  Radiation therapy (RT) aims to deliver tumoricidal doses with minimal
radiation-induced normal-tissue toxicity. Compared to conventional RT (of
conventional dose rate), FLASH-RT (of ultra-high dose rate) can provide
additional normal tissue sparing, which however has created a new nonconvex and
nonsmooth optimization problem that is highly challenging to solve. In this
paper, we propose a stochastic three-operator splitting (STOS) algorithm to
address the FLASH optimization problem. We establish the convergence and
convergence rates of the STOS algorithm under the nonconvex framework for both
unbiased gradient estimators and variance-reduced gradient estimators. These
stochastic gradient estimators include the most popular ones, such as SGD,
SAGA, SARAH, and SVRG, among others. The effectiveness of the STOS algorithm is
validated using FLASH radiotherapy planning for patients.
