  In this paper, we investigate the framework of Online Convex Optimization
(OCO) for online learning. OCO offers a very powerful online learning framework
for many applications. In this context, we study a specific framework of OCO
called {\it OCO with long term constraints}. Long term constraints are
introduced typically as an alternative to reduce the complexity of the
projection at every update step in online optimization. While many algorithmic
advances have been made towards online optimization with long term constraints,
these algorithms typically assume that the sequence of cost functions over a
certain $T$ finite steps that determine the cost to the online learner are
adversarially generated. In many circumstances, the sequence of cost functions
may not be unrelated, and thus predictable from those observed till a point of
time. In this paper, we study the setting where the sequences are predictable.
We present a novel online optimization algorithm for online optimization with
long term constraints that can leverage such predictability. We show that, with
a predictor that can supply the gradient information of the next function in
the sequence, our algorithm can achieve an overall regret and constraint
violation rate that is strictly less than the rate that is achievable without
prediction.
