 The problem falls into the entropy-regularized  relaxed stochastic control framework recently introduced in Wang et al. (2019). We derive the feedback exploration policy as the Gaussiandistribution , with time-decaying variance.
<clarity>  The problem falls into the entropy-regularized  relaxed stochastic control framework recently introduced in Wang et al. (2019). We derive the feedback exploration policy as the Gaussiandistribution , with time-decaying variance.
 The problem falls into the entropy-regularized relaxed stochastic control problem. We prove that the optimal feedback policy for this problem must be Gaussian , with time-decaying variance.