Configuration Balancing for Stochastic Requests

TL;DR

This paper studies a resource allocation problem with stochastic requests, proposing algorithms for offline and online settings that approximate optimal policies and close the adaptivity gap.

Contribution

It introduces non-adaptive policies with near-optimal approximation ratios for stochastic configuration balancing, closing the adaptivity gap and providing tight bounds.

Findings

Offline non-adaptive policy $O(rac{ ext{log} m}{ ext{log} ext{log} m})$-approximate

Online non-adaptive policy $O( ext{log} m)$-competitive

Leverages adaptivity for related machines to achieve constant and $O( ext{log} ext{log} m)$ approximations

Abstract

The configuration balancing problem with stochastic requests generalizes many well-studied resource allocation problems such as load balancing and virtual circuit routing. In it, we have $m$ resources and $n$ requests. Each request has multiple possible configurations, each of which increases the load of each resource by some amount. The goal is to select one configuration for each request to minimize the makespan: the load of the most-loaded resource. In our work, we focus on a stochastic setting, where we only know the distribution for how each configuration increases the resource loads, learning the realized value only after a configuration is chosen. We develop both offline and online algorithms for configuration balancing with stochastic requests. When the requests are known offline, we give a non-adaptive policy for configuration balancing with stochastic requests that $O(\frac{\log m}{\log \log m})$-approximates the optimal adaptive policy. In particular, this closes the adaptivity gap for this problem as there is an asymptotically matching lower bound even for the very special case of load balancing on identical machines. When requests arrive online in a list, we give a non-adaptive policy that is $O(\log m)$ competitive. Again, this result is asymptotically tight due to information-theoretic lower bounds for very special cases (e.g., for load balancing on unrelated machines). Finally, we show how to leverage adaptivity in the special case of load balancing on related machines to obtain a constant-factor approximation offline and an $O(\log \log m)$-approximation online. A crucial technical ingredient in all of our results is a new structural characterization of the optimal adaptive policy that allows us to limit the correlations between its decisions.