Retail pricing for stochastic demand with unknown parameters: An online machine learning approach

The problem of dynamically pricing of electricity by a retailer for customers in a demand response program is considered. It is assumed that the retailer obtains electricity in a two-settlement wholesale market consisting of a day ahead market and a real-time market. Under a day ahead dynamic pricing mechanism, the retailer aims to learn the aggregated demand function of its customers while maximizing its retail profit. A piecewise linear stochastic approximation algorithm is proposed. It is shown that the accumulative regret of the proposed algorithm grows with the learning horizon T at the order of O(log T). It is also shown that the achieved growth rate cannot be reduced by any piecewise linear policy.