Online learning and pricing for demand response in smart distribution networks

The problem of online learning of consumer response to retail pricing of electricity in a distribution network is considered. In a two-settlement market, the retailer who sets the retail price is exposed to risks from the stochastic response of its consumers and the real-time price fluctuation in the wholesale market. The optimal price maximizing the expected profit is a function of consumer's response to prices, and any pricing scheme under unknown demand model accumulates regret measured by the difference between the total expected profit of the retailer under known and unknown demand model. This paper presents an online learning approach to dynamic pricing aimed at minimizing the regret of the retailer for consumers with unknown Markov jumped affine demand. It is shown that the proposed policy has the lowest order of regret growth characterized by the square-root of the learning horizon.