arXiv:2511.17351v1 Announce Type: new 
Abstract: Hierarchical Reinforcement Learning promises, among other benefits, to efficiently capture and utilize the temporal structure of a decision-making problem and to enhance continual learning capabilities, but theoretical guarantees lag behind practice. In this paper, we propose a Feudal Q-learning scheme and investigate under which conditions its coupled updates converge and are stable. By leveraging the theory of Stochastic Approximation and the ODE method, we present a theorem stating the convergence and stability properties of Feudal Q-learning. This provides a principled convergence and stability analysis tailored to Feudal RL. Moreover, we show that the updates converge to a point that can be interpreted as an equilibrium of a suitably defined game, opening the door to game-theoretic approaches to Hierarchical RL. Lastly, experiments based on the Feudal Q-learning algorithm support the outcomes anticipated by theory.

دراسة جديدة حول التعلم المعزز الهرمي تقدم مخطط Q-learning الإقطاعي، حيث يتم فحص الظروف التي تتقارب فيها تحديثاته وتبقى مستقرة. تعتمد الدراسة على التقريب العشوائي وطريقة ODE لتقديم نظرية توضح خصائص التقارب والاستقرار لـ Q-learning الإقطاعي، مما يشير إلى أن التحديثات تصل إلى نقطة يمكن تفسيرها على أنها توازن في سيناريو لعبة مناسب.

Un nuevo estudio sobre el Aprendizaje por Refuerzo Jerárquico presenta un esquema de Q-learning Feudal, examinando las condiciones bajo las cuales sus actualizaciones convergen y permanecen estables. La investigación utiliza la Aproximación Estocástica y el método ODE para establecer un teorema que describe las propiedades de convergencia y estabilidad del Q-learning Feudal, sugiriendo que las actualizaciones alcanzan un equilibrio similar a un escenario de juego.

Une nouvelle étude sur l'apprentissage par renforcement hiérarchique présente un schéma de Q-learning féodal, examinant les conditions sous lesquelles ses mises à jour convergent et restent stables. La recherche s'appuie sur l'approximation stochastique et la méthode ODE pour établir un théorème qui décrit les propriétés de convergence et de stabilité du Q-learning féodal, suggérant que les mises à jour atteignent un équilibre semblable à un scénario de jeu.

A new study on Hierarchical Reinforcement Learning introduces a Feudal Q-learning scheme, examining the conditions under which its updates converge and remain stable. The research leverages Stochastic Approximation and the ODE method to establish a theorem that outlines the convergence and stability properties of Feudal Q-learning, suggesting that updates reach an equilibrium akin to a game scenario.

Convergence and stability of Q-learning in Hierarchical Reinforcement Learning

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