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Budgeted Reinforcement Learning in Continuous State Space

Nicolas Carrara
Edouard Leurent
Romain Laroche
Tanguy Urvoy
Odalric-Ambrym Maillard
Olivier Pietquin
NeurIPS (2019)


A Budgeted Markov Decision Process (BMDP) is an extension of a Markov Decision Process to critical applications requiring safety constraints. It relies on a notion of risk implemented in the shape of a cost signal constrained to lie below a threshold that -- importantly -- can be modified in real-time. So far, BMDPs could only be solved in the case of finite state spaces with known dynamics. This work extends the state-of-the-art to continuous spaces environments and unknown dynamics. We show that the solution to a BMDP is a fixed point of a novel Budgeted Bellman Optimality operator. This observation allows us to introduce natural extensions of Deep Reinforcement Learning algorithms to address large-scale BMDPs. We validate our approach on two simulated applications: spoken dialogue and autonomous driving.