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This paper introduces a novel operator, termed the Y operator, to elevatecontrol performance in Actor-Critic(AC) based reinforcement learning forsystems governed by stochastic differential equations(SDEs). The Y operatoringeniously integrates the stochasticity of a class of child-mother system intothe Critic network's loss function, yielding substantial advancements in thecontrol performance of RL algorithms.Additionally, the Y operator elegantlyreformulates the challenge of solving partial differential equations for thestate-value function into a parallel problem for the drift and diffusionfunctions within the system's SDEs.A rigorous mathematical proof confirms theoperator's validity.This transformation enables the Y Operator-basedReinforcement Learning(YORL) framework to efficiently tackle optimal controlproblems in both model-based and data-driven systems.The superiority of YORL isdemonstrated through linear and nonlinear numerical examples showing itsenhanced performance over existing methods post convergence.

A Method to Improve the Performance of Reinforcement Learning Based on  the Y Operator for a Class of Stochastic Differential Equation-Based  Child-Mother Systems