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arXiv · 1302.2137

On the Tradeoff between Stability and Fit

Edith Cohen·Graham Cormode·Nick Duffield·Carsten Lund
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Abstract

In computing, as in many aspects of life, changes incur cost. Many optimization problems are formulated as a one-time instance starting from scratch. However, a common case that arises is when we already have a set of prior assignments, and must decide how to respond to a new set of constraints, given that each change from the current assignment comes at a price. That is, we would like to maximize the fitness or efficiency of our system, but we need to balance it with the changeout cost from the previous state. We provide a precise formulation for this tradeoff and analyze the resulting {\em stable extensions} of some fundamental problems in measurement and analytics. Our main technical contribution is a stable extension of PPS (probability proportional to size) weighted random sampling, with applications to monitoring and anomaly detection problems. We also provide a general framework that applies to top-$k$, minimum spanning tree, and assignment. In both cases, we are able to provide exact solutions, and discuss efficient incremental algorithms that can find new solutions as the input changes.

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Edith Cohen, Graham Cormode, Nick Duffield, Carsten Lund. 2013-02-08. On the Tradeoff between Stability and Fit. https://arxiv.org/abs/1302.2137

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