What quantile is used for the initial DummyRegressor for Gradient Boosting Regressor in scikit-learn?
Yes, a GBM with Huber loss initializes with the median.  The relevant bit of code is the method init_estimator of the loss class, in the file _gb_losses.py.  For HuberLossFunction:
def init_estimator(self):
    return DummyRegressor(strategy='quantile', quantile=.5)

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