  Many off-policy prediction learning algorithms have been proposed in the past
decade, but it remains unclear which algorithms learn faster than others. We
empirically compare 11 off-policy prediction learning algorithms with linear
function approximation on two small tasks: the Rooms task, and the High
Variance Rooms task. The tasks are designed such that learning fast in them is
challenging. In the Rooms task, the product of importance sampling ratios can
be as large as $2^{14}$ and can sometimes be two. To control the high variance
caused by the product of the importance sampling ratios, step size should be
set small, which in turn slows down learning. The High Variance Rooms task is
more extreme in that the product of the ratios can become as large as
$2^{14}\times 25$. This paper builds upon the empirical study of off-policy
prediction learning algorithms by Ghiassian and Sutton (2021). We consider the
same set of algorithms as theirs and employ the same experimental methodology.
The algorithms considered are: Off-policy TD($\lambda$), five Gradient-TD
algorithms, two Emphatic-TD algorithms, Tree Backup($\lambda$),
Vtrace($\lambda$), and ABTD($\zeta$). We found that the algorithms' performance
is highly affected by the variance induced by the importance sampling ratios.
The data shows that Tree Backup($\lambda$), Vtrace($\lambda$), and
ABTD($\zeta$) are not affected by the high variance as much as other algorithms
but they restrict the effective bootstrapping parameter in a way that is too
limiting for tasks where high variance is not present. We observed that
Emphatic TD($\lambda$) tends to have lower asymptotic error than other
algorithms, but might learn more slowly in some cases. We suggest algorithms
for practitioners based on their problem of interest, and suggest approaches
that can be applied to specific algorithms that might result in substantially
improved algorithms.
