Towards Optimal Pricing of Demand Response -- A Nonparametric
  Constrained Policy Optimization Approach
Jun Song Chaoyue Zhao
Demand response (DR) has been demonstrated to be an effective method for
reducing peak load and mitigating uncertainties on both the supply and demand
sides of the electricity market. One critical question for DR research is how
to appropriately adjust electricity prices in order to shift electrical load
from peak to off-peak hours. In recent years, reinforcement learning (RL) has
been used to address the price-based DR problem because it is a model-free
technique that does not necessitate the identification of models for end-use
customers. However, the majority of RL methods cannot guarantee the stability
and optimality of the learned pricing policy, which is undesirable in
safety-critical power systems and may result in high customer bills. In this
paper, we propose an innovative nonparametric constrained policy optimization
approach that improves optimality while ensuring stability of the policy
update, by removing the restrictive assumption on policy representation that
the majority of the RL literature adopts: the policy must be parameterized or
fall into a certain distribution class. We derive a closed-form expression of
optimal policy update for each iteration and develop an efficient on-policy
actor-critic algorithm to address the proposed constrained policy optimization
problem. The experiments on two DR cases show the superior performance of our
proposed nonparametric constrained policy optimization method compared with
state-of-the-art RL algorithms.