In this paper, we develop a new checkpointing scheme for a uniprocess application. First, we model the checkpointing scheme by a semi-Markov decision process, and apply the reinforcement learning algorithm to estimate statistically the optimal checkpointing policy. More specifically, the representative reinforcement learning algorithm, called the Q-learning algorithm, is used to develop an adaptive checkpointing scheme. In simulation experiments, we examine the asymptotic behavior of the system overhead with adaptive checkpointing and show quantitatively that the proposed dynamic checkpoint algorithm is useful and robust under an incomplete knowledge on the failure time distribution.