  We study nonparametric density estimation in non-stationary drift settings.
Given a sequence of independent samples taken from a distribution that
gradually changes in time, the goal is to compute the best estimate for the
current distribution. We prove tight minimax risk bounds for both discrete and
continuous smooth densities, where the minimum is over all possible estimates
and the maximum is over all possible distributions that satisfy the drift
constraints. Our technique handles a broad class of drift models, and
generalizes previous results on agnostic learning under drift.
