  Demand response is designed to motivate electricity customers to modify their
loads at critical time periods. The accurate estimation of impact of demand
response signals to customers' consumption is central to any successful
program. In practice, learning these response is nontrivial because operators
can only send a limited number of signals. In addition, customer behavior also
depends on a large number of exogenous covariates. These two features lead to a
high dimensional inference problem with limited number of observations. In this
paper, we formulate this problem by using a multivariate linear model and adopt
an experimental design approach to estimate the impact of demand response
signals. We show that randomized assignment, which is widely used to estimate
the average treatment effect, is not efficient in reducing the variance of the
estimator when a large number of covariates is present. In contrast, we present
a tractable algorithm that strategically assigns demand response signals to
customers. This algorithm achieves the optimal reduction in estimation
variance, independent of the number of covariates. The results are validated
from simulations on synthetic data.
