  Emphatic algorithms are temporal-difference learning algorithms that change
their effective state distribution by selectively emphasizing and
de-emphasizing their updates on different time steps. Recent works by Sutton,
Mahmood and White (2015), and Yu (2015) show that by varying the emphasis in a
particular way, these algorithms become stable and convergent under off-policy
training with linear function approximation. This paper serves as a unified
summary of the available results from both works. In addition, we demonstrate
the empirical benefits from the flexibility of emphatic algorithms, including
state-dependent discounting, state-dependent bootstrapping, and the
user-specified allocation of function approximation resources.
