Song Xuanye
Biography
Dr. Song Xuanye is a Research Fellow at Nanyang Technological University (NTU), Singapore, specializing in applied mathematics, reinforcement learning, and mean-field control systems. He earned his Ph.D. in Applied Mathematics from the University Paris-Cite, where his research focused on theoretical and numerical aspects of continuous-time reinforcement learning. His work includes contributions to stochastic differential equations, policy gradient methods, and actor-critic algorithms, with applications in finance, machine learning, and neuroscience. Dr. Song has published in leading journals such as the Journal of Machine Learning Research (JMLR) and presented at international conferences including the INFORMS Conference on Financial Engineering & FinTech and the NUS Quantitative Finance Conference
Research Interest
Project title: Theoretical analysis and learning algorithms for the Mean-field control problems with common noise, under the supervision of Yu Xiang, Research internship for the project entitled Propagation of Waves in Randomly Perturbed Media
Abstract
On the convergence of the Euler-Maruyama scheme for McKean-Vlasov SDEs:
Building on the well-posedness of the backward Kolmogorov partial differential equation in the Wasserstein space, we analyze the strong and weak convergence rates for approximating the unique solution of a class of McKean-Vlasov stochastic differential equations via the Euler-Maruyama time discretization scheme applied to the associated system of interacting particles. We consider two distinct settings. In the first, the coefficients and test function are irregular, but the diffusion coefficient remains non-degenerate. Leveraging the smoothing properties of the underlying heat kernel, we establish the strong and weak convergence rates of the scheme in terms of the number of particles $N$ and the mesh size $h$. In the second setting, where both the coefficients and the test function are smooth, we demonstrate that the weak error rate at the level of the semigroup is optimal, achieving an error of order $N^{-1} + h$.
