Continuous-time q-learning for mean-field control with common noise, part-I: Theoretical foundations
This paper investigates the continuous-time counterpart of the Q-function for entropy-regularized mean-field control (MFC) with controlled common noise, coined as q-function by Jia and Zhou (2023) in the single agent's model. We first show that, under discretely sampled actions, the value function in the exploratory formulation converges to the one in the relaxed control formulation as the time grid refines. Leveraging the relaxed control formulation, we derive the exploratory Hamilton-Jacobi-Bellman (HJB) equation, in which the controlled common noise gives rise to an additional nonlinear functional of policy, rendering the policy iteration intricate. Under certain concavity condition, w...
| Authors | Zhenjie Ren, Xiaoli Wei, Xiang Yu et al. |
|---|---|
| Primary category | math.OC |
| Published | 30 April 2026 |
| Last updated at source | 30 April 2026 |
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