  The objective of this paper is to investigate the finite-time analysis of a
Q-learning algorithm applied to two-player zero-sum Markov games. Specifically,
we establish a finite-time analysis of both the minimax Q-learning algorithm
and the corresponding value iteration method. To enhance the analysis of both
value iteration and Q-learning, we employ the switching system model of minimax
Q-learning and the associated value iteration. This approach provides further
insights into minimax Q-learning and facilitates a more straightforward and
insightful convergence analysis. We anticipate that the introduction of these
additional insights has the potential to uncover novel connections and foster
collaboration between concepts in the fields of control theory and
reinforcement learning communities.
