Complex Network Optimization for Fixed-Time Continuous Action Iteration Dilemma by Using Reinforcement Learning

In this paper, an optimization algorithm based on deep reinforcement learning is proposed to optimize complex networks in fixed-time convergence of continuous action iteration dilemmas. The field of continuous action iterative dilemmas has long been studied, with prior research primarily emphasizing the effectiveness of strategy selection and the stability of strategy evolution. However, the impact of topology on strategy evolution has remained under-explored. The present study fills this gap by examining how the structure of complex networks influences the time required for players to reach Nash Equilibrium and overall payoff. To identify the optimal complex network that ensures fixed-time convergence of continuous action iteration dilemma, achieves the shortest time, and attains the highest overall payoff in the Nash Equilibrium state, a deep reinforcement learning algorithm is designed to optimize the complex network. Firstly, the paper applies the Lyapunov stability theory to analyze the convergence of the fixed-time continuous action iteration dilemma and compute the upper bound of convergence time. Secondly, based on the fixed-time convergence of continuous action iteration dilemma, we establish evaluation criteria based on the time taken by players to reach the Nash Equilibrium and the overall payoff, subsequently designing evaluation functions for complex networks utilizing these criteria. Thirdly, this paper applies a deep reinforcement learning algorithm to resolve the optimization issue associated with the proposed evaluation function, while analyzing the convergence of complex network optimization methods. Lastly, the effectiveness of the proposed method is verified by simulating the dynamic model of snowdrift games and prisoner dilemmas.