We address the contextual bandit problem for high-dimensional combinatorial action spaces involving a class of structured discrete constrained optimization problems. In this setting, key quantities within the optimization formulation, such as performance indicators contributing to the objective or constraints, must be estimated from data during the trial sequence of optimized actions. These problems frequently arise in the many operations management domains including IT resource allocation and retail assortment price optimization. We propose a novel, practical, and transparent approach based on general-purpose regression oracles, leveraging Inverse Gap Weighting (IGW) for seamless integration within an optimization framework. IGW sampling is efficiently managed by: (a) a column generation reformulation of the underlying Mixed Integer Programming (MIP) model which allows for flexible lower-level predictors, causal coherence, and efficient representation of large action spaces;(b) a diverse solution pool generation to balance the exploration-exploitation trade-off in large action spaces. To address non-smoothness in the reward function due to optimization constraints, we incorporate a risk-averse phased learning strategy. We validate our approach on a real-world auto-scaling problem in IT automation, achieving a significant reduction in cumulative regret through skillful exploration, with additional gains from risk-averse methods that effectively manage constraint violations.

The emergence of proactive autoscaling aims to guarantee the Quality of Service (QoS) in accordance with the Service Level Agreement (SLA) between cloud providers and users, while promoting efficient resource utilization and minimizing operational costs. Despite its benefits, proactive autoscaling remains complex due to challenges in accurately forecasting resource needs amid workload fluctuations and implementing effective actions based on these forecasts. To address these issues, we propose a mechanism for forecasting workload and cloud resources using a variant of the Transformer. This multivariate, multi–horizon forecasting approach provides both forecasts and insights into the significance of the features associated with the forecasting results, enabling time–granular autoscaling. Through experiments with real–world data, we demonstrate that, rather than first forecasting workload and then estimating resource usage, we can directly forecast resource usage. This method yields the same conclusions regarding the feature importance in workload and resource forecasting, thereby simplifying the existing autoscaling approaches.

The recent advances in Graph Neural Networks (GNN) are poised to improve machine learning of IoT systems at the edge. Particularly, GNNs allow modeling the topology of distributed systems, including their physical laws, from sensors data. However, one of the main limitations of using GNNs arises from their adjacency matrix. The adjacency matrix of GNNs needs to be defined a priori and represents the connectivity between the edges of a network. Usually, the adjacency matrix of GNNs consists of binary values that are equal to 1 when two edges are physically connected and 0 otherwise. This representation considers connectivity in terms of proximity and assumes that they are of equal significance. However, in certain applications, areas that are not physically connected can share more properties than physically connected areas. This necessitates new methods for devising the adjacency matrix and leads us to propose an efficient approach for determining the adjacency matrix of GNNs. Our approach extends GNNs in two ways. First, we employ a mechanism that utilizes the time series data at the edges to determine the eigenvalues and eigenvectors associated with each edge, allowing us to compute the proportion of variance. Subsequently, we use the proportion of variance to construct our adjacency matrix. Second, we utilize Dynamic Time Warping (DTW) to cluster related time series at the edge and construct our adjacency matrix. We then integrate the newly derived adjacency matrix into the GNN operating with a sequence to sequence learner to infer insights at the edges. Through extensive experiments, we demonstrate the strength and performance of our proposed GNN approach.

The classical two-sample test of Kolmogorov-Smirnov(KS) is widely used to test whether empirical samples come from the same distribution. Even though most statistical packages provide an implementation, carrying out the test in big data settings can be challenging because it requires a full sort of the data. The popular Apache Spark system for big data processing provides a 1-sample KS test, but not the 2-sample version. Moreover, recent Spark versions provide the approxQuantile method for querying $\epsilon$-approximate quantiles. We build on approxQuantile to propose a variation of the classical Kolmogorov-Smirnov two-sample test that constructs approximate cumulative distribution functions (CDF) from $\epsilon$-approximate quantiles. We derive error bounds of the approximate CDF and show how to use this information to carry out KS tests. Psuedocode for the approach requires 15 executable lines. A Python® implementation appears in the appendix.