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# [theory-seminar] Theory Lunch 08/12: Mingda Qiao

David Wajc wajc at stanford.edu
Mon Aug 9 10:08:41 PDT 2021

```Hi all,

This week's theory lunch will take place Thursday at noon (PDT), at this
zoom room
<https://stanford.zoom.us/j/98932206471?pwd=YXdubytLVGNTbXhGeXFxNmJaVnhrUT09>.
As
usual, we'll start with some socializing, followed by a talk starting at
12:30pm. Pras will be MCing. Thanks Pras!
Mingda will tell us about: *Exponential Weights Algorithms for Selective
Learning*

*Abstract:* We study the selective learning problem, in which a learner
observes \$n\$ labeled data points one at a time. At a time of its choosing,
the learner picks a window length \$w\$ and a hypothesis \$h\$ from a given
hypothesis class \$H\$, and then labels the next \$w\$ data points using \$h\$.
The excess risk incurred by the learner is defined as the difference
between the average loss of \$h\$ over the \$w\$ data points and the smallest
possible average loss among all hypotheses in \$H\$ over those data points.

We give an improved algorithm, termed the hybrid exponential weights
algorithm, that achieves an expected excess risk of \$O((\log\log|H| +
\log\log n)/\log n)\$. This gives a doubly exponential improvement in the
dependence on \$|H|\$ over the best known upper bound. We also prove an
almost matching lower bound, showing that the \$\log\log|H|\$ dependence is
necessary.

Based on joint work with Greg Valiant.

Cheers, David
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