Optimal control of stochastic reaction networks

Optimal control problems for the population of interacting particles arise in various fields, including pandemic management, species conservation, cancer therapy, and chemical engineering. When the population size is small, the time evolution of the particle numbers is inherently noisy and modeled by stochastic reaction networks, a class of jump processes on the space of particle number distributions. However, compared to deterministic and other stochastic models, optimal control problems for stochastic reaction networks have not been extensively studied. In this talk, I will review a formulation of stochastic reaction networks and present a new class of optimal control problems that are efficiently solvable and widely applicable. The optimal solution can be efficiently obtained using the Kullback–Leibler divergence as a control cost. We apply this framework to the control of interacting random walkers, birth-death processes, and stochastic SIR models. Both numerical and analytical solutions will be presented, highlighting the practical applications and theoretical significance of this approach.