Speaker: Zhenjie Ren is a Professor at LaMME, Université Évry Paris-Saclay since 2024. Prior to this, he was an Associate Professor at CEREMADE, Université Paris Dauphine-PSL, where he served from 2016. He earned his PhD in applied mathematics and subsequently held a postdoctoral fellowship at CMAP, École Polytechnique. His research interests lie in applied mathematics with a focus on quantitative finance and machine learning. His work primarily explores areas at the intersection of stochastic processes and optimal control theory, including McKean-Vlasov diffusions, particle systems, mean-field games, optimal contract theory, backward stochastic differential equations, and viscosity solutions.

Date: October 16, 2026

Time: 19:30-20:30

Location: Scan the QR code to watch the live broadcast.

Sponsor: Research Center for Mathematics and Interdisciplinary Sciences, Shandong University

Abstract:

Reinforcement learning has achieved remarkable success in landmark applications such as AlphaGo and AlphaFold, and is increasingly expected to play a central role in emerging domains such as autonomous driving. A substantial body of work has established theoretical foundations for classical reinforcement learning algorithms, including temporal-difference learning, policy iteration, and Q-learning. By contrast, policy gradient descent, despite its widespread use, remains less well understood from a theoretical perspective, largely because of its non-convex structure and the complexity of the underlying functional space. Existing convergence analyses typically require uniform regularity assumptions on the policy, viewed as a feedback control function, along the gradient flow; moreover, the resulting convergence rates depend on these regularity bounds. In this work, we significantly strengthen the existing convergence theory. Our key insight is to relate policy gradient descent to a mirror flow on the space of probability measures over controlled trajectories, where the Bregman divergence is induced by the convex control cost. We rigorously prove a JKO-type convergence result showing that the discrete-time mirror flow converges to its continuous-time counterpart, and we identify the limiting dynamics as a preconditioned policy gradient descent flow on the space of control processes. Leveraging this mirror-flow perspective, we establish an exponential convergence rate that is independent of policy regularity. The convergence holds both in Bregman divergence and in the value of the associated control problem.

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