  In reinforcement learning, the TD($\lambda$) algorithm is a fundamental
policy evaluation method with an efficient online implementation that is
suitable for large-scale problems. One practical drawback of TD($\lambda$) is
its sensitivity to the choice of the step-size. It is an empirically well-known
fact that a large step-size leads to fast convergence, at the cost of higher
variance and risk of instability. In this work, we introduce the implicit
TD($\lambda$) algorithm which has the same function and computational cost as
TD($\lambda$), but is significantly more stable. We provide a theoretical
explanation of this stability and an empirical evaluation of implicit
TD($\lambda$) on typical benchmark tasks. Our results show that implicit
TD($\lambda$) outperforms standard TD($\lambda$) and a state-of-the-art method
that automatically tunes the step-size, and thus shows promise for wide
applicability.
