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Max-plus approximation for reinforcement learning
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DOI：10.1016/j.automatica.2021.109623.png)
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Abstract
En 中文
Max-Plus Algebra has been applied in several contexts, especially in the control of discrete events systems. In this article, we discuss another application closely related to control: the use of Max-Plus algebra concepts in the context of reinforcement learning. Max-Plus Algebra and reinforcement learning are strongly linked due to the latter's dependence on the Bellman Equation which, in some cases, is a linear Max-Plus equation. This fact motivates the application of Max-Plus algebra to approximate the value function, central to the Bellman Equation and thus also to reinforcement learning. This article proposes conditions so that this approach can be done in a simple way and following the philosophy of reinforcement learning: explore the environment, receive the rewards and use this information to improve the knowledge of the value function. The proposed conditions are related to two matrices and impose on them a relationship that is analogous to the concept of weak inverses in traditional algebra. (C) 2021 Elsevier Ltd. All rights reserved.
Keywords:
Max-Plus Algebra
Reinforcement learning
Dynamic programming
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