基于在线鞍点优化算法的博弈决策求解研究

Research on solving game decision based on online saddle point optimization algorithm

最优决策选择问题一直是优化中的热点话题。本文首先提出FTL算法来进行最优决策更新,并加入正则化方法以稳定时变的决策。其次,用SP-regret度量累积收益和总收益函数的鞍点值之间的差值,证明了结果能达到次线性。进一步地,将算法推广到存在Byzantine故障的3f+1的网络拓扑中,得到了在拜占庭环境下基于在线鞍点优化的正则化跟随领导者算法BOSP-RFTL。数值仿真结果表明:加入正则化后双方的决策变量能够稳定在一定范围内波动。

The optimal decision-making problem has always been a hot topic in optimization. This paper studies the online saddle point optimization algorithm to solve the optimal decision value. Firstly, the Follow the Leader algorithm is proposed to update the optimal decision, and a regularization method is added to stabilize the time-varying decision. Secondly, SP-regret is measured the difference between the cumulative payoff and the saddle point value of the total payoff function and the result can reach sublinear. Furthermore, the algorithm is extended to the 3f+1 network topology with Byzantine faults, and the regularized Follow the Leader algorithm BOSP-RFTL based on online saddle point optimization in Byzantine environment is obtained. Finally, the numerical simulation results show that after adding regularization, the decision variables of both players can stabilize within a certain range of fluctuations.