@inproceedings{89fe95d94ef34a008eb3f87d65bde889,
title = "Convex Analytic Theory for Convex Q-Learning",
abstract = "In recent years there has been a collective research effort to find new formulations of reinforcement learning that are simultaneously more efficient and more amenable to analysis. This paper concerns one approach that builds on the linear programming (LP) formulation of optimal control of Manne. A primal version is called logistic Q-learning, and a dual variant is convex Q-learning. This paper focuses on the latter, while building bridges with the former. The main contributions follow: (i) The dual of convex Q-learning is not precisely Manne's LP or a version of logistic Q-learning, but has similar structure that reveals the need for regularization to avoid over-fitting. (ii) A sufficient condition is obtained for a bounded solution to the Q-learning LP. (iii) Simulation studies reveal numerical challenges when addressing sampled-data systems based on a continuous time model. The challenge is addressed using state-dependent sampling. The theory is illustrated with applications to examples from OpenAI gym. It is shown that convex Q-learning is successful in cases where standard Q-learning diverges, such as the LQR problem.",
author = "Fan Lu and Mehta, {Prashant G.} and Meyn, {Sean P.} and Gergely Neu",
note = "Publisher Copyright: {\textcopyright} 2022 IEEE.; 61st IEEE Conference on Decision and Control, CDC 2022 ; Conference date: 06-12-2022 Through 09-12-2022",
year = "2022",
doi = "10.1109/CDC51059.2022.9992867",
language = "English (US)",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "4065--4071",
booktitle = "2022 IEEE 61st Conference on Decision and Control, CDC 2022",
address = "United States",
}