A Stochastic Maximum Principle Approach for Reinforcement Learning with Parameterized Environment

From Optimal Control to Mean Field Optimal Transport via Stochastic Neural Networks

“…We refer to [26] for an extensive treatment of McKean-Vlasov control problems (20). By considering the joint optimization problem of the entire population, MFC enables the analysis of large-scale systems with cooperative agents and provides insights into the emergence of collective behavior.…”

“…For the sake of completeness, let us also cite [20], where the authors introduce a BSDE technique to solve the related Stochastic Maximum Principle, allowing us to consider the uncertainty associated with NN. The authors employ a Stochastic Differential Equation (SDE) in place of the ODE appearing in (6) to continuously approximate a Stochastic Neural Network (SNN).…”