Abstract--Edge robotics involves frequent exchanges of large-volume multi-modal data. Existing methods ignore the inter - dependency between robotic functionalities and communica tion conditions, leading to excessive communication overhead. As such, rob ots can dynamically adapt their communication strategies (i.e ., compression ratio, transmission frequency, transmit powe r) by leveraging the knowledge of robotic perception and motion d y-namics, thus reducing the need for excessive sensor data upl oads. Furthermore, by leveraging the learning to optimize (L TO) paradigm, an imitation learning neural network is designed and implemented, which reduces the computational complexi ty by over 10x compared to state-of-the art optimization solve rs. Experiments demonstrate the superiority of the proposed IP MC and the real-time execution capability of L TO. Index T erms --Edge robotics, learning to optimize. Edge robotics (ER) enables resource-constrained mobile robots to offload computation-intensive tasks to edge serve rs [1]-[5] .

In the Industrial Internet of Things (IIoT), the frequent transmission of large amounts of data over wireless networks should meet the stringent timeliness requirements. Particularly, the freshness of packet status updates has a significant impact on the system performance. In this paper, we propose an age-of-information (AoI)-aware multi-base station (BS) real-time monitoring framework to support extensive IIoT deployments. To meet the freshness requirements of IIoT, we formulate a joint task offloading and resource allocation optimization problem with the goal of minimizing long-term average AoI. Tackling the core challenges of combinatorial explosion in multi-BS decision spaces and the stochastic dynamics of IIoT systems is crucial, as these factors render traditional optimization methods intractable. Firstly, an innovative branching-based Dueling Double Deep Q-Network (Branching-D3QN) algorithm is proposed to effectively implement task offloading, which optimizes the convergence performance by reducing the action space complexity from exponential to linear levels. Then, an efficient optimization solution to resource allocation is proposed by proving the semi-definite property of the Hessian matrix of bandwidth and computation resources. Finally, we propose an iterative optimization algorithm for efficient joint task offloading and resource allocation to achieve optimal average AoI performance. Extensive simulations demonstrate that our proposed Branching-D3QN algorithm outperforms both state-of-the-art DRL methods and classical heuristics, achieving up to a 75% enhanced convergence speed and at least a 22% reduction in the long-term average AoI.

Reformulating nonlinear optimization problems is largely manual and expertise-intensive, yet it remains essential for solving such problems with linear optimization solvers or applying special-purpose algorithms. We introduce \textit{LinearizeLLM}, an agent-based framework that solves this task by leveraging Large Language Models (LLMs). The framework assigns each nonlinear pattern to a \textit{reformulation agent} that is explicitly instructed to derive an exact linear reformulation for its nonlinearity pattern, for instance, absolute-value terms or bilinear products of decision variables. The agents then coordinate to assemble a solver-ready linear model equivalent to the original problem. To benchmark the approach, we create a dataset of 20 real-world nonlinear optimization problems derived from the established ComplexOR dataset of linear optimization problems. We evaluate our approach with several LLMs. Our results indicate that specialized LLM agents can automate linearization tasks, opening a path toward fully conversational modeling pipelines for nonlinear optimization.

Consistency Models (CMs) have shown promise for efficient one-step generation. However, most existing CMs rely on manually designed discretization schemes, which can cause repeated adjustments for different noise schedules and datasets. To address this, we propose a unified framework for the automatic and adaptive discretization of CMs, formulating it as an optimization problem with respect to the discretization step. Concretely, during the consistency training process, we propose using local consistency as the optimization objective to ensure trainability by avoiding excessive discretization, and taking global consistency as a constraint to ensure stability by controlling the denoising error in the training target. We establish the trade-off between local and global consistency with a Lagrange multiplier. Building on this framework, we achieve adaptive discretization for CMs using the Gauss-Newton method. We refer to our approach as ADCMs. Experiments demonstrate that ADCMs significantly improve the training efficiency of CMs, achieving superior generative performance with minimal training overhead on both CIFAR-10 and ImageNet. Moreover, ADCMs exhibit strong adaptability to more advanced DM variants. Code is available at https://github.com/rainstonee/ADCM.

Classic zeroth-order optimization approaches typically optimize for a smoothed version of the original function, i.e., the expected objective under randomly perturbed model parameters. This can be interpreted as encouraging the loss values in the perturbation set to be small on average. Popular sharpness-aware minimization (SAM) objectives, however, typically focus on the largest loss within the neighborhood to arrive at flat minima more effectively. In this work, we connect zeroth-order optimization (and its corresponding objectives) with SAM approaches explicitly, through an exponential tilting objective that provides a smooth transition between the average- and the max-loss formulations. We explore new zeroth-order algorithms to solve a soft SAM objective parameterized by a tilting parameter $t$. We provide precise characterizations of the sharpness notions of the tilted SAM framework. Practically, our approach can be used as a gradient-free and memory-efficient alternative to SAM variants, and it achieves better generalization compared to vanilla zeroth-order baselines on a wide range of downstream tasks, including classification, multiple choice QA, and language generation.

Pseudo-labeling is a commonly used paradigm in semi-supervised learning, yet its application to semi-supervised regression (SSR) remains relatively under-explored. Unlike classification, where pseudo-labels are discrete and confidence-based filtering is effective, SSR involves continuous outputs with heteroscedastic noise, making it challenging to assess pseudo-label reliability. As a result, naive pseudo-labeling can lead to error accumulation and overfitting to incorrect labels. To address this, we propose an uncertainty-aware pseudo-labeling framework that dynamically adjusts pseudo-label influence from a bi-level optimization perspective. By jointly minimizing empirical risk over all data and optimizing uncertainty estimates to enhance generalization on labeled data, our method effectively mitigates the impact of unreliable pseudo-labels. We provide theoretical insights and extensive experiments to validate our approach across various benchmark SSR datasets, and the results demonstrate superior robustness and performance compared to existing methods. Our code is available at https://github.com/sxq/Heteroscedastic-Pseudo-Labels.

Recent research has shown that optimization proxies can be trained to high fidelity, achieving average optimality gaps under 1% for large-scale problems. However, worst-case analyses show that there exist in-distribution queries that result in orders of magnitude higher optimality gap, making it difficult to trust the predictions in practice. This paper aims at striking a balance between classical solvers and optimization proxies in order to enable trustworthy deployments with interpretable speed-optimality tradeoffs based on a user-defined optimality threshold. To this end, the paper proposes a hybrid solver that leverages duality theory to efficiently bound the optimality gap of predictions, falling back to a classical solver for queries where optimality cannot be certified. To improve the achieved speedup of the hybrid solver, the paper proposes an alternative training procedure that combines the primal and dual proxy training. Experiments on large-scale transmission systems show that the hybrid solver is highly scalable. The proposed hybrid solver achieves speedups of over 1000x compared to a parallelized simplex-based solver while guaranteeing a maximum optimality gap of 2%.

Quantum computing has the potential to revolutionize fields like quantum optimization and quantum machine learning. However, current quantum devices are hindered by noise, reducing their reliability. A key challenge in gate-based quantum computing is improving the reliability of quantum circuits, measured by process fidelity, during the transpilation process, particularly in the routing stage. In this paper, we address the Fidelity Maximization in Routing Stage (FMRS) problem by introducing FIDDLE, a novel learning framework comprising two modules: a Gaussian Process-based surrogate model to estimate process fidelity with limited training samples and a reinforcement learning module to optimize routing. Our approach is the first to directly maximize process fidelity, outperforming traditional methods that rely on indirect metrics such as circuit depth or gate count. We rigorously evaluate FIDDLE by comparing it with state-of-the-art fidelity estimation techniques and routing optimization methods. The results demonstrate that our proposed surrogate model is able to provide a better estimation on the process fidelity compared to existing learning techniques, and our end-to-end framework significantly improves the process fidelity of quantum circuits across various noise models.

Reasoning models have gained significant attention due to their strong performance, particularly when enhanced with retrieval augmentation. However, these models often incur high computational costs, as both retrieval and reasoning tokens contribute substantially to the overall resource usage. In this work, we make the following contributions: (1) we propose a retrieval-augmented reasoning model that dynamically adjusts the length of the retrieved document list based on the query and retrieval results; (2) we develop a cost-aware advantage function for training of efficient retrieval-augmented reasoning models through reinforcement learning; and (3) we explore both memory- and latency-bound implementations of the proposed cost-aware framework for both proximal and group relative policy optimization algorithms. We evaluate our approach on seven public question answering datasets and demonstrate significant efficiency gains, without compromising effectiveness. In fact, we observed that the model latency decreases by ~16-20% across datasets, while its effectiveness increases by ~5% on average, in terms of exact match.

Deep neural networks have achieved remarkable success in a wide range of classification tasks. However, they remain highly susceptible to adversarial examples - inputs that are subtly perturbed to induce misclassification while appearing unchanged to humans. Among various attack strategies, Universal Adversarial Perturbations (UAPs) have emerged as a powerful tool for both stress testing model robustness and facilitating scalable adversarial training. Despite their effectiveness, most existing UAP methods neglect domain specific constraints that govern feature relationships. Violating such constraints, such as debt to income ratios in credit scoring or packet flow invariants in network communication, can render adversarial examples implausible or easily detectable, thereby limiting their real world applicability. In this work, we advance universal adversarial attacks to constrained feature spaces by formulating an augmented Lagrangian based min max optimization problem that enforces multiple, potentially complex constraints of varying importance. We propose Constrained Adversarial Perturbation (CAP), an efficient algorithm that solves this problem using a gradient based alternating optimization strategy. We evaluate CAP across diverse domains including finance, IT networks, and cyber physical systems, and demonstrate that it achieves higher attack success rates while significantly reducing runtime compared to existing baselines. Our approach also generalizes seamlessly to individual adversarial perturbations, where we observe similar strong performance gains. Finally, we introduce a principled procedure for learning feature constraints directly from data, enabling broad applicability across domains with structured input spaces.