  Self-learning Monte Carlo (SLMC) method is a general algorithm to speedup MC
simulations. Its efficiency has been demonstrated in various systems by
introducing an effective model to propose global moves in the configuration
space. In this paper, we show that deep neural networks can be naturally
incorporated into SLMC, and without any prior knowledge, can learn the original
model accurately and efficiently. Demonstrated in quantum impurity models, we
reduce the complexity for a local update from $ \mathcal{O}(\beta^2) $ in
Hirsch-Fye algorithm to $ \mathcal{O}(\beta \ln \beta) $, which is a
significant speedup especially for systems at low temperatures.
