  In this paper, we investigate the problem of controlling probabilistic
Boolean control networks (PBCNs) to achieve reachability with maximum
probability in the finite time horizon. We address three questions: 1) finding
control policies that achieve reachability with maximum probability under
fixed, and particularly, varied finite time horizon, 2) leveraging prior
knowledge to solve question 1) with faster convergence speed in scenarios where
time is a variable framework, and 3) proposing an enhanced Q-learning (QL)
method to efficiently address the aforementioned questions for large-scale
PBCNs. For question 1), we demonstrate the applicability of QL method on the
finite-time reachability problem. For question 2), considering the possibility
of varied time frames, we incorporate transfer learning (TL) technique to
leverage prior knowledge and enhance convergence speed. For question 3), an
enhanced model-free QL approach that improves upon the traditional QL algorithm
by introducing memory-efficient modifications to address these issues in
large-scale PBCNs effectively. Finally, we apply the proposed method to two
examples: a small-scale PBCN and a large-scale PBCN, demonstrating the
effectiveness of our approach.
