Neural combinatorial optimization (NCO) has gained significant attention due to the potential of deep learning to efficiently solve combinatorial optimization problems. NCO has been widely applied to job shop scheduling problems (JSPs) with the current focus predominantly on deterministic problems. In this paper, we propose a novel attention-based scenario processing module (SPM) to extend NCO methods for solving stochastic JSPs. Our approach explicitly incorporates stochastic information by an attention mechanism that captures the embedding of sampled scenarios (i.e., an approximation of stochasticity). Fed with the embedding, the base neural network is intervened by the attended scenarios, which accordingly learns an effective policy under stochasticity. We also propose a training paradigm that works harmoniously with either the expected makespan or Value-at-Risk objective. Results demonstrate that our approach outperforms existing learning and non-learning methods for the flexible JSP problem with stochastic processing times on a variety of instances. In addition, our approach holds significant generalizability to varied numbers of scenarios and disparate distributions.

We present a novel class of projected gradient (PG) methods for minimizing a smooth but not necessarily convex function over a convex compact set. We first provide a novel analysis of the "vanilla" PG method, achieving the best-known iteration complexity for finding an approximate stationary point of the problem. We then develop an "auto-conditioned" projected gradient (AC-PG) variant that achieves the same iteration complexity without requiring the input of the Lipschitz constant of the gradient or any line search procedure. The key idea is to estimate the Lipschitz constant using first-order information gathered from the previous iterations, and to show that the error caused by underestimating the Lipschitz constant can be properly controlled. We then generalize the PG methods to the stochastic setting, by proposing a stochastic projected gradient (SPG) method and a variance-reduced stochastic gradient (VR-SPG) method, achieving new complexity bounds in different oracle settings. We also present auto-conditioned stepsize policies for both stochastic PG methods and establish comparable convergence guarantees.

Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the $\epsilon$-contamination model, where an adversary can inspect and replace up to an $\epsilon$-fraction of the samples, a fundamental open problem is determining the optimal rates for robust stochastic convex optimization (SCO) under such contamination. We develop novel algorithms that achieve minimax-optimal excess risk (up to logarithmic factors) under the $\epsilon$-contamination model. Our approach improves over existing algorithms, which are not only suboptimal but also require stringent assumptions, including Lipschitz continuity and smoothness of individual sample functions. By contrast, our optimal algorithms do not require these restrictive assumptions, and can handle nonsmooth but Lipschitz population loss functions. We complement our algorithmic developments with a tight lower bound for robust SCO.

We study a censored variant of the data-driven newsvendor problem, where the decision-maker must select an ordering quantity that minimizes expected overage and underage costs based only on offline censored sales data, rather than historical demand realizations. Our goal is to understand how the degree of historical demand censoring affects the performance of any learning algorithm for this problem. To isolate this impact, we adopt a distributionally robust optimization framework, evaluating policies according to their worst-case regret over an ambiguity set of distributions. This set is defined by the largest historical order quantity (the observable boundary of the dataset), and contains all distributions matching the true demand distribution up to this boundary, while allowing them to be arbitrary afterwards. We demonstrate a spectrum of achievability under demand censoring by deriving a natural necessary and sufficient condition under which vanishing regret is an achievable goal. In regimes in which it is not, we exactly characterize the information loss due to censoring: an insurmountable lower bound on the performance of any policy, even when the decision-maker has access to infinitely many demand samples. We then leverage these sharp characterizations to propose a natural robust algorithm that adapts to the historical level of demand censoring. We derive finite-sample guarantees for this algorithm across all possible censoring regimes and show its near-optimality with matching lower bounds (up to polylogarithmic factors). We moreover demonstrate its robust performance via extensive numerical experiments on both synthetic and real-world datasets.

The frequency or volume estimation of unending data streams is a concern in many domains, starting with telecommunications but spreading to social networks, finance, and learning-augmented streaming algorithms [10-15] is receiving website engine. In network fields, for example, professionals significant attention due to the powerful potential of machine want to keep track of the activity frequency to identify overall learning (ML) to relieve or eliminate the binding of data network health and potential anomalies or changes in behavior, characteristics and the sketch design. Their typical workflow which, however, is often challenging because the amount of involves training a heavy hitter oracle, which receives a key information may be too large to store in an embedded device and returns a prediction of whether it will be heavy or not, then or to keep conveniently in fast storage [1]. As a consequence, inserts the most frequent keys into unique buckets and applies sketch, which is a set of counters or bitmaps associated with a sketch to the remaining keys. Although filtering heavy items hash functions, and a set of simple operations that record has been proven to improve the overall sketch performance on approximate information [2], has grown in popularity in the heavy-tailed distribution [4, 10], these offline and supervised context of high-velocity data streams and limited computational methods could hardly work in real-world applications.

In the realm of gradient-based optimization, Nesterov's accelerated gradient method (NAG) is a landmark advancement, achieving an accelerated convergence rate that outperforms the vanilla gradient descent method for convex function. However, for strongly convex functions, whether NAG converges linearly remains an open question, as noted in the comprehensive review by Chambolle and Pock [2016]. This issue, aside from the critical step size, was addressed by Li et al. [2024a] using a high-resolution differential equation framework. Furthermore, Beck [2017, Section 10.7.4] introduced a monotonically convergent variant of NAG, referred to as M-NAG. Despite these developments, the Lyapunov analysis presented in [Li et al., 2024a] cannot be directly extended to M-NAG. In this paper, we propose a modification to the iterative relation by introducing a gradient term, leading to a new gradient-based iterative relation. This adjustment allows for the construction of a novel Lyapunov function that excludes kinetic energy. The linear convergence derived from this Lyapunov function is independent of both the parameters of the strongly convex functions and the step size, yielding a more general and robust result. Notably, we observe that the gradient iterative relation derived from M-NAG is equivalent to that from NAG when the position-velocity relation is applied. However, the Lyapunov analysis does not rely on the position-velocity relation, allowing us to extend the linear convergence to M-NAG. Finally, by utilizing two proximal inequalities, which serve as the proximal counterparts of strongly convex inequalities, we extend the linear convergence to both the fast iterative shrinkage-thresholding algorithm (FISTA) and its monotonic counterpart (M-FISTA).

Mixed Integer Linear Programs (MILPs) are highly flexible and powerful tools for modeling and solving complex real-world combinatorial optimization problems. Recently, machine learning (ML)-guided approaches have demonstrated significant potential in improving MILPsolving efficiency. However, these methods typically rely on separate offline data collection and training processes, which limits their scalability and adaptability. This paper introduces the first multi-task learning framework for ML-guided MILP solving. The proposed framework provides MILP embeddings helpful in guiding MILP solving across solvers (e.g., Gurobi and SCIP) and across tasks (e.g., Branching and Solver configuration). Through extensive experiments on three widely used MILP benchmarks, we demonstrate that our multi-task learning model performs similarly to specialized models within the same distribution. Moreover, it significantly outperforms them in generalization across problem sizes and tasks. Keywords: Deep Learning Mixed Integer Linear Programming Multitask Learning Graph Neural Networks.

Driven by the vision of ubiquitous connectivity and wireless intelligence, the evolution of ultra-dense constellation-based satellite-integrated Internet is underway, now taking preliminary shape. Nevertheless, the entrenched institutional silos and limited, nonrenewable heterogeneous network resources leave current satellite systems struggling to accommodate the escalating demands of next-generation intelligent applications. In this context, the distributed satellite information networks (DSIN), exemplified by the cohesive clustered satellites system, have emerged as an innovative architecture, bridging information gaps across diverse satellite systems, such as communication, navigation, and remote sensing, and establishing a unified, open information network paradigm to support resilient space information services. This survey first provides a profound discussion about innovative network architectures of DSIN, encompassing distributed regenerative satellite network architecture, distributed satellite computing network architecture, and reconfigurable satellite formation flying, to enable flexible and scalable communication, computing and control. The DSIN faces challenges from network heterogeneity, unpredictable channel dynamics, sparse resources, and decentralized collaboration frameworks. To address these issues, a series of enabling technologies is identified, including channel modeling and estimation, cloud-native distributed MIMO cooperation, grant-free massive access, network routing, and the proper combination of all these diversity techniques. Furthermore, to heighten the overall resource efficiency, the cross-layer optimization techniques are further developed to meet upper-layer deterministic, adaptive and secure information services requirements. In addition, emerging research directions and new opportunities are highlighted on the way to achieving the DSIN vision.

Data from multiple environments offer valuable opportunities to uncover causal relationships among variables. Leveraging the assumption that the causal outcome model remains invariant across heterogeneous environments, state-of-the-art methods attempt to identify causal outcome models by learning invariant prediction models and rely on exhaustive searches over all (exponentially many) covariate subsets. These approaches present two major challenges: 1) determining the conditions under which the invariant prediction model aligns with the causal outcome model, and 2) devising computationally efficient causal discovery algorithms that scale polynomially, instead of exponentially, with the number of covariates. To address both challenges, we focus on the additive intervention regime and propose nearly necessary and sufficient conditions for ensuring that the invariant prediction model matches the causal outcome model. Exploiting the essentially necessary identifiability conditions, we introduce Negative Weight Distributionally Robust Optimization (NegDRO), a nonconvex continuous minimax optimization whose global optimizer recovers the causal outcome model. Unlike standard group DRO problems that maximize over the simplex, NegDRO allows negative weights on environment losses, which break the convexity. Despite its nonconvexity, we demonstrate that a standard gradient method converges to the causal outcome model, and we establish the convergence rate with respect to the sample size and the number of iterations. Our algorithm avoids exhaustive search, making it scalable especially when the number of covariates is large. The numerical results further validate the efficiency of the proposed method.

The long-run average payoff per transition (mean payoff) is the main tool for specifying the performance and dependability properties of discrete systems. The problem of constructing a controller (strategy) simultaneously optimizing several mean payoffs has been deeply studied for stochastic and game-theoretic models. One common issue of the constructed controllers is the instability of the mean payoffs, measured by the deviations of the average rewards per transition computed in a finite "window" sliding along a run. Unfortunately, the problem of simultaneously optimizing the mean payoffs under local stability constraints is computationally hard, and the existing works do not provide a practically usable algorithm even for non-stochastic models such as two-player games. In this paper, we design and evaluate the first efficient and scalable solution to this problem applicable to Markov decision processes.