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    "148617-21904532":
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        "event_title":"Policy Gradient Flow for Stochastic Control",
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        "combined_title":"Policy Gradient Flow for Stochastic Control: Zhenjie Ren, University of Evry",
        "event_subtitle":"Zhenjie Ren, University of Evry",
        "event_type":"Workshop \/ Seminar",
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        "description":"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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    {
        "datetime_modified":"20261017T184842",
        "datetime_start":"20261028T160000",
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        "date_start":"2026-10-28",
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        "time_zone":"America\/Detroit",
        "event_title":"Probability and Analysis Seminar: Conformal removability and bubble connectivity of non-simple SLE",
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        "combined_title":"Probability and Analysis Seminar: Conformal removability and bubble connectivity of non-simple SLE: Haoyu Liu (PKU\/MIT)",
        "event_subtitle":"Haoyu Liu (PKU\/MIT)",
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        "description":"Schramm-Loewner evolution (SLE_\\kappa) is a one-parameter family of random fractal curves arising as scaling limits of interfaces in two-dimensional statistical mechanics models. For \\kappa \\in (4, 8), the SLE_\\kappa curve is self-intersecting but not space-filling, forming complementary connected components known as bubbles. In this talk, I will discuss the relationship between the conformal removability of SLE traces and connectivity of the bubble adjacency graph, as well as a sharp phase transition as \\kappa varies. Joint work with Zijie Zhuang (UNIGE).",
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