Efficient Model-Based Concave Utility Reinforcement Learning through Greedy Mirror Descent

Bianca Marin Moreno (1) , Margaux Brégère (2, 3, 4) , Pierre Gaillard (1) , Nadia Oudjane (2)

1 Thoth - Apprentissage de modèles à partir de données massives
2 EDF R&D - EDF R&D
3 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation
4 SU - Sorbonne Université

Many machine learning tasks can be solved by minimizing a convex function of an occupancy measure over the policies that generate them. These include reinforcement learning, imitation learning, among others. This more general paradigm is called the Concave Utility Reinforcement Learning problem (CURL). Since CURL invalidates classical Bellman equations, it requires new algorithms. We introduce MD-CURL, a new algorithm for CURL in a finite horizon Markov decision process. MD-CURL is inspired by mirror descent and uses a non-standard regularization to achieve convergence guarantees and a simple closed-form solution, eliminating the need for computationally expensive projection steps typically found in mirror descent approaches. We then extend CURL to an online learning scenario and present Greedy MD-CURL, a new method adapting MD-CURL to an online, episode-based setting with partially unknown dynamics. Like MD-CURL, the online version Greedy MD-CURL benefits from low computational complexity, while guaranteeing sub-linear or even logarithmic regret, depending on the level of information available on the underlying dynamics.

Mots clés: model-based reinforcement learning; mirror descent; online learning; convex optimisation; mean field control; concave utility reinforcement learning

Domaines: Machine Learning [stat.ML]; Optimisation et contrôle [math.OC]; Analyse de données, Statistiques et Probabilités [physics.data-an]

Bianca Marin Moreno, Margaux Brégère, Pierre Gaillard, Nadia Oudjane. Efficient Model-Based Concave Utility Reinforcement Learning through Greedy Mirror Descent. 2023. ⟨hal-04302000⟩