  In this paper, we address a pursuit-evasion game involving multiple players
by utilizing tools and techniques from reinforcement learning and matrix game
theory. In particular, we consider the problem of steering an evader to a goal
destination while avoiding capture by multiple pursuers, which is a
high-dimensional and computationally intractable problem in general. In our
proposed approach, we first formulate the multi-agent pursuit-evasion game as a
sequence of discrete matrix games. Next, in order to simplify the solution
process, we transform the high-dimensional state space into a low-dimensional
manifold and the continuous action space into a feature-based space, which is a
discrete abstraction of the original space. Based on these transformed state
and action spaces, we subsequently employ min-max Q-learning, to generate the
entries of the payoff matrix of the game, and subsequently obtain the optimal
action for the evader at each stage. Finally, we present extensive numerical
simulations to evaluate the performance of the proposed learning-based evading
strategy in terms of the evader's ability to reach the desired target location
without being captured, as well as computational efficiency.
