  We consider the setting in which an electric power utility seeks to curtail
its peak electricity demand by offering a fixed group of customers a uniform
price for reductions in consumption relative to their predetermined baselines.
The underlying demand curve, which describes the aggregate reduction in
consumption in response to the 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 utility, we investigate the extent to which the utility might dynamically
adjust its offered prices to maximize its cumulative risk-sensitive payoff over
a finite number of $T$ days. In order to do so effectively, the utility must
design its pricing policy to balance the tradeoff between the need to learn the
unknown demand model (exploration) and maximize its payoff (exploitation) over
time. In this paper, we propose such a pricing policy, which is shown to
exhibit an expected payoff loss over $T$ days that is at most
$O(\sqrt{T}\log(T))$, relative to an oracle pricing policy that knows the
underlying demand model. Moreover, the proposed pricing policy is shown to
yield a sequence of prices that converge to the oracle optimal prices in the
mean square sense.
