Sample Complexity of Risk-Neutral Optimal Control with Application to Vaccination Scheduling for Epidemic Control

Abstract

The SEIR model is a widely used framework for simulating the spread of infectious diseases, and optimal control problems can be formulated to design effective intervention strategies, such as vaccination schedules. However, the SEIR model's parameters are often uncertain. To account for this, we model the parameters as random variables and formulate a risk-neutral optimal control problem by the average over their possible values. Building on this idea, we consider a broad class of risk-neutral optimal control problems involving nonlinear ordinary differential equations with uncertain inputs. By sampling these uncertain inputs, we approximate the original problem using empirical risk minimization. Leveraging metric entropy techniques, we derive non-asymptotic sample complexity bounds for the sample-based optimal values and critical points. Numerical simulations for the vaccination scheduling problem confirm our theoretical findings.