In this paper we address a new problem in reinforcement learning. Here we consider an agent that faces multiple learning tasks within its lifetime. The agent’s objective is to maximize its total reward in the lifetime as well as a conventional return in each task. To realize this, it has to be endowed an important ability to keep its past learning experiences and utilize them for improving future learning performance. This time we try to phrase this problem formally. The central idea is to introduce an environmental class, BV-MDPs that is defined with the distribution of MDPs. As an approach to exploiting past learning experiences, we focus on statistical information (mean and deviation) about the agent’s value tables. The mean can be used as initial values of the table when a new task is presented. The deviation can be viewed as measuring reliability of the mean, and we utilize it in calculating priority of simulated backups. We conduct experiments in computer simulation to evaluate the effectiveness.