Elad Hazan, Princeton University

Abstract

Linear dynamical systems, a.k.a. Kalman filtering, are a class of time-series models widely used in robotics, finance, engineering, and meteorology. In its general form (unknown system), learning LDS is a classic non-convex problem, typically tackled with heuristics like gradient descent ("backpropagation through time") or the EM algorithm. I will present our new "spectral filtering" approach to the identification and control of discrete-time general linear dynamical systems with multi-dimensional inputs, outputs, and a latent state. This approach yields a simple and efficient algorithm for low-regret prediction (i.e. asymptotically vanishing MSE) as well as finite-time control.

Based on work with Karan Singh and Cyril Zhang, and follow up works with Holden Lee, Yi Zhang and Sanjeev Arora.