Continuous time reinforcement learning: A random measure approach

Christian Bender and Nguyen Tran Thuan

Stochastic Processes and their Applications, 2026, vol. 194, issue C

Abstract: We present a random measure approach for modeling exploration, i.e., the execution of measure-valued controls, in continuous-time reinforcement learning with controlled diffusion and jumps. We begin with the case when sampling the randomized control in continuous time takes place on a discrete-time grid and reformulate the resulting SDE as an equation driven by suitable random measures. Our main result is a limit theorem for these random measures as the mesh-size of the sampling grid goes to zero. The resulting limit SDE can be applied for the theoretical analysis of exploratory control problems and for the derivation of learning algorithms.

Keywords: Exploratory control; Orthogonal martingale measures; Poisson random measures; Reinforcement learning; Weak convergence. (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2025.104848

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