  The \textit{Smoothed Bellman Error Embedding} algorithm~\citep{dai2018sbeed},
known as SBEED, was proposed as a provably convergent reinforcement learning
algorithm with general nonlinear function approximation. It has been
successfully implemented with neural networks and achieved strong empirical
results. In this work, we study the theoretical behavior of SBEED in batch-mode
reinforcement learning. We prove a near-optimal performance guarantee that
depends on the representation power of the used function classes and a tight
notion of the distribution shift. Our results improve upon prior guarantees for
SBEED in ~\citet{dai2018sbeed} in terms of the dependence on the planning
horizon and on the sample size. Our analysis builds on the recent work of
~\citet{Xie2020} which studies a related algorithm MSBO, that could be
interpreted as a \textit{non-smooth} counterpart of SBEED.
