Target Tracking for Contextual Bandits: Application to Demand Side Management

Margaux Brégère (1, 2, 3, 4) , Pierre Gaillard (3) , Yannig Goude (1) , Gilles Stoltz (2, 4)

1 EDF R&D - EDF R&D
2 LMO - Laboratoire de Mathématiques d'Orsay
3 SIERRA - Statistical Machine Learning and Parsimony
4 CELESTE - Statistique mathématique et apprentissage

We propose a contextual-bandit approach for demand side management by offering price incentives. More precisely, a target mean consumption is set at each round and the mean consumption is modeled as a complex function of the distribution of prices sent and of some contextual variables such as the temperature, weather, and so on. The performance of our strategies is measured in quadratic losses through a regret criterion. We offer $T^{2/3}$ upper bounds on this regret (up to poly-logarithmic terms)---and even faster rates under stronger assumptions---for strategies inspired by standard strategies for contextual bandits (like LinUCB, see Li et al., 2010). Simulations on a real data set gathered by UK Power Networks, in which price incentives were offered, show that our strategies are effective and may indeed manage demand response by suitably picking the price levels.

Domains: Machine Learning [stat.ML]; Machine Learning [cs.LG]; Statistics [math.ST]; Electric power

Margaux Brégère, Pierre Gaillard, Yannig Goude, Gilles Stoltz. Target Tracking for Contextual Bandits: Application to Demand Side Management. Thirty-sixth International Conference on Machine Learning, Jun 2019, Long Beach, United States. pp.754-763. ⟨hal-01994144v2⟩