  Emphatic Temporal Difference (TD) methods are a class of off-policy
Reinforcement Learning (RL) methods involving the use of followon traces.
Despite the theoretical success of emphatic TD methods in addressing the
notorious deadly triad of off-policy RL, there are still two open problems.
First, followon traces typically suffer from large variance, making them hard
to use in practice. Second, though Yu (2015) confirms the asymptotic
convergence of some emphatic TD methods for prediction problems, there is still
no finite sample analysis for any emphatic TD method for prediction, much less
control. In this paper, we address those two open problems simultaneously via
using truncated followon traces in emphatic TD methods. Unlike the original
followon traces, which depend on all previous history, truncated followon
traces depend on only finite history, reducing variance and enabling the finite
sample analysis of our proposed emphatic TD methods for both prediction and
control.
