We leverage multilevel Monte Carlo (MLMC) to improve the performance of multi-step look- ahead Bayesian optimization (BO) methods that involve nested expectations and maximizations. Often these expectations must be computed by Monte Carlo (MC). The complexity rate of naive MC degrades for nested operations, whereas MLMC is capable of achieving the canonical MC convergence rate for this type of problem, independently of dimension and without any smoothness assumptions. Our theoretical study focuses on the approximation improvements for two- and three-step look-ahead acquisition functions, but, as we discuss, the approach is generalizable in various ways, including beyond the context of BO. Our findings are verified numerically and the benefits of MLMC for BO are illustrated on several benchmark examples. Code is available at https://github.com/Shangda-Yang/MLMCBO.

We provide a queueing-theoretic framework for job replication schemes based on the principle “replicate a job as soon as the system detects it as a straggler”. This is called jobspeculation. Recent works have analyzed replication on arrival, which we refer to asreplication. Replication is motivated by its implementation in Google’s BigTable. However, systems such as Apache Spark and Hadoop MapReduce implement speculative job execution. The performance and optimization of speculative job execution is not well understood. To this end, we propose a queueing network model for load balancing where each server can speculate on the execution time of a job. Specifically, each job is initially assigned to a single server by a frontend dispatcher. Then, when its execution begins, the server sets a timeout. If the job completes before the timeout, it leaves the network, otherwise the job is terminated and relaunched or resumed at another server where it will complete. We provide a necessary and sufficient condition for the stability of speculative queueing networks with heterogeneous servers, general job sizes and scheduling disciplines. We find that speculation can increase the stability region of the network when compared with standard load balancing models and replication schemes. We provide general conditions under which timeouts increase the size of the stability region and derive a formula for the optimal speculation time, i.e., the timeout that minimizes the load induced through speculation. We compare speculation with redundant-$d$and redundant-to-idle-queue-$d$rules under an$S\& X$model. For light loaded systems, redundancy schemes provide better response times. However, for moderate to heavy loadings, redundancy schemes can lose capacity and have markedly worse response times when compared with the proposed speculative scheme.

Optical sensing has the potential to be an important tool in the automated monitoring of food quality. Specifically, hyperspectral imaging has enjoyed success in a variety of tasks ranging from plant species classification to ripeness evaluation in produce. Although effective, hyperspectral imaging is prohibitively expensive to deploy at scale in a retail setting. With this in mind, we develop a method to assist in designing a low-cost multispectral imager for produce monitoring by using a genetic algorithm (GA) that simultaneously selects a subset of informative wavelengths and identifies effective filter bandwidths for such an imager. Instead of selecting the single fittest member of the final population as our solution, we fit a univariate Gaussian mixture model to the histogram of the overall GA population, selecting the wavelengths associated with the peaks of the distributions as our solution. By evaluating the entire population, rather than a single solution, we are also able to specify filter bandwidths by calculating the standard deviations of the Gaussian distributions and computing the full-width at half-maximum values. In our experiments, we find that this novel histogram-based method for feature selection is effective when compared to both the standard GA and partial least squares discriminant analysis.

We consider a large-scale Ad-auction where adverts are assigned over a potentially infinite number of searches. We capture the intrinsic asymmetries in information between advertisers, the advert platform and the space of searches: advertisers know and can optimize the average performance of their advertisement campaign; the platform knows and can optimize on each search instance; and, neither party knows the distribution of the infinite number of searches that can occur. We look at maximizing the aggregate utility of the click-through rates of advertisers subject to the matching constraints of online ad allocation.

Switched queueing networks model wireless networks, input queued switches and numerous other networked communications systems. For single-hop networks, we consider a (α,g)-switch policy} which combines the MaxWeight policies with bandwidth sharing networks -- a further well studied model of Internet congestion. We prove the maximum stability property for this class of randomized policies. Thus these policies have the same first order behavior as the MaxWeight policies. However, for multihop networks some of these generalized polices address a number of critical weakness of the MaxWeight/BackPressure policies.

We consider a switched (queueing) network in which there are constraints on which queues may be served simultaneously; such networks have been used to effectively model input-queued switches and wireless networks. The scheduling policy for such a network specifies which queues to serve at any point in time, based on the current state or past history of the system. In the main result of this paper, we provide a new class of online scheduling policies that achieve optimal average queue-size scaling for a class of switched networks including input-queued switches. In particular, it establishes the validity of a conjecture about optimal queue-size scaling for input-queued switches.