Standard reinforcement learning methods assume they can identify each state distinctly before making an action decision. In reality, a robot agent only has a limited sensing capability and identifying each state by extensive sensing can be time consuming. This paper describes an approach that learns active perception strategies in reinforcement learning and considers sensing costs explicitly. The approach integrates cost-sensitive learning with reinforcement learning to learn an efficient internal state representation and a decision policy simultaneously in a finite, deterministic environment. It not only maximizes the long-term discounted reward per action but also reduces the average sensing cost per state. The initial experimental results in a simulated robot navigation domain are encouraging.