  Deep neural networks are the most commonly used function approximators in
offline reinforcement learning. Prior works have shown that neural nets trained
with TD-learning and gradient descent can exhibit implicit regularization that
can be characterized by under-parameterization of these networks. Specifically,
the rank of the penultimate feature layer, also called \textit{effective rank},
has been observed to drastically collapse during the training. In turn, this
collapse has been argued to reduce the model's ability to further adapt in
later stages of learning, leading to the diminished final performance. Such an
association between the effective rank and performance makes effective rank
compelling for offline RL, primarily for offline policy evaluation. In this
work, we conduct a careful empirical study on the relation between effective
rank and performance on three offline RL datasets : bsuite, Atari, and DeepMind
lab. We observe that a direct association exists only in restricted settings
and disappears in the more extensive hyperparameter sweeps. Also, we
empirically identify three phases of learning that explain the impact of
implicit regularization on the learning dynamics and found that bootstrapping
alone is insufficient to explain the collapse of the effective rank. Further,
we show that several other factors could confound the relationship between
effective rank and performance and conclude that studying this association
under simplistic assumptions could be highly misleading.
