# Mostly Biomathematics Lunchtime Seminar

#### Training a stochastic controller for automatic insulin dosing via machine learning optimization methods

**Speaker:**
Jonathan Goodman, Department of Mathematics, Courant Institute of Mathematical Sciences, New York University

**Location:**
Warren Weaver Hall 1314

**Date:**
Tuesday, October 22, 2019, 12:30 p.m.

**Synopsis:**

An artificial pancreas is a device for diabetics to automatically measure glucose levels and supply insulin. This talk describes a student project that studied the automatic stochastic control aspect of such a device. We created a simple model of the insulin/glucose system with some stochastic components and a noisy glucose measurement. We designed a simple filter and feedback controller related to controllers used for linear stochastic systems. We then trained (optimized) the parameters in the filter and controller using variants of stochastic gradient descent, SGD, that have proven useful in machine learning training (optimization). The talk will describe the classical theory of linear stochastic control and how well SGD like optimization works on this problem that has (thanks to Kalman) an explicit solution.

Much remains to be done. The objective function used to design the controller should be based on the harm done by hypo and hyperglycemia, but at present it is simply square distance to a desired baseline glucose level. In principle, one can use a more sophisticated model for training the controller offline than would be used online in the controller. The optimization requires thousands of sample paths and sometimes seems to stall.