Stochastic compositional optimization (SCO) has attracted considerable attention because of its broad applicability to important real-world problems. However, existing work on SCO typically assumes that the projection within a solution update is straightforward, which is not the case for problem instances where constraints are in the form of expectations, such as empirical conditional value-at-risk constraints. In this paper, we introduce a novel model that integrates single-level expected-value and two-level compositional constraints into the existing SCO framework. Our model has wide applicability to data-driven optimization, fairness optimization, and risk management, including risk-averse optimization and high-moment portfolio selection, and is capable of handling multiple constraints. Additionally, we propose a class of primal-dual algorithms that generate sequences converging to the optimal solution at a rate of [Formula: see text] under both single-level and two-level compositional expected-value constraints, where N is the iteration counter, thus establishing benchmarks in expected-value-constrained SCO. Numerical experiments show the efficiency of our algorithm over real-world applications. Funding: S. Yang’s research was supported by the Research Grants Council of the Hong Kong Special Administrative Region, China [Grant Early Career Scheme 26209422]. W. You’s research is generously supported by the Research Grants Council of the Hong Kong Special Administrative Region, China [Grant Early Career Scheme 26212320 and Grant General Research Fund 16212823]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoo.2023.0024 .

Single-server queues with customer abandonment arise in call centers and many service systems, but steady-state performance measures remain analytically intractable beyond Markovian assumptions. This paper develops Robust Queueing (RQ) approximations for the mean steady-state virtual waiting time (offered waiting time) in the GI/GI/1+GI model. The approach starts from a reverse-time supremum representation of the virtual waiting time as the reflection of an effective net-input process that accounts for abandonments. We approximate effective net-input increments by their mean plus a robustness parameter times their standard deviation. For the drift, we introduce a Poisson-surrogate compensator and show that the associated correction term is asymptotically negligible in the long-patience regime. For variability, we propose two implementable surrogates: (i) a deterministic time-change approximation that yields a first RQ algorithm, and (ii) a refined algorithm based on a heavy-traffic limit that produces a scale-dependent variance function capturing the variance-reduction effect of abandonment. The resulting steady-state approximation reduces to a one-dimensional fixed point solvable by bisection and takes as input the arrival index of dispersion for counts (IDC), the service-time squared coefficient of variation, and the patience-time distribution. We further show how to extend the method to queues in series by feeding an approximation of the upstream departure IDC into the downstream RQ algorithm. Extensive numerical experiments demonstrate that the refined RQ approximation is accurate across underload, critical loading, and overload, and remains robust relative to existing heavy-traffic and hazard-rate-scaling benchmarks.

We study contextual dynamic pricing, where a decision maker posts personalized prices based on observable contexts and receives binary purchase feedback indicating whether the customer's valuation exceeds the price. Each valuation is modeled as an unknown latent function of the context, corrupted by independent and identically distributed market noise from an unknown distribution. Relying only on Lipschitz continuity of the noise distribution and bounded valuations, we propose a minimax-optimal algorithm. To accommodate the unknown distribution, our method discretizes the relevant noise range to form a finite set of candidate prices, then applies layered data partitioning to obtain confidence bounds substantially tighter than those derived via the elliptical potential lemma. A key advantage is that estimation bias in the valuation function cancels when comparing upper confidence bounds, eliminating the need to know the Lipschitz constant. The framework extends beyond linear models to general function classes through offline regression oracles. Our regret analysis depends solely on the oracle's estimation error, typically governed by the statistical complexity of the class. These techniques yield a regret upper bound matching the minimax lower bound up to logarithmic factors. Furthermore, we refine these guarantees under additional structures-for example, linear valuation models, second-order smoothness, sparsity, and known noise distribution or observable valuations-and compare our bounds and assumptions with prior dynamic-pricing methods. Finally, numerical experiments corroborate the theory and show clear improvements over benchmark methods.

We study pure exploration in structured stochastic multi-armed bandits, aiming to efficiently identify the correct hypothesis from a finite set of alternatives. For a broad class of tasks, asymptotic analyses reduce to a maximin optimization that admits a two-player zero-sum game interpretation between an experimenter and a skeptic: the experimenter allocates measurements to rule out alternatives while the skeptic proposes alternatives. We reformulate the game by allowing the skeptic to adopt a mixed strategy, yielding a concave-convex saddle-point problem. This viewpoint leads to Frank-Wolfe Self-Play (FWSP): a projection-free, regularization-free, tuning-free method whose one-hot updates on both sides match the bandit sampling paradigm. However, structural constraints introduce sharp pathologies that complicate algorithm design and analysis: our linear-bandit case study exhibits nonunique optima, optimal designs with zero mass on the best arm, bilinear objectives, and nonsmoothness at the boundary. We address these challenges via a differential-inclusion argument, proving convergence of the game value for best-arm identification in linear bandits. Our analysis proceeds through a continuous-time limit: a differential inclusion with a Lyapunov function that decays exponentially, implying a vanishing duality gap and convergence to the optimal value. Although Lyapunov analysis requires differentiability of the objective, which is not guaranteed on the boundary, we show that along continuous trajectories the algorithm steers away from pathological nonsmooth points and achieves uniform global convergence to the optimal game value. We then embed the discrete-time updates into a perturbed flow and show that the discrete game value also converges. Building on FWSP, we further propose a learning algorithm based on posterior sampling. Numerical experiments demonstrate a vanishing duality gap.

Although experimental design often focuses on selecting the single best alternative from a finite set, many pure-exploration problems pursue richer goals. Given a specific goal, adaptive experimentation aims to achieve it by strategically allocating sampling effort, with the underlying sample complexity characterized by a maximin optimization problem. In "Dual-Directed Algorithm Design for Efficient Pure Exploration," Qin and You introduce a unified dual-directed framework for efficiently solving general pure-exploration problems, yielding a unified algorithm design principle that extends the top-two approach beyond best-arm identification. Their theoretical analysis proves asymptotic optimality for classical problems, such as Gaussian best-arm identification, thresholding bandits, and epsilon-best-arm identification. Extensive numerical experiments confirm these theoretical insights, showcasing significant improvements over existing methods. This dual-directed framework offers researchers and practitioners a powerful and versatile tool to navigate uncertainty and optimize exploration strategies effectively.

We consider the best-k-arm identification problem for multi-armed bandits, where the objective is to select the exact set of k arms with the highest mean rewards by sequentially allocating measurement effort. We characterize the necessary and sufficient conditions for the optimal allocation using dual variables. Remarkably these optimality conditions lead to the extension of top-two algorithm design principle (Russo, 2020), initially proposed for best-arm identification. Furthermore, our optimality conditions induce a simple and effective selection rule dubbed information-directed selection (IDS) that selects one of the top-two candidates based on a measure of information gain. As a theoretical guarantee, we prove that integrated with IDS, top-two Thompson sampling is (asymptotically) optimal for Gaussian best-arm identification, solving a glaring open problem in the pure exploration literature (Russo, 2020). As a by-product, we show that for k > 1, top-two algorithms cannot achieve optimality even when the algorithm has access to the unknown "optimal" tuning parameter. Numerical experiments show the superior performance of the proposed top-two algorithms with IDS and considerable improvement compared with algorithms without adaptive selection.

We consider the top-k arm identification problem for multi-armed bandits with rewards belonging to a one-parameter canonical exponential family. The objective is to select the set of k arms with the highest mean rewards by sequential allocation of sampling efforts. We propose a unified optimal allocation problem that identifies the complexity measures of this problem under the fixed-confidence, fixed-budget settings, and the posterior convergence rate from the Bayesian perspective. We provide the first characterization of its optimality. We provide the first provably optimal algorithm in the fixed-confidence setting for k > 1 . We also propose an efficient heuristic algorithm for the top-k identification problem. Extensive numerical experiments demonstrate superior performance compare to existing methods in all three settings.

The 3D human body skeleton conveys rich information of human action and is regarded as an important data modality for action recognition. Due to the diversity of human action and the noise in skeleton data, skeleton-based action recognition methods face the challenges of overcoming the interference of irrelevant data and learning enough valid information of human action. Previous research has led us to a variety of effective skeleton features and many deep network models with strong learning abilities. However, a single model using a single feature cannot make full use of the valid information in the skeleton. To address this problem, this paper proposes the multi-level kinematic constraints to construct multiple skeleton features. By using different levels of constraints, a set of features containing information from local to global are extracted. The variability among these features leads to significant variability in classifiers trained on them, thus enhancing the ensemble performance of these classifiers. Extensive experiments on three representative datasets and four kinds of classification models demonstrate the generality of the proposed method. A substantial improvement can be achieved on multiple kinds of existing well-performing models and our method surpasses most state-of-the-art skeleton-based action recognition methods.

Self-supervised learning methods have received much attention in skeleton-based human action recognition. These methods rely on pretext tasks to utilize unlabeled data and learn an effective feature encoder. In this paper, a novel self-supervised learning method is proposed. First, we design a new pretext task called view enhanced jigsaw puzzle (VEJP) to improve the learning difficulty of the encoder. The VEJP introduces multi-view information into the jigsaw puzzle, thus forcing the encoder to learn view-independent high-level features of human skeletons. Based on the encoder trained by VEJP, we propose the view pooling encoder (VPE) to integrate the information of multiple views with the pooling mechanism, and the features extracted by VPE are more robust and distinguishable. In addition, by adjusting the difficulty of VEJP, the influence of the pretext task difficulty on the downstream task performance is studied, and the experimental results show that the pretext tasks should be moderately difficult to achieve effective feature learning. Our method achieves competitive results on representative benchmark datasets. It provides a strong baseline for the jigsaw puzzle task and shows advantages in situations where the number of labeled data is minimal.

We develop a robust queueing network analyzer algorithm to approximate the steady-state performance of a single-class open queueing network of single-server queues with Markovian routing. The algorithm allows non-renewal external arrival processes, general service-time distributions and customer feedback. We focus on the customer flows, defined as the continuous-time processes counting customers flowing into or out of the network, or flowing from one queue to another. Each flow is partially characterized by its rate and a continuous function that measures the stochastic variability over time. This function is a scaled version of the variance-time curve, called the index of dispersion for counts (IDC). The required IDC functions for the flows can be calculated from the model primitives, estimated from data or approximated by solving a set of linear equations. A robust queueing technique is used to generate approximations of the mean steady-state performance at each queue from the IDC of the total arrival flow and the service specification at that queue. The algorithm effectiveness is supported by extensive simulation studies and heavy-traffic limits.

This paper studies stationary customer flows in an open queueing network. The flows are the processes counting customers flowing from one queue to another or out of the network. We establish the existence of unique stationary flows in generalized Jackson networks and convergence to the stationary flows as time increases. We establish heavy-traffic limits for the stationary flows, allowing an arbitrary subset of the queues to be critically loaded. The heavy-traffic limit with a single bottleneck queue is especially tractable because it yields limit processes involving one-dimensional reflected Brownian motion. That limit plays an important role in our new nonparametric decomposition approximation of the steady-state performance using indices of dispersion and robust optimization.

Hybrid active contour models with the combination of region and edge information have attracted great interests in image segmentation. To the best of our knowledge, however, the theoretical foundation of these hybrid models with level set evolution is insufficient and limited. More specifically, the weighting factors of their energy terms are difficult to select and are often empirically determined without definite theoretical basis. This problem is particularly prominent in the case of multi-object segmentation when more level set functions must be computed simultaneously. To cope with these challenges, this paper proposes a new level set approach for constructing hybrid active contour models with reliable energy weights, where the weights of region and edge terms can be constrained by the optimization condition deduced from the proposed method. It can be regarded as a general approach since many existing region-based models can be easily used to construct new hybrid models using their equivalent two-phase formulations. Some representative as well as state-of-the-art models are taken as examples to demonstrate the generality of our method. The respective comparative studies validate that under the guidance of the optimization condition, segmentation accuracy, robustness, and computational efficiency can be improved compared with the original models which are used to construct the new hybrid ones.

The natural queueing models for many operations research applications have time-varying arrival rates. In addition, the natural models often are not Markov stochastic processes, so that they are not amenable to exact mathematical analysis. In “Time-Varying Robust Queueing,” Ward Whitt and Wei You propose a time-varying robust queueing algorithm to approximate the time-varying distribution of the workload (virtual waiting time) in a non-Markovian single-server queue with a time-varying arrival-rate function. They apply simulation and asymptotic methods to examine the performance of periodic robust queueing. They show that periodic robust queueing converges to a proper limit in appropriate long-cycle and heavy-traffic regimes and coincides with long-cycle fluid limits and heavy-traffic diffusion limits for long cycles. Simulation examples show that the mean and the full distribution (specified by the quantiles) of the periodic steady-state workload are remarkably well approximated.

The active contour models with level set evolution have been visited with a vast number of methods for image segmentation. They can be mainly classified into region-based and edge-based models, and it has been validated that the hybrid variants combining both region and edge information can improve the segmentation performance. However, to the best of our knowledge, the theoretical foundation of collaboration mechanism between the region and the edge information is limited. Specifically, most existing hybrid models are just combining all the energy terms together, resulting in great challenges of choosing an appropriate weight coefficient for each term and accommodating different modalities of imaging. To overcome these difficulties, this paper proposes a region and edge synergetic level set framework named RESLS. It provides an approach to construct new hybrid level set models using a normalized intensity indicator function that allows the region information easily embedding into the edge-based model. In this case, the energy weights of region and edge terms can be constrained by the global optimization condition deduced from the framework. Some representative as well as state-of-the-art models are taken as examples to demonstrate the generality of our method. The experiments validate that under the guidance of the optimization condition, the weighting parameter of each term can be reliably chosen. Meanwhile, the segmentation accuracy, robustness, and computational efficiency of RESLS can be improved compared with its component models.

A recent robust queueing approximation for open queueing networks exploits partial characterizations of each arrival process by its rate and index of dispersion for counts (IDC), which is a scaled version of the variance–time curve. Even though only means and variances (as functions of time) are involved, we show that the IDC provides a basis for more accurate approximations than traditional two-moment partial characterizations. For the G I ∕ G I ∕ 1 queue, this approach applied to the arrival and service processes fully characterizes the model.

People's mental workload profoundly affects their work efficiency and health. Mental workload assessment can be used to effectively avoid serious accidents caused by excessive mental workload. Both electroencephalogram (EEG) spectral features and its temporal features have proven to be useful in addressing this problem. The fusion of the two types of features can provide rich distinguishing information for improving mental workload assessment. Benefiting from the progress of deep learning, this study proposes the two-stream neural networks (TSNN) for fusing the two types of EEG features. Compared with hand-crafted features, the TSNN can learn and fuse EEG features from the spectral and temporal dimensions automatically without prior knowledge. The TSNN includes a spectral stream and a temporal stream. Each stream consists of a convolutional neural network (CNN) and a temporal convolutional network (TCN) to learn spectral or temporal features from EEG topographic maps. To fuse the learned spectral and temporal information, we concatenate the output of the two streams prior to the fully connected layer. EEG data were collected from 17 subjects who performed n-back tasks with easy, medium, and hard difficulty levels, leading to a three-class mental workload classification. The results show that the TSNN achieves an average accuracy of 91.9%, which is a significant improvement over baseline classifiers based on hand-crafted features. The TSNN also outperforms state-of-the-art deep learning methods developed for EEG classification. The results indicate that the proposed structure is promising for fusing spectral and temporal features for mental workload assessment. In addition, it provides a high-precision approach for potential applications during cognitive activities.

Queueing applications are often complicated by dependence among interarrival times and service times. Such dependence is common in networks of queues, where arrivals are departures from other queues or superpositions of such complicated processes, especially when there are multiple customer classes with class-dependent service-time distributions. We show that the robust queueing approach for single-server queues proposed in the literature can be extended to yield improved steady-state performance approximations in the standard stochastic setting that includes dependence among interarrival times and service times. We propose a new functional robust queueing formulation for the steady-state workload that is exact for the steady-state mean in the M/GI/1 model and is asymptotically correct in both heavy traffic and light traffic. Simulation experiments show that it is effective more generally. The online appendix is available at https://doi.org/10.1287/opre.2017.1649.

Heavy-traffic limits are established for the stationary departure process from a GI/GI/1 queue and its variance function. The limit process is a function of the Brownian motion limits of the arrival and service processes plus the stationary reflected Brownian motion (RBM) limit of the queue-length process. An explicit expression is given for the variance function, which depends only on the first two moments of the interarrival times and service times plus the previously determined correlation function of canonical (drift −1, diffusion coefficient 1) RBM. The limit for the variance function here is used to show that the approximation for the index of dispersion for counts of the departure process used in our new robust queueing network analyzer is asymptotically correct in the heavy-traffic limit.

Non-intrusive load monitoring (NILM) is a technique for analyzing changes in the voltage and current flowing through the main feeder and determining the appliances in operation as well as their energy consumption. With the increase in amount and type of electric loads nowadays, it is of increasing significance to extract unique load signatures and build robust classification models for NILM. However, the electric loads of different households differ materially from one another, which makes it difficult to collect enough label data and train classification models with strong representation and generalization ability. In this paper, a voltage-current (V-I) trajectory enabled transfer learning method has been proposed for NILM. Different from the existing methods, a deep learning model pretrained on a visual recognition dataset is transferred to train the classifier for NILM, linking the knowledge between different domains. Moreover, the V-I trajectory is also transferred to visual representation by color encoding, which not only enhances the load signature's uniqueness but also enables the NILM implementation of transfer learning. The experimental results on NILM datasets show that the proposed method significantly improves the accuracy and can be efficiently generalized compared with state-of-the-art methods.

Face image-video retrieval refers to retrieving videos of a specific person with image query or searching face images of one person by using a video clip query. It has attracted much attention for broad applications like suspect tracking and identifying. This paper proposes a novel implicit relative attribute enabled cross-modality hashing (IRAH) method for large-scale face image-video retrieval. To cope with large-scale data, the proposed IRAH method facilitates fast cross-modality retrieval through embedding two entirely heterogeneous spaces, i.e., face images in Euclidean space and face videos on a Riemannian manifold, into a unified compact Hamming space. In order to resolve the semantic gap, IRAH maps the original low-level kernelized features to discriminative high-level implicit relative attributes. Therefore, the retrieval accuracy can be improved by leveraging both the label information across different modalities and the semantic structure obtained from the implicit relative attributes in each modality. To evaluate the proposed method, we conduct extensive experiments on two publicly available databases, i.e., the Big Bang Theory (BBT) and Buffy the Vampire Slayer (BVS). The experimental results demonstrate the superiority of the proposed method over different state-of-the-art cross-modality hashing methods. The performance gains are especially significant in the case that the hash code length is 8 bits, up to 12% improvements over the second best method among tested methods.