Bianca Marin Moreno

Bianca Marin Moreno, Margaux Brégère, Pierre Gaillard et al.

Integrating renewable energy into the power grid while balancing supply and demand is a complex issue, given its intermittent nature. Demand side management (DSM) offers solutions to this challenge. We propose a new method for DSM, in particular the problem of controlling a large population of electrical devices to follow a desired consumption signal. We model it as a finite horizon Markovian mean field control problem. We develop a new algorithm, MD-MFC, which provides theoretical guarantees for convex and Lipschitz objective functions. What distinguishes MD-MFC from the existing load control literature is its effectiveness in directly solving the target tracking problem without resorting to regularization techniques on the main problem. A non-standard Bregman divergence on a mirror descent scheme allows dynamic programming to be used to obtain simple closed-form solutions. In addition, we show that general mean-field game algorithms can be applied to this problem, which expands the possibilities for addressing load control problems. We illustrate our claims with experiments on a realistic data set.

Bianca Marin Moreno, Khaled Eldowa, Pierre Gaillard et al.

We study online learning in episodic finite-horizon Markov decision processes (MDPs) with convex objective functions, known as the concave utility reinforcement learning (CURL) problem. This setting generalizes RL from linear to convex losses on the state-action distribution induced by the agent's policy. The non-linearity of CURL invalidates classical Bellman equations and requires new algorithmic approaches. We introduce the first algorithm achieving near-optimal regret bounds for online CURL without any prior knowledge on the transition function. To achieve this, we use an online mirror descent algorithm with varying constraint sets and a carefully designed exploration bonus. We then address for the first time a bandit version of CURL, where the only feedback is the value of the objective function on the state-action distribution induced by the agent's policy. We achieve a sub-linear regret bound for this more challenging problem by adapting techniques from bandit convex optimization to the MDP setting.