A Multiarmed Bandit Based Incentive Mechanism for a Subset Selection of Customers for Demand Response in Smart Grids

Demand response is a crucial tool to maintain the stability of the smart grids. With the upcoming research trends in the area of electricity markets, it has become a possibility to design a dynamic pricing system, and consumers are made aware of what they are going to pay. Though the dynamic pricing system (pricing based on the total demand a distributor company is facing) seems to be one possible solution, the current dynamic pricing approaches are either too complex for a consumer to understand or are too naive leading to inefficiencies in the system (either consumer side or distributor side). Due to these limitations, the recent literature is focusing on the approach to provide incentives to the consumers to reduce the electricity, especially in peak hours. For each round, the goal is to select a subset of consumers to whom the distributor should offer incentives so as to minimize the loss which comprises of cost of buying the electricity from the market, uncertainties at consumer end, and cost incurred to the consumers to reduce the electricity which is a private information to the consumers. Due to the uncertainties in the loss function (arising from renewable energy resources as well as consumption needs), traditional auction theory-based incentives face manipulation challenges. Towards this, we propose a novel combinatorial multi-armed bandit (MAB) algorithm, which we refer to as to learn the uncertainties along with an auction to elicit true costs incurred by the consumers. We prove that our mechanism is regret optimal and is incentive compatible. We further demonstrate efficacy of our algorithms via simulations.