GENERAL PROOF OF CONVERGENCE OF THE NASH-Q-LEARNING ALGORITHM

Jun Wang (), Lei Cao, Xiliang Chen and Jun Lai
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Jun Wang: Command Control Engineering Institute, Army Engineering University of PLA, Nanjing 211101, P. R. China
Lei Cao: Command Control Engineering Institute, Army Engineering University of PLA, Nanjing 211101, P. R. China
Xiliang Chen: Command Control Engineering Institute, Army Engineering University of PLA, Nanjing 211101, P. R. China
Jun Lai: Command Control Engineering Institute, Army Engineering University of PLA, Nanjing 211101, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-9

Abstract: In this paper, the convergence of the Nash-Q-Learning algorithm will be studied mainly. In the previous proof of convergence, each stage of the game must have a global optimal point or a saddle point. Obviously, the assumption is so strict that there are not many application scenarios for the algorithm. At the same time, the algorithm can also get a convergent result in the two Grid-World Games, which do not meet the above assumptions. Thus, previous researchers proposed that the assumptions may be appropriately relaxed. However, a rigorous theoretical proof is not given. The convergence point is a fractal attractor from the view of Fractals, general proof of convergence of the Nash-Q-Learning algorithm will be shown by the mathematical method. Meanwhile, some discussions on the efficiency and scalability of the algorithm are also described in detail.

Keywords: Nash-Q-Learning; Game Theory; Schauder; Fractals (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X2250027X

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