Learning from a Sample in Online Algorithms

C.J. Argue, Alan Frieze, Anupam Gupta, Christopher Seiler

Keywords: Learning Augmented Algorithms, Online Algorithms, Sample Complexity, Load Balancing, Optimization, Steiner tree, Facility Location, Clustering

Abstract:

We consider three central problems in optimization: the restricted
assignment load-balancing problem, the Steiner tree network design
problem, and facility location clustering. We consider the online
setting, where the input arrives over time, and irrevocable decisions
must be made without knowledge of the future.
For all these problems, any online algorithm must incur a cost that is
approximately $\log |I|$ times the optimal cost in the worst-case,
where $|I|$ is the length of the input. But can we go beyond the
worst-case? In this work we give algorithms that perform substantially
better when a $p$-fraction of the input is given as a sample: the
algorithm use this sample to \emph{learn} a good strategy to use
for the rest of the input.