  This paper studies the problem of expected loss minimization given a data
distribution that is dependent on the decision-maker's action and evolves
dynamically in time according to a geometric decay process. Novel algorithms
for both the information setting in which the decision-maker has a first order
gradient oracle and the setting in which they have simply a loss function
oracle are introduced. The algorithms operate on the same underlying principle:
the decision-maker repeatedly deploys a fixed decision over the length of an
epoch, thereby allowing the dynamically changing environment to sufficiently
mix before updating the decision. The iteration complexity in each of the
settings is shown to match existing rates for first and zero order stochastic
gradient methods up to logarithmic factors. The algorithms are evaluated on a
"semi-synthetic" example using real world data from the SFpark dynamic pricing
pilot study; it is shown that the announced prices result in an improvement for
the institution's objective (target occupancy), while achieving an overall
reduction in parking rates.
