Reinforcement learning is one of the intellectual operations applied to autonomously moving robots etc. It is a system having excellent sides, for example, enabling operation in unknown environments. However, it has the basic problem called the “incomplete perception problem”. A variety of solution has been proposed, but none has been decisive. The systems also become complex. A simple and effective method of solution has been desired.A complex value function defining a state-action value by a complex number is introduced. Time series information is introduced into a phase part of the complex number value. Due to this, the time series information is introduced into the value function without using a complex algorithm, so the incomplete perception problem is effectively solved by simple loading of the method.