhD in Applied Mathematics, RWTH Aachen University, Germany, topic: Simultaneous Optimization with Unsteady PDEs, applications to aerodynamic shape optimization/computational fluid dynamics
- 2018-2019 PostDoc at TU Kaiserslautern, Germany, focus on Parallel-in-Time integration and optimization methods for unsteady PDEs
- 2019-2020 PostDoc at Lawrence Livermore National Laboratory, Center for Applied Scientific Computing (CASC), Projects in Time-parallel optimal control for quantum computing
- 2020-now PostDoc Fellow under the Sidney Fernbach Fellowship at Lawrence Livermore National Lab (CASC): Scientific Machine Learning at Extreme Scale - Optimal Control for Deep Learning (and still optimal control for quantum computing)