  We study a demand response problem from utility (also referred to as
operator)'s perspective with realistic settings, in which the utility faces
uncertainty and limited communication. Specifically, the utility does not know
the cost function of consumers and cannot have multiple rounds of information
exchange with consumers. We formulate an optimization problem for the utility
to minimize its operational cost considering time-varying demand response
targets and responses of consumers. We develop a joint online learning and
pricing algorithm. In each time slot, the utility sends out a price signal to
all consumers and estimates the cost functions of consumers based on their
noisy responses. We measure the performance of our algorithm using regret
analysis and show that our online algorithm achieves logarithmic regret with
respect to the operating horizon. In addition, our algorithm employs linear
regression to estimate the aggregate response of consumers, making it easy to
implement in practice. Simulation experiments validate the theoretic results
and show that the performance gap between our algorithm and the offline
optimality decays quickly.
