This paper addresses the detection problem of flip attacks to sensor network systems where the attacker flips the distribution of manipulated sensor measurements of a binary state. The detector decides to continue taking observations or to stop based on the sensor measurements, and the goal is to have the flip attack recognized as fast as possible while trying to avoid terminating the measurements when no attack is present. The detection problem can be modeled as a partially observable Markov decision process (POMDP) by assuming an attack probability, with the dynamics of the hidden states of the POMDP characterized by a stochastic shortest path (SSP) problem. The optimal policy of the SSP solely depends on the transition costs and is independent of the assumed attack possibility. By using a fixed-length window and suitable feature function of the measurements, a Markov decision process (MDP) is used to approximate the behavior of the POMDP. The optimal solution of the approximated MDP can then be solved by any standard reinforcement learning methods. Numerical evaluations demonstrates the effectiveness of the method.