  We adopt the perspective of an aggregator, which seeks to coordinate its
purchase of demand reductions from a fixed group of residential electricity
customers, with its sale of the aggregate demand reduction in a two-settlement
wholesale energy market. The aggregator procures reductions in demand by
offering its customers a uniform price for reductions in consumption relative
to their predetermined baselines. Prior to its realization of the aggregate
demand reduction, the aggregator must also determine how much energy to sell
into the two-settlement energy market. In the day-ahead market, the aggregator
commits to a forward contract, which calls for the delivery of energy in the
real-time market. The underlying aggregate demand curve, which relates the
aggregate demand reduction to the aggregator's offered price, is assumed to be
affine and subject to unobservable, random shocks. Assuming that both the
parameters of the demand curve and the distribution of the random shocks are
initially unknown to the aggregator, we investigate the extent to which the
aggregator might dynamically adapt its offered prices and forward contracts to
maximize its expected profit over a time window of $T$ days. Specifically, we
design a dynamic pricing and contract offering policy that resolves the
aggregator's need to learn the unknown demand model with its desire to maximize
its cumulative expected profit over time. In particular, the proposed pricing
policy is proven to incur a regret over $T$ days that is no greater than
$O(\log(T)\sqrt{T})$.
