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Abstract The configuration balancing problem with stochastic requests generalizes well-studied resource allocation problems such as load balancing and virtual circuit routing. There are givenmresources andnrequests; each request has multiple possibleconfigurations, each of which increases the load of each resource by some amount. The goal is to select one configuration for each request to minimize themakespan: the load of the most-loaded resource. In the stochastic setting, the amount by which a configuration increases the resource load is uncertain until the configuration is chosen, but we are given a probability distribution. 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$$O(\frac{\log m}{\log \log m})$$ $O\left(\frac{logm}{loglogm}\right)$-approximates the optimal adaptive policy, which matches a known lower bound for the special case of load balancing on identical machines. When requests arrive online in a list, we give a non-adaptive policy that is$$O(\log m)$$ $O(logm)$competitive. Again, this result is asymptotically tight due to information-theoretic lower bounds for special cases (e.g., for load balancing on unrelated machines). Finally, we show how to leverage adaptivity in the special case of load balancing onrelatedmachines to obtain a constant-factor approximation offline and an$$O(\log \log m)$$ $O(loglogm)$-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. 

Adaptivity in Stochastic Submodular Cover Solutions to stochastic optimization problems are typically sequential decision processes that make decisions one by one, waiting for (and using) the feedback from each decision. Whereas such “adaptive” solutions achieve the best objective, they can be very time-consuming because of the need to wait for feedback after each decision. A natural question is are there solutions that only adapt (i.e., wait for feedback) a few times whereas still being competitive with the fully adaptive optimal solution? In “The Power of Adaptivity for Stochastic Submodular Cover,” Ghuge, Gupta, and Nagarajan resolve this question in the context of stochastic submodular cover, which is a fundamental stochastic covering problem. They provide algorithms that achieve a smooth trade-off between the number of adaptive “rounds” and the solution quality. The authors also demonstrate via experiments on real-world and synthetic data sets that, even for problems with more than 1,000 decisions, about six rounds of adaptivity suffice to obtain solutions nearly as good as fully adaptive solutions.