Abstract: This work explores how to learn robust and generalizable state representation from image-based observations with deep reinforcement learning methods. Addressing the computational complexity, stringent assumptions, and representation collapse challenges in existing work of bisimulation metric, we devise Simple State Representation (SimSR) operator, which achieves equivalent functionality while reducing the complexity by an order in comparison with bisimulation metric. SimSR enables us to design a stochastic-approximation-based method that can practically learn the mapping functions (encoders) from observations to latent representation space. Besides the theoretical analysis, we experimented and compared our work with recent state-of-the-art solutions in visual MuJoCo tasks. The results shows that our model generally achieves better performance and has better robustness and good generalization.