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Distribution network scheduling (DNS) is the basis for distribution network management, which is computed in a periodical way via solving the formulated mixed-integer programming (MIP). To achieve the online scheduling, a provably robust learn-to-optimize approach for online DNS is proposed in this paper, whose key lies in the transformation of the MIP-based DNS into the simple linear program problem with a much faster solving time. It formulates the parametric DNS model to construct the offline training dataset and then proposes the provably robust learning approach to learn the integer variables of MIP. The proposed learning approach is adversarial to minor perturbation of input scenario. After training, the learning model can predict the integer variables to achieve online scheduling. Case study verifies the acceleration effectiveness for online DNS.