  In this paper, we consider the problem of learning online to manage Demand
Response (DR) resources. A typical DR mechanism requires the DR manager to
assign a baseline to the participating consumer, where the baseline is an
estimate of the counterfactual consumption of the consumer had it not been
called to provide the DR service. A challenge in estimating baseline is the
incentive the consumer has to inflate the baseline estimate. We consider the
problem of learning online to estimate the baseline and to optimize the
operating costs over a period of time under such incentives. We propose an
online learning scheme that employs least-squares for estimation with a
perturbation to the reward price (for the DR services or load curtailment) that
is designed to balance the exploration and exploitation trade-off that arises
with online learning. We show that, our proposed scheme is able to achieve a
very low regret of $\mathcal{O}\left((\log{T})^2\right)$ with respect to the
optimal operating cost over $T$ days of the DR program with full knowledge of
the baseline, and is individually rational for the consumers to participate.
Our scheme is significantly better than the averaging type approach, which only
fetches $\mathcal{O}(T^{1/3})$ regret.
