Optimization plays an important role across data science, from guiding decision-making under uncertainty, to modeling equilibrium in game dynamics. In this talk, I will begin by describing a line of work studying information-theoretic complexity in optimization using higher-order derivatives and parallel access to the gradient of the objective function, aiming to shed light on efficient algorithm design under these novel computational models.

Sampling, on the other hand, is a fundamental task underlying many scientific pursuits, from molecular dynamics to Lattice QCD simulations. In the second part of the talk, I will introduce ways to conceptualize designing dynamics in infinite-dimensional metric spaces, leading to geometry-aware MCMC sampling algorithms and controlled diffusion processes that adopt a learning-driven approach for such numerical tasks.

I will end by highlighting (1) theoretically, the connection between optimization, sampling, physics-inspired dynamical system, mean-field game goes much deeper than one may expect; (2) computationally, bringing powerful function fitting NN-architecture to solve more traditional tasks in PDE, sampling, control etc., offers many exciting opportunities for both methodology developments and applications.

Pierce 301 or Zoom (password: 687666)