Explicit approximation of stochastic optimal feedback control for combined therapy of cancer

TL;DR

This paper introduces a new method for approximating stochastic optimal feedback control in cancer therapy, utilizing fixed-point value iteration, variance penalties, and machine learning for complexity reduction, demonstrated on a model with high uncertainty.

Contribution

The paper presents a novel tractable approach combining stochastic dynamic programming, variance penalties, and machine learning to improve cancer therapy control strategies.

Findings

Variance-related penalty improves safety constraint handling.

Method effectively approximates optimal feedback control.

Successful application to a complex model with 12 uncertain parameters.

Abstract

In this paper, a tractable methodology is proposed to approximate stochastic optimal feedback treatment in the context of mixed immuno-chemo therapy of cancer. The method uses a fixed-point value iteration that approximately solves a stochastic dynamic programming-like equation. It is in particular shown that the introduction of a variance-related penalty in the latter induces better results that cope with the consequences of softening the health safety constraints in the cost function. The convergence of the value function iteration is revisited in the presence of the variance related term. The implementation involves some Machine Learning tools in order to represent the optimal function and to perform complexity reduction by clustering. Quantitative illustration is given using a commonly used model of combined therapy involving twelve highly uncertain parameters.