PRISMA webinars follow a colloquium-style format designed to foster exchange and discussion within the Italian probability and statistics community. Each session features two speakers, who give two closely connected 30-minute talks providing the community with
a perspective on their research area. Over the past few years, recordings of the seminars have been made available on the UMI YouTube channel:
The next event is scheduled for Monday, April 13, 2026. The speakers will be Jodi Dianetti (Università di Roma Tor Vergata) and Giorgio Ferrari (University of Bielefeld), who will speak on:
Singular Stochastic Controls in Reinforcement Learning and Mean-field Problems
According to the following schedule
16:00 1st seminar
16:30 Break and discussions
16:45 2nd seminar
17:15 Conclusions and discussions
The abstract can be found
below. The seminars will be streamed on Teams at the following link:
We look forward to seeing many of you there!
Luciano Campi, Maurizia Rossi
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SPEAKERS: Jodi Dianetti (Università di Roma Tor Vergata) and Giorgio
Ferrari (Bielefeld University)
TITLE: Singular Stochastic Controls in Reinforcement Learning and Mean-field Problems
ABSTRACT: This talk is divided into two parts, both devoted to stochastic control problems with singular controls. In both cases, a connection with optimal stopping plays a key role, although it arises in different ways
and from different perspectives.
In the first part, we consider optimal stopping problems from a reinforcement learning perspective. We formulate the stopping decision through randomized stopping times, modeled by bounded, nondecreasing, càdlàg control processes,
and introduce an entropy regularization that promotes exploration. The resulting problem can be rewritten as a degenerate, finite-fuel singular stochastic control problem. Using dynamic programming, we characterize the optimal exploratory policy, obtain semi-explicit
solutions in a real-option setting, analyze the vanishing-entropy limit, and propose a policy-iteration reinforcement learning algorithm with convergence guarantees.
In the second part, we turn to mean-field control problems with singular controls over a finite horizon, allowing for general dependence on the distribution of the state. We show that these problems can be linked to a mean-field
game with singular controls, and that equilibria of this game yield optimal controls for the original problem. For a mean-field version of the classical monotone follower problem, the associated equilibrium is characterized by exploiting its connection with
optimal stopping together with a Kakutani-Fan-Glicksberg fixed-point argument, leading to a complete characterization of the optimal control in terms of a moving free boundary that uniquely solves a nonlinear integral equation.
The talk is based on (ongoing) joint works with Andrea Amato, Federico Cannerozzi, and Renyuan Xu.
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