  The divergence of the Q-value estimation has been a prominent issue in
offline RL, where the agent has no access to real dynamics. Traditional beliefs
attribute this instability to querying out-of-distribution actions when
bootstrapping value targets. Though this issue can be alleviated with policy
constraints or conservative Q estimation, a theoretical understanding of the
underlying mechanism causing the divergence has been absent. In this work, we
aim to thoroughly comprehend this mechanism and attain an improved solution. We
first identify a fundamental pattern, self-excitation, as the primary cause of
Q-value estimation divergence in offline RL. Then, we propose a novel
Self-Excite Eigenvalue Measure (SEEM) metric based on Neural Tangent Kernel
(NTK) to measure the evolving property of Q-network at training, which provides
an intriguing explanation of the emergence of divergence. For the first time,
our theory can reliably decide whether the training will diverge at an early
stage, and even predict the order of the growth for the estimated Q-value, the
model's norm, and the crashing step when an SGD optimizer is used. The
experiments demonstrate perfect alignment with this theoretic analysis.
Building on our insights, we propose to resolve divergence from a novel
perspective, namely improving the model's architecture for better extrapolating
behavior. Through extensive empirical studies, we identify LayerNorm as a good
solution to effectively avoid divergence without introducing detrimental bias,
leading to superior performance. Experimental results prove that it can still
work in some most challenging settings, i.e. using only 1 transitions of the
dataset, where all previous methods fail. Moreover, it can be easily plugged
into modern offline RL methods and achieve SOTA results on many challenging
tasks. We also give unique insights into its effectiveness.
