On the Tradeoff between Stability and Fit

TL;DR

This paper explores the balance between stability and adaptability in optimization problems, introducing a formal framework and algorithms for stable solutions that minimize change costs while maintaining system efficiency.

Contribution

It provides a formal formulation of the stability-fit tradeoff, extends PPS sampling to stable settings, and offers efficient algorithms for dynamic problem adjustments.

Findings

Exact solutions for stable extensions of key problems

Efficient incremental algorithms for dynamic updates

Application to monitoring and anomaly detection

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.