Prossimi seminari del Dipartimento di Matematica

TBA

TBA

In this talk we discuss continuous-time and state-space optimal stopping problems from a reinforcement learning perspective. We begin by formulating the stopping problem using randomized stopping times, where the decision maker's control is represented by the probability of stopping within a given time--specifically, a bounded, non-decreasing, càdlàg control process. To encourage exploration and facilitate learning, we introduce a regularized version of the problem by penalizing it with the cumulative residual entropy of the randomized stopping time. The regularized problem takes the form of an (n+1)-dimensional degenerate singular stochastic control with finite-fuel. We address this through the dynamic programming principle, which enables us to identify the unique optimal exploratory strategy. For the specific case of a real option problem, we derive a semi-explicit solution to the regularized problem, allowing us to assess the impact of entropy regularization and analyze the vanishing entropy limit. Finally, we propose a reinforcement learning algorithm based on policy iteration. We show policy improvement results for our proposed algorithm. This talk is based on a joint project together with Giorgio Ferrari and Renyuan Xu.

This lecture deals with evolution problem for the 1-Laplacian with mixed boundary conditions on bounded open sets. We prove existence and uniqueness of strong solutions for square-integrable data means of the theory of maximal monotone operator. We also see that if the flux on the boundary is 1 (that is, the maximum possible) then these strong solutions can be seen as the large solutions introduced in [Journal Functional Analysis 262 (2012), 1566–1602 ]. We give explicit examples of solutions. Joint work with N. Igbida and J. Toledo