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[theory-seminar] Theory Lunch 12/10: Ellen Vitercik

David Wajc wajc at stanford.edu
Wed Dec 9 09:01:56 PST 2020


Hi all,

The last Theory lunch of the quarter will be happening tomorrow at noon
(PDT), at our gather space:
https://gather.town/app/lR6jRBPK44nZ7V68/StanfordTheory (*password:*
 SongComplexity).
Ellen will tell us about *How much data is sufficient to learn
high-performing algorithms?*

*Abstract:*
Algorithms often have tunable parameters that impact runtime and solution
quality. For many algorithms used in practice, no parameter setting admits
a meaningful worst-case guarantee, so the parameters are explicitly made
available for the user to tune. Alternatively, the parameters may be tuned
implicitly within the proof of a worst-case approximation ratio or runtime
bound. Worst-case instances, however, may be rare or nonexistent in
practice. A growing body of research has demonstrated that data-driven
algorithm design can lead to significant gains in runtime and solution
quality. Data-driven algorithm design uses a training set of problem
instances sampled from an unknown, application-specific distribution and
returns a parameter setting with strong average performance on the training
set.

We provide a broadly applicable theory for deriving generalization
guarantees for data-driven algorithm design, which bound the difference
between the algorithm's expected performance and its average performance
over the training set. The challenge is that for many combinatorial
algorithms, performance is a volatile function of the parameters: slightly
perturbing the parameters can cause a cascade of changes in the algorithm’s
behavior. Prior research has proved generalization bounds by employing
case-by-case analyses of parameterized greedy algorithms, clustering
algorithms, integer programming algorithms, and selling mechanisms. We
uncover a unifying structure which we use to prove extremely general
guarantees, yet we recover the bounds from prior research. Our guarantees
apply whenever an algorithm's performance is a piecewise-constant, -linear,
or—more generally—piecewise-structured function of its parameters. As we
demonstrate, our theory also implies novel bounds for dynamic programming
algorithms used in computational biology.

This talk is based on joint work with Nina Balcan, Dan DeBlasio, Travis
Dick, Carl Kingsford, and Tuomas Sandholm.

Cheers,
David

PS
*Pro tip:* To join the zoom talk:
(1) go to the lecture hall,
(2) grab a seat, and
(3)* press X to join the zoom lecture*.
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