  Making use of predictions is a crucial, but under-explored, area of online
algorithms. This paper studies a class of online optimization problems where we
have external noisy predictions available. We propose a stochastic prediction
error model that generalizes prior models in the learning and stochastic
control communities, incorporates correlation among prediction errors, and
captures the fact that predictions improve as time passes. We prove that
achieving sublinear regret and constant competitive ratio for online algorithms
requires the use of an unbounded prediction window in adversarial settings, but
that under more realistic stochastic prediction error models it is possible to
use Averaging Fixed Horizon Control (AFHC) to simultaneously achieve sublinear
regret and constant competitive ratio in expectation using only a
constant-sized prediction window. Furthermore, we show that the performance of
AFHC is tightly concentrated around its mean.
