  Q($\sigma$) is a recently proposed temporal-difference learning method that
interpolates between learning from expected backups and sampled backups. It has
been shown that intermediate values for the interpolation parameter $\sigma \in
[0,1]$ perform better in practice, and therefore it is commonly believed that
$\sigma$ functions as a bias-variance trade-off parameter to achieve these
improvements. In our work, we disprove this notion, showing that the choice of
$\sigma=0$ minimizes variance without increasing bias. This indicates that
$\sigma$ must have some other effect on learning that is not fully understood.
As an alternative, we hypothesize the existence of a new trade-off: larger
$\sigma$-values help overcome poor initializations of the value function, at
the expense of higher statistical variance. To automatically balance these
considerations, we propose Adaptive Tree Backup (ATB) methods, whose weighted
backups evolve as the agent gains experience. Our experiments demonstrate that
adaptive strategies can be more effective than relying on fixed or
time-annealed $\sigma$-values.
