Title: SHE2: Stochastic Hamiltonian Exploration and Exploitation for Derivative-Free Optimization. Abstract: Derivative-free optimization (DFO) using trust region methods is frequently used for machine learning applications, such as (hyper-)parameter optimization without the derivatives of objective functions known.  Inspired by the recent work in continuous-time minimizers, our work models the common trust region methods with the exploration-exploitation using a dynamical system coupling a pair of dynamical processes. While the first exploration process searches the minimum of the blackbox function through minimizing a time-evolving surrogation function, another exploitation process updates the surrogation function time-to-time using the points traversed by the exploration process. The efficiency of derivative-free optimization thus depends on ways the two processes couple. In this paper, we propose a novel dynamical system, namely \ThePrev---\underline{S}tochastic \underline{H}amiltonian \underline{E}xploration and \underline{E}xploitation, that surrogates the subregions of blackbox function using a time-evolving quadratic function, then explores and tracks the minimum of the quadratic functions using a fast-converging Hamiltonian system. The \ThePrev\ algorithm is later provided as a discrete-time numerical approximation to the system. To further accelerate optimization, we present \TheName\ that parallelizes multiple \ThePrev\ threads for concurrent exploration and exploitation. Experiment results based on a wide range of machine learning applications show that \TheName\ outperform a boarder range of derivative-free optimization algorithms with faster convergence speed under the same settings.