Ergodic control of a heterogeneous population and application to electricity pricing

Quentin Jacquet (1, 2) , Wim van Ackooij (1) , Clémence Alasseur (1) , Stéphane Gaubert (2)

1 EDF R&D OSIRIS - Optimisation, Simulation, Risque et Statistiques pour les Marchés de l’Energie
2 TROPICAL - TROPICAL

We consider a control problem for a heterogeneous population composed of customers able to switch at any time between different contracts, depending not only on the tariff conditions but also on the characteristics of each individual. A provider aims to maximize an average gain per time unit, supposing that the population is of infinite size. This leads to an ergodic control problem for a "mean-field" MDP in which the state space is a product of simplices, and the population evolves according to a controlled linear dynamics. By exploiting contraction properties of the dynamics in Hilbert's projective metric, we show that the ergodic eigenproblem admits a solution. This allows us to obtain optimal strategies, and to quantify the gap between steady-state strategies and optimal ones. We illustrate this approach on examples from electricity pricing, and show in particular that the optimal policies may be cyclic-alternating between discount and profit taking stages.

Domaines: Optimisation et contrôle [math.OC]

Quentin Jacquet, Wim van Ackooij, Clémence Alasseur, Stéphane Gaubert. Ergodic control of a heterogeneous population and application to electricity pricing. 2022. ⟨hal-03629189v1⟩