Explicit approximation of stochastic optimal feedback control for combined therapy of cancer
For cancer treatment planning, this provides a more practical approach to stochastic optimal control under parameter uncertainty, though the improvement is incremental.
The paper proposes a tractable method for approximating stochastic optimal feedback control in combined immuno-chemo therapy of cancer, showing that adding a variance-related penalty improves results under softened safety constraints. The method uses fixed-point value iteration with machine learning tools for function representation and complexity reduction.
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.