Скачать с ютуб From Moderate Deviations Theory to Distributionally Robust Optimization: Correlated Data в хорошем качестве

From Moderate Deviations Theory to Distributionally Robust Optimization: Correlated Data

Full title: From Moderate Deviations Theory to Distributionally Robust Optimization: Learning from Correlated Data Abstract: We aim to learn a performance function of the invariant state distribution of an unknown linear dynamical system based on a single trajectory of correlated state observations. The function to be learned may represent, for example, an identification objective or a value function. To this end, we develop a distributionally robust estimation scheme that evaluates the worst- and best-case values of the given performance function across all stationary state distributions that are sufficiently likely to have generated the observed state trajectory. By leveraging new insights from moderate deviations theory, we prove that our estimation scheme offers consistent upper and lower confidence bounds whose exponential convergence rate can be actively tuned. In the special case of a quadratic cost, we show that the proposed confidence bounds can be computed efficiently by solving Riccati equations. We exemplify the proposed methods in the context of reinforcement learning, hypothesis testing and system identification. This is joint work with Tobias Sutter, Wouter Jongeneel and Soroosh Shafieezadeh-Abadeh. Short Bio: Daniel Kuhn holds the Chair of Risk Analytics and Optimization at EPFL. Before joining EPFL, he was a faculty member at Imperial College London (2007–2013) and a postdoctoral researcher at Stanford University (2005–2006). He received a Ph.D. in Economics from the University of St. Gallen in 2004 and an M.Sc. in Theoretical Physics from ETH Zürich in 1999. His research interests revolve around stochastic programming and robust optimization.