Dual Control at Scale: Learning-based control for systems with millions of states.

ongoing

In recent years, data-driven control in high dimensions has penetrated into many new application areas. Examples include control of autonomous vehicles based on video data, simulation based prediction of turbulent flows and precision medicine based on gene sequencing time series data. Large data sets come with significant computational challenges. Tremendous algorithmic progress has been made in machine learning and related areas, but application to dynamical systems is hampered when the number of time samples is small compared to state dimensions, while latency and stability remain central concerns. As a result, learning-based feedback in high dimensions is still carried out without a solid theoretical foundation. This leads to unpredictable behavior, which is a major bottleneck for efficient and resilient control of complex systems in engineering and medicine. The term dual control was introduced in the 1960s to describe the tradeoff between short term control objectives and actions to promote learning for long term performance. A variety of algorithms have been developed to address the problem, but rigorous dynamic analysis is still restricted to systems of low dimension. We propose to address the high-dimensional challenges using a new set of tools based on system theory for positive cones. The cone concept is already well established in the context of sparse matrix theory, compartment models and optimal transport. However, its systematic use for dual and adaptive control remains unexplored. Preliminary results suggest that we are still very far from full exploitation of its algorithmic and analytic potential. Theory and algorithms will in this project be developed in close interaction with researchers studying single cell genetic time series data as a basis for cancer immunotherapy. Learning-based control laws for individually optimized therapy will be developed based on data from cancer tumors.