  While bisimulation-based approaches hold promise for learning robust state
representations for Reinforcement Learning (RL) tasks, their efficacy in
offline RL tasks has not been up to par. In some instances, their performance
has even significantly underperformed alternative methods. We aim to understand
why bisimulation methods succeed in online settings, but falter in offline
tasks. Our analysis reveals that missing transitions in the dataset are
particularly harmful to the bisimulation principle, leading to ineffective
estimation. We also shed light on the critical role of reward scaling in
bounding the scale of bisimulation measurements and of the value error they
induce. Based on these findings, we propose to apply the expectile operator for
representation learning to our offline RL setting, which helps to prevent
overfitting to incomplete data. Meanwhile, by introducing an appropriate reward
scaling strategy, we avoid the risk of feature collapse in representation
space. We implement these recommendations on two state-of-the-art
bisimulation-based algorithms, MICo and SimSR, and demonstrate performance
gains on two benchmark suites: D4RL and Visual D4RL. Codes are provided at
\url{https://github.com/zanghyu/Offline_Bisimulation}.
