| When solving a problem with a new algorithm, it is of great interest to know: how good is the algorithm comparing with others.The study of computational complexity can illustrate. Analysis of algorithm can let us better understand and improve it. Especially, the correct analysis of algorithm required comprehensive review, and usually make it better and more effective.Reinforcement learning (RL) has attracted most researchers in the area of robotics, because of its strong on-line adaptability and self-learning ability for complex system. So far, reinforcement learning still has many problems to waiting for solving during the process of scaling up to realistic tasks, including the problems associated with very large state spaces, partially observable states, rarely occurring states and un-known environments . But only when the results of analysis is the same as the empirical studies, we will believe that the algorithm and the analysis of the process turned out to be correct and reasonable. To illustrate the method being reasonable and correct, this paper should like to think about the results of analytical and empirical research .In this research, the analysis of Virtual water flow algorithms are studied, the results are presented as follows:(1) This paper provides a introduction to the methods and the primary techniques used in the mathematical analysis of algorithms.(2) The repulsion force function and the gravitation force function of the potential field are introduced. A reinforcement learning problem is transferred to a path planning problem by using artificial potential field and it is the main contents of this thesis. (3) The performance of RPFM is tested by the well-known gridworld problems. Experimental results show that the RPFM is simple and effective to give an optimal solution .(4) The mathematical model is presented.The Worst-case Analysis of the Complexity algorithms is O((n(n-1))/2) .and it is proved by the Mathematical Method. Its space complexity is presented. |
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