Princeton Robotics Seminar - Stephen Tu

Event Date/Time


EQuad D Wing
D221 and

Series/Event Type

Speaker: Stephen Tu, Google Brain NYC

Title: Learning from many trajectories


Abstract: We initiate a study of supervised learning from many independent sequences ("trajectories") of non-independent covariates, reflecting tasks in sequence modeling, control, and reinforcement learning.  Conceptually, our multi-trajectory setup sits between two traditional settings in statistical learning theory: learning from independent examples and learning from a single auto-correlated sequence.  Our conditions for efficient learning generalize the former setting---trajectories must be non-degenerate in ways that extend standard requirements for independent examples. They do not require that trajectories be ergodic, long, nor strictly stable.

For linear least-squares regression, given n-dimensional examples produced by m trajectories, each of length T, we observe a notable change in statistical efficiency as the number of trajectories increases from a few (namely m <= n) to many (namely m >= n).  Specifically, we establish that the worst-case error rate for this problem is n/(mT) whenever m >= n.  Meanwhile, when m <= n, we establish a (sharp) lower bound of n^2/(m^2 T) on the worst-case error rate, realized by a simple, marginally unstable linear dynamical system.  A key upshot is that, in domains where trajectories regularly reset, the error rate eventually behaves as if all of the examples were independent altogether, drawn from their marginals.  As a corollary of our analysis, we also improve guarantees for the linear system identification problem. 


This is joint work with Roy Frostig and Mahdi Soltanolkotabi.

Speaker Bio

Stephen Tu is a research scientist in the Google Brain robotics team in NYC. He obtained his PhD in EECS from UC Berkeley under the supervision of Ben Recht. Broadly speaking, his research is focused on understanding the statistical complexity of learning to control.

Hosting Group

Princeton Robotics Group

Research Area(s)