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Mastane Achab

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TMLR Journal 2023 Journal Article

One-Step Distributional Reinforcement Learning

Mastane Achab
Reda Alami
YASSER ABDELAZIZ DAHOU DJILALI
Kirill Fedyanin
Eric Moulines

Reinforcement learning (RL) allows an agent interacting sequentially with an environment to maximize its long-term expected return. In the distributional RL (DistrRL) paradigm, the agent goes beyond the limit of the expected value, to capture the underlying probability distribution of the return across all time steps. The set of DistrRL algorithms has led to improved empirical performance. Nevertheless, the theory of DistrRL is still not fully understood, especially in the control case. In this paper, we present the simpler one-step distributional reinforcement learning (OS-DistrRL) framework encompassing only the randomness induced by the one-step dynamics of the environment. Contrary to DistrRL, we show that our approach comes with a unified theory for both policy evaluation and control. Indeed, we propose two OS-DistrRL algorithms for which we provide an almost sure convergence analysis. The proposed approach compares favorably with categorical DistrRL on various environments.

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NeurIPS Conference 2017 Conference Paper

Ranking Data with Continuous Labels through Oriented Recursive Partitions

Stéphan Clémençon
Mastane Achab

We formulate a supervised learning problem, referred to as continuous ranking, where a continuous real-valued label Y is assigned to an observable r. v. X taking its values in a feature space X and the goal is to order all possible observations x in X by means of a scoring function s: X → R so that s(X) and Y tend to increase or decrease together with highest probability. This problem generalizes bi/multi-partite ranking to a certain extent and the task of finding optimal scoring functions s(x) can be naturally cast as optimization of a dedicated functional cri- terion, called the IROC curve here, or as maximization of the Kendall τ related to the pair (s(X), Y ). From the theoretical side, we describe the optimal elements of this problem and provide statistical guarantees for empirical Kendall τ maximiza- tion under appropriate conditions for the class of scoring function candidates. We also propose a recursive statistical learning algorithm tailored to empirical IROC curve optimization and producing a piecewise constant scoring function that is fully described by an oriented binary tree. Preliminary numerical experiments highlight the difference in nature between regression and continuous ranking and provide strong empirical evidence of the performance of empirical optimizers of the criteria proposed.

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