Selecting the right resources for big data analytics jobs is hard because of the wide variety of configuration options like machine type and cluster size. As poor choices can have a significant impact on resource efficiency, cost, and energy usage, automated approaches are gaining popularity. Most existing methods rely on profiling recurring workloads to find near-optimal solutions over time. Due to the cold-start problem, this often leads to lengthy and costly profiling phases. However, big data analytics jobs across users can share many common properties: they often operate on similar infrastructure, using similar algorithms implemented in similar frameworks. The potential in sharing aggregated profiling runs to collaboratively address the cold start problem is largely unexplored. We present Karasu, an approach to more efficient resource configuration profiling that promotes data sharing among users working with similar infrastructures, frameworks, algorithms, or datasets. Karasu trains lightweight performance models using aggregated runtime information of collaborators and combines them into an ensemble method to exploit inherent knowledge of the configuration search space. Moreover, Karasu allows the optimization of multiple objectives simultaneously. Our evaluation is based on performance data from diverse workload executions in a public cloud environment. We show that Karasu is able to significantly boost existing methods in terms of performance, search time, and cost, even when few comparable profiling runs are available that share only partial common characteristics with the target job.

Autonomous mobile robots (AMRs) play a crucial role in transportation and service tasks at hospitals, contributing to enhanced efficiency and meeting medical demands. This paper investigates the optimization problem of scheduling strategies for AMRs at smart hospitals, where the service and travel times of AMRs are stochastic. A stochastic mixed-integer programming model is formulated to minimize the total cost of the hospital by reducing the number of AMRs and travel distance while satisfying constraints such as AMR battery state of charge, AMR capacity, and time windows for medical requests. To address this objective, some properties of the solutions with time window constraints are identified. The variable neighborhood search (VNS) algorithm is adjusted by incorporating the properties of the AMR scheduling problem to solve the model. Experimental results demonstrate that VNS generates high-quality solutions. Both enhanced efficiency and the meeting of medical demands are achieved through intelligently arranging the driving routes of AMRs for both charging and service requests, resulting in substantial cost reductions for hospitals and enhanced utilization of medical resources.

Autonomous terrain traversal of articulated tracked robots can reduce operator cognitive load to enhance task efficiency and facilitate extensive deployment. We present a novel hybrid trajectory optimization method aimed at generating efficient, stable, and smooth traversal motions. To achieve this, we develop a planar robot-terrain contact model and divide the robot's motion into hybrid modes of driving and traversing. By using a generalized coordinate description, the configuration space dimension is reduced, which facilitates real-time planning. The hybrid trajectory optimization is transcribed into a nonlinear programming problem and divided into subproblems to be solved in a receding-horizon planning fashion. Mode switching is facilitated by associating optimized motion durations with a predefined traversal sequence. A multi-objective cost function is formulated to further improve the traversal performance. Additionally, map sampling, terrain simplification, and tracking controller modules are integrated into the autonomous terrain traversal system. Our approach is validated in simulation and real-world scenarios with the Searcher robotic platform. Comparative experiments with expert operator control and state-of-the-art methods show advantages in terms of time and energy efficiency, stability, and smoothness of motion.

Several recent unsupervised learning methods use probabilistic approaches to solve combinatorial optimization (CO) problems based on the assumption of statistically independent solution variables. We demonstrate that this assumption imposes performance limitations in particular on difficult problem instances. Our results corroborate that an autoregressive approach which captures statistical dependencies among solution variables yields superior performance on many popular CO problems. We introduce subgraph tokenization in which the configuration of a set of solution variables is represented by a single token. This tokenization technique alleviates the drawback of the long sequential sampling procedure which is inherent to autoregressive methods without sacrificing expressivity. Importantly, we theoretically motivate an annealed entropy regularization and show empirically that it is essential for efficient and stable learning.

Recently, numerous tensor SVD (t-SVD)-based tensor recovery methods have emerged, showing promise in processing visual data. However, these methods often suffer from performance degradation when confronted with high-order tensor data exhibiting non-smooth changes, commonly observed in real-world scenarios but ignored by the traditional t-SVD-based methods. Our objective in this study is to provide an effective tensor recovery technique for handling non-smooth changes in tensor data and efficiently explore the correlations of high-order tensor data across its various dimensions without introducing numerous variables and weights. To this end, we introduce a new tensor decomposition and a new tensor norm called the Tensor $U_1$ norm. We utilize these novel techniques in solving the problem of high-order tensor completion problem and provide theoretical guarantees for the exact recovery of the resulting tensor completion models. An optimization algorithm is proposed to solve the resulting tensor completion model iteratively by combining the proximal algorithm with the Alternating Direction Method of Multipliers. Theoretical analysis showed the convergence of the algorithm to the Karush-Kuhn-Tucker (KKT) point of the optimization problem. Numerical experiments demonstrated the effectiveness of the proposed method in high-order tensor completion, especially for tensor data with non-smooth changes.

Stochastic gradient-based optimization methods such as SGD and Adam (Kingma & Ba, 2014) are the main workhorse behind modern machine learning. Such methods sequentially apply stochastic gradient steps to update the trained model and their performance crucially depends on the choice of a learning rate sequence, or schedule, used throughout this process to determine the magnitude of the sequential updates. All in all, effectively tuning the learning rate schedule is widely considered a tedious task requiring extensive, sometimes prohibitive, hyper-parameter search, resulting in a significant excess of engineering time and compute resources usage in ML training. A prominent approach to address this issue gave rise to a plethora of adaptive optimization methods (most notably Duchi et al., 2011 and Kingma & Ba, 2014), where the learning rate parameter is automatically tuned during the optimization process based on previously received stochastic gradients. In some important applications these methods provide superior convergence performance, while their theoretical guarantees match the state-of-the-art in the stochastic convex and (smooth) non-convex optimization settings (Li & Orabona, 2019; Ward et al., 2020; Attia & Koren, 2023). However, despite the adaptivity incorporated into these methods, auxiliary learning rate schedules are often still required to actually attain their optimal performance (e.g., Loshchilov & Hutter, 2016), and the nuisance of laborious and extensive manual tuning still remain relevant for these methods as well.

Quantum computers can solve problems that are beyond the capabilities of conventional computers. As quantum computers are expensive and hard to maintain, the typical model for performing quantum computation is to send the circuit to a quantum cloud provider. This leads to privacy concerns for commercial entities as an untrusted server can learn protected information from the provided circuit. Current proposals for Secure Quantum Computing (SQC) either rely on emerging technologies (such as quantum networks) or incur prohibitive overheads (for Quantum Homomorphic Encryption). The goal of our paper is to enable low-cost privacy-preserving quantum computation that can be used with current systems. We propose Enigma, a suite of privacy-preserving schemes specifically designed for the Quantum Approximate Optimization Algorithm (QAOA). Unlike previous SQC techniques that obfuscate quantum circuits, Enigma transforms the input problem of QAOA, such that the resulting circuit and the outcomes are unintelligible to the server. We introduce three variants of Enigma. Enigma-I protects the coefficients of QAOA using random phase flipping and fudging of values. Enigma-II protects the nodes of the graph by introducing decoy qubits, which are indistinguishable from primary ones. Enigma-III protects the edge information of the graph by modifying the graph such that each node has an identical number of connections. For all variants of Enigma, we demonstrate that we can still obtain the solution for the original problem. We evaluate Enigma using IBM quantum devices and show that the privacy improvements of Enigma come at only a small reduction in fidelity (1%-13%).

Feature alignment methods are used in many scientific disciplines for data pooling, annotation, and comparison. As an instance of a permutation learning problem, feature alignment presents significant statistical and computational challenges. In this work, we propose the covariance alignment model to study and compare various alignment methods and establish a minimax lower bound for covariance alignment that has a non-standard dimension scaling because of the presence of a nuisance parameter. This lower bound is in fact minimax optimal and is achieved by a natural quasi MLE. However, this estimator involves a search over all permutations which is computationally infeasible even when the problem has moderate size. To overcome this limitation, we show that the celebrated Gromov-Wasserstein algorithm from optimal transport which is more amenable to fast implementation even on large-scale problems is also minimax optimal. These results give the first statistical justification for the deployment of the Gromov-Wasserstein algorithm in practice.

There are a lot of real-world black-box optimization problems that need to optimize multiple criteria simultaneously. However, in a multi-objective optimization (MOO) problem, identifying the whole Pareto front requires the prohibitive search cost, while in many practical scenarios, the decision maker (DM) only needs a specific solution among the set of the Pareto optimal solutions. We propose a Bayesian optimization (BO) approach to identifying the most preferred solution in the MOO with expensive objective functions, in which a Bayesian preference model of the DM is adaptively estimated by an interactive manner based on the two types of supervisions called the pairwise preference and improvement request. To explore the most preferred solution, we define an acquisition function in which the uncertainty both in the objective functions and the DM preference is incorporated. Further, to minimize the interaction cost with the DM, we also propose an active learning strategy for the preference estimation. We empirically demonstrate the effectiveness of our proposed method through the benchmark function optimization and the hyper-parameter optimization problems for machine learning models.

We study the problem of allocating scarce societal resources of different types (e.g., permanent housing, deceased donor kidneys for transplantation, ventilators) to heterogeneous allocatees on a waitlist (e.g., people experiencing homelessness, individuals suffering from end-stage renal disease, Covid-19 patients) based on their observed covariates. We leverage administrative data collected in deployment to design an online policy that maximizes expected outcomes while satisfying budget constraints, in the long run. Our proposed policy waitlists each individual for the resource maximizing the difference between their estimated mean treatment outcome and the estimated resource dual-price or, roughly, the opportunity cost of using the resource. Resources are then allocated as they arrive, in a first-come first-serve fashion. We demonstrate that our data-driven policy almost surely asymptotically achieves the expected outcome of the optimal out-of-sample policy under mild technical assumptions. We extend our framework to incorporate various fairness constraints. We evaluate the performance of our approach on the problem of designing policies for allocating scarce housing resources to people experiencing homelessness in Los Angeles based on data from the homeless management information system. In particular, we show that using our policies improves rates of exit from homelessness by 1.9% and that policies that are fair in either allocation or outcomes by race come at a very low price of fairness.