  In this paper, we study a continuous-time exploratory mean-variance (EMV)
problem under the framework of reinforcement learning (RL), and the Choquet
regularizers are used to measure the level of exploration. By applying the
classical Bellman principle of optimality, the Hamilton-Jacobi-Bellman equation
of the EMV problem is derived and solved explicitly via maximizing statically a
mean-variance constrained Choquet regularizer. In particular, the optimal
distributions form a location-scale family, whose shape depends on the choices
of the Choquet regularizer. We further reformulate the continuous-time
Choquet-regularized EMV problem using a variant of the Choquet regularizer.
Several examples are given under specific Choquet regularizers that generate
broadly used exploratory samplers such as exponential, uniform and Gaussian.
Finally, we design a RL algorithm to simulate and compare results under the two
different forms of regularizers.
