  The main challenge of offline reinforcement learning, where data is limited,
arises from a sequence of counterfactual reasoning dilemmas within the realm of
potential actions: What if we were to choose a different course of action?
These circumstances frequently give rise to extrapolation errors, which tend to
accumulate exponentially with the problem horizon. Hence, it becomes crucial to
acknowledge that not all decision steps are equally important to the final
outcome, and to budget the number of counterfactual decisions a policy make in
order to control the extrapolation. Contrary to existing approaches that use
regularization on either the policy or value function, we propose an approach
to explicitly bound the amount of out-of-distribution actions during training.
Specifically, our method utilizes dynamic programming to decide where to
extrapolate and where not to, with an upper bound on the decisions different
from behavior policy. It balances between the potential for improvement from
taking out-of-distribution actions and the risk of making errors due to
extrapolation. Theoretically, we justify our method by the constrained
optimality of the fixed point solution to our $Q$ updating rules. Empirically,
we show that the overall performance of our method is better than the
state-of-the-art offline RL methods on tasks in the widely-used D4RL
benchmarks.
