I think the "global optimization" aspect of the main result and the fast (i.e., linear) convergence rate are very interesting, and perhaps also surprising. For example, for the least square problem min_z A G(z) - b prior works such as Hand & Voroninski [2017] and Heckel et al [2019] have established the global optimization aspect of simple gradient descent like algorithms. But the result obtained in this paper is much more general, and also applies to formulations with extra nonsmooth terms, with a practical numerical method. Moreover, general understanding of ADMM applied to nonconvex problems is still very rare. I think this result is definitely a beautiful addition to this line of literature also.

Originality: -Compared to Cotter et al, they have shown more classes of problems (i.e. My understanding is that even with surrogate approaches, the authors of this paper have shown that there's a way to get convergence by having both max and min players play no regret algorithms (with respect to true lagragian and surrogate lagrangian respectively). In Cotter et al, the non-zero sum issue can be side-stepped with one player playing to minimize no-swap regret. Quality: -Overall, the paper flows nicely with sections divided up to account for different problems (rate metric, objective & constraint, sum of ratios). Also, most of proofs in the appendix seem to to be good.

This paper proposes a new multi-task hierarchical reinforcement learning algorithm. The high-level policy achieves the assignment of tasks by solving a linear programming problem(or a quadratic programming problem), and the low-level policy is pre-defined. The biggest contribution of this paper is to get rid of the limitation of the number of agents and the number of tasks by modeling the multi-task assignment problem as an optimization problem, which based on the correlation between the agent and the task and the correlation between the tasks. After training the correlation in a simple task, you only need to re-solve the optimization problem in the complex task, without retraining, thus achieving zero-shot generalization. In this paper, the collaboration patterns between agents in the multi-task problem, such as creating subgroups of agents or spreading agents across tasks at the same time, are transformed into constraints to be added to the optimization problem corresponding to the high-level policy.

We study the dynamic pricing problem with knapsack, addressing the challenge of balancing exploration and exploitation under resource constraints. We introduce three algorithms tailored to different informational settings: a Boundary Attracted Re-solve Method for full information, an online learning algorithm for scenarios with no prior information, and an estimate-then-select re-solve algorithm that leverages machine-learned informed prices with known upper bound of estimation errors. The Boundary Attracted Re-solve Method achieves logarithmic regret without requiring the non-degeneracy condition, while the online learning algorithm attains an optimal $O(\sqrt{T})$ regret. Our estimate-then-select approach bridges the gap between these settings, providing improved regret bounds when reliable offline data is available. Numerical experiments validate the effectiveness and robustness of our algorithms across various scenarios. This work advances the understanding of online resource allocation and dynamic pricing, offering practical solutions adaptable to different informational structures.

Deploying complex machine learning models on resource-constrained devices is challenging due to limited computational power, memory, and model retrainability. To address these limitations, a hybrid system can be established by augmenting the local model with a server-side model, where samples are selectively deferred by a rejector and then sent to the server for processing. The hybrid system enables efficient use of computational resources while minimizing the overhead associated with server usage. The recently proposed Learning to Help (L2H) model trains a server model given a fixed local (client) model, differing from the Learning to Defer (L2D) framework, which trains the client for a fixed (expert) server. In both L2D and L2H, the training includes learning a rejector at the client to determine when to query the server. In this work, we extend the L2H model from binary to multi-class classification problems and demonstrate its applicability in a number of different scenarios of practical interest in which access to the server may be limited by cost, availability, or policy. We derive a stage-switching surrogate loss function that is differentiable, convex, and consistent with the Bayes rule corresponding to the 0-1 loss for the L2H model. Experiments show that our proposed methods offer an efficient and practical solution for multi-class classification in resource-constrained environments.

Recent advances in neural models have shown considerable promise in solving Traveling Salesman Problems (TSPs) without relying on much hand-crafted engineering. However, while non-autoregressive (NAR) approaches benefit from faster inference through parallelism, they typically deliver solutions of inferior quality compared to autoregressive ones. To enhance the solution quality while maintaining fast inference, we propose DEITSP, a diffusion model with efficient iterations tailored for TSP that operates in a NAR manner. Firstly, we introduce a one-step diffusion model that integrates the controlled discrete noise addition process with self-consistency enhancement, enabling optimal solution prediction through simultaneous denoising of multiple solutions. Secondly, we design a dual-modality graph transformer to bolster the extraction and fusion of features from node and edge modalities, while further accelerating the inference with fewer layers. Thirdly, we develop an efficient iterative strategy that alternates between adding and removing noise to improve exploration compared to previous diffusion methods. Additionally, we devise a scheduling framework to progressively refine the solution space by adjusting noise levels, facilitating a smooth search for optimal solutions. Extensive experiments on real-world and large-scale TSP instances demonstrate that DEITSP performs favorably against existing neural approaches in terms of solution quality, inference latency, and generalization ability. Our code is available at $\href{https://github.com/DEITSP/DEITSP}{https://github.com/DEITSP/DEITSP}$.

The field of quantum computing is generating significant anticipation within the scientific and industrial communities due to its potential to revolutionize computing paradigms. Recognizing this potential, this paper explores the integration of transfer of knowledge techniques, traditionally used in classical artificial intelligence, into quantum computing. We present a comprehensive classification of the transfer models, focusing on Transfer Learning and Transfer Optimization. Additionally, we analyze relevant schemes in quantum computing that can benefit from knowledge sharing, and we delve into the potential synergies, supported by theoretical insights and initial experimental results. Our findings suggest that leveraging the transfer of knowledge can enhance the efficiency and effectiveness of quantum algorithms, particularly in the context of hybrid solvers. This approach not only accelerates the optimization process but also reduces the computational burden on quantum processors, making it a valuable tool for advancing quantum computing technologies.

We develop a new methodology to select scenarios of DER adoption most critical for distribution grids. Anticipating risks of future voltage and line flow violations due to additional PV adopters is central for utility investment planning but continues to rely on deterministic or ad hoc scenario selection. We propose a highly efficient search framework based on multi-objective Bayesian Optimization. We treat underlying grid stress metrics as computationally expensive black-box functions, approximated via Gaussian Process surrogates and design an acquisition function based on probability of scenarios being Pareto-critical across a collection of line- and bus-based violation objectives. Our approach provides a statistical guarantee and offers an order of magnitude speed-up relative to a conservative exhaustive search. Case studies on realistic feeders with 200-400 buses demonstrate the effectiveness and accuracy of our approach.

A common characteristic in integer linear programs (ILPs) is symmetry, allowing variables to be permuted without altering the underlying problem structure. Recently, GNNs have emerged as a promising approach for solving ILPs. However, a significant challenge arises when applying GNNs to ILPs with symmetry: classic GNN architectures struggle to differentiate between symmetric variables, which limits their predictive accuracy. In this work, we investigate the properties of permutation equivariance and invariance in GNNs, particularly in relation to the inherent symmetry of ILP formulations. We reveal that the interaction between these two factors contributes to the difficulty of distinguishing between symmetric variables. To address this challenge, we explore the potential of feature augmentation and propose several guiding principles for constructing augmented features. Building on these principles, we develop an orbit-based augmentation scheme that first groups symmetric variables and then samples augmented features for each group from a discrete uniform distribution. Empirical results demonstrate that our proposed approach significantly enhances both training efficiency and predictive performance. Integer Linear Programs (ILPs) are fundamental optimization problems characterized by a linear objective function and linear constraints, where the decision variables are restricted to integer values. These problems play a critical role in various fields, including operations research, computer science, and engineering (Pochet & Wolsey, 2006; Liu & Fan, 2018; Watson & Woodruff, 2011; Luathep et al., 2011; Schöbel, 2001).

The Hierarchical Navigable Small World (HNSW) algorithm is widely used for approximate nearest neighbor (ANN) search, leveraging the principles of navigable small-world graphs. However, it faces some limitations. The first is the local optima problem, which arises from the algorithm's greedy search strategy, selecting neighbors based solely on proximity at each step. This often leads to cluster disconnections. The second limitation is that HNSW frequently fails to achieve logarithmic complexity, particularly in high-dimensional datasets, due to the exhaustive traversal through each layer. To address these limitations, we propose a novel algorithm that mitigates local optima and cluster disconnections while enhancing the construction speed, maintaining inference speed. The first component is a dual-branch HNSW structure with LID-based insertion mechanisms, enabling traversal from multiple directions. This improves outlier node capture, enhances cluster connectivity, accelerates construction speed and reduces the risk of local minima. The second component incorporates a bridge-building technique that bypasses redundant intermediate layers, maintaining inference and making up the additional computational overhead introduced by the dual-branch structure. Experiments on various benchmarks and datasets showed that our algorithm outperforms the original HNSW in both accuracy and speed. We evaluated six datasets across Computer Vision (CV), and Natural Language Processing (NLP), showing recall improvements of 18\% in NLP, and up to 30\% in CV tasks while reducing the construction time by up to 20\% and maintaining the inference speed. We did not observe any trade-offs in our algorithm. Ablation studies revealed that LID-based insertion had the greatest impact on performance, followed by the dual-branch structure and bridge-building components.