  Learning the value function of a given policy from data samples is an
important problem in Reinforcement Learning. TD($\lambda$) is a popular class
of algorithms to solve this problem. However, the weights assigned to different
$n$-step returns in TD($\lambda$), controlled by the parameter $\lambda$,
decrease exponentially with increasing $n$. In this paper, we present a
$\lambda$-schedule procedure that generalizes the TD($\lambda$) algorithm to
the case when the parameter $\lambda$ could vary with time-step. This allows
flexibility in weight assignment, i.e., the user can specify the weights
assigned to different $n$-step returns by choosing a sequence $\{\lambda_t\}_{t
\geq 1}$. Based on this procedure, we propose an on-policy algorithm -
TD($\lambda$)-schedule, and two off-policy algorithms - GTD($\lambda$)-schedule
and TDC($\lambda$)-schedule, respectively. We provide proofs of almost sure
convergence for all three algorithms under a general Markov noise framework.
