We study unconstrained smooth convex optimization under stochastic first- and zeroth-order oracles subject only to finite-moment bounds, naturally admitting persistent bias and heavy-tailed noise. In this hostile environment, integrating momentum into adaptive step search to secure acceleration poses an inherent structural challenge, because momentum propagates oracle errors across iterations, inevitably undermining the stabilizing effect of local search. To address this difficulty, we propose , a robust accelerated adaptive search method with tunable momentum intervention. Theoretically, we develop a general high-probability framework for adaptive search methods under stochastic oracle feedback, and instantiate it through the strongly convex and general convex analyses of . This yields high-probability stopping-time complexity bounds for reaching the attainable precision neighborhood. The resulting guarantees also clarify how the algorithmic parameters trade off early-stage acceleration against late-stage stability, and motivate a simple switching heuristic that performs well empirically.

Nonconvex and nonsmooth composite optimization problems with linear constraints have attracted widespread attention in artificial intelligence and computer science due to their extensive applications in machine learning. Variance-reduced stochastic ADMM algorithms are extensively employed to address these problems, with most existing methods relying on the classical SVRG double-loop framework. In this study, we introduce the SVRRM-ADMM algorithm, which leverages a novel stochastic variance-reduced recursive momentum (SVRRM) estimator constructed on the loopless-SVRG framework and integrates it with the Stochastic ADMM (SADMM). The proposed algorithm facilitates implementation, requires fewer tuning parameters, and retains equivalent theoretical properties. We demonstrate that SVRRM-ADMM converges to a stationary solution without assuming bounded variance. Moreover, we extend the SVRRM-ADMM algorithm by incorporating acceleration techniques to yield the ASVRRM-ADMM. We establish that both SVRRM-ADMM and ASVRRM-ADMM achieve a worst-case convergence rate of O(1/T), where T denotes the number of iterations. Under the additional Kurdyka-Lojasiewicz (KL) property assumption, we further show that the sequences generated by both algorithms have finite expected length and attain different convergence rates determined by the KL exponent. Finally, numerical experiments validate the effectiveness of the proposed algorithms.

Traveling salesman problem (TSP) is an important problem in combinatorial optimization, which serves as the foundation for significant frontier scientific issues, including integrated circuit design and genomics. Learning-based methods have shown impressive results in solving the TSP, demonstrating efficient perception and decision-making abilities. However, as the scale of modern scenarios continues to expand, efficiently improving existing solutions through learning approaches remains a challenging and urgent task. A general framework for re-insertion improvement in the TSP is proposed. Focusing the core decision on the selection of re-insertion positions, we design a neural re-insertion improvement (NRII) algorithm based on deep reinforcement learning. NRII integrates multiple attention mechanisms and neural components to achieve the perception and parameterization of re-insertion positions, followed by model training through a policy optimization method. Extensive numerical experiments validate that the NRII algorithm can be combined with various solving methods to efficiently improve the solution quality across different scales and distributions. Additionally, detailed sensitivity analyses of the hyperparameter in NRII are also conducted.

Although stochastic gradient descent (SGD) is well-established theoretically, most widely used machine learning implementations employ sampling without replacement because of its empirical superiority. Specifically, training data are randomly shuffled (or permuted) before each epoch, a strategy known as random reshuffling (RR), and training proceeds sequentially according to the shuffled order. In this paper, we propose an accelerated variance-reduced random reshuffling gradient descent algorithm (AVR-RRGD) for nonconvex finite-sum optimization problems. Although the convergence and acceleration effects of random reshuffling methods combined with variance reduction are well studied in the convex setting, the nonconvex case remains significantly less explored. Under mild assumptions, we first establish weak convergence under appropriate stepsize conditions. Leveraging the Kurdyka-& Lstrok;ojasiewicz (KL) inequality, we then prove strong limit-point convergence and derive convergence rates dependent on the KL exponent and stepsize choices. Finally, experiments on ridge regression and logistic regression confirm the efficiency of our approach.

Contrastive Learning (CL) has established itself as a dominant paradigm in self-supervised representation learning. However, its efficacy can be limited by discriminative information overfitting, where models learn overly specialized features for instance discrimination while insufficiently preserving semantic and structural information needed for downstream generalization. In this work, we re-examine CL through the lens of the Information Bottleneck (IB) principle and propose Information Bottleneck Contrastive Learning (IBCL), an IB-inspired framework that characterizes contrastive representation learning as a compression–preservation trade-off. Specifically, IBCL introduces two conceptual criteria: minimum sufficient augmentation, which encourages compact contrastive views by reducing redundant input information, and information-generalized representations, which aim to preserve useful semantic and structural information beyond pretext discrimination. Guided by this perspective, we propose Masked Reconstruction Contrastive Learning (MRCL), a plug-and-play instantiation of IBCL for classical contrastive learning frameworks. MRCL uses random patch masking as a controllable view-level compression mechanism and incorporates a lightweight reconstruction objective as an auxiliary semantic-structural regularizer to mitigate excessive information loss caused by masking. Extensive experiments demonstrate that MRCL consistently improves conventional CL baselines across ImageNet classification, ADE20K semantic segmentation, and COCO detection/instance segmentation. Notably, MRCL shows favorable scalability on large Vision Transformers and achieves competitive transfer performance on dense prediction benchmarks. These results suggest that the proposed compression–preservation design provides a practical and effective way to improve the generalization ability of contrastive representations.

Achieving optimality and adversarial robustness in deep reinforcement learning has long been regarded as conflicting goals. Nonetheless, recent theoretical insights presented in CAR suggest a potential alignment, raising the important question of how to realize this in practice. This paper first identifies a key gap between theory and practice by comparing standard policy optimization (SPO) and adversarially robust policy optimization (ARPO). Although they share theoretical consistency, *a fundamental tension between robustness and optimality arises in practical policy gradient methods*. SPO tends toward convergence to vulnerable first-order stationary policies (FOSPs) with strong natural performance, whereas ARPO typically favors more robust FOSPs at the expense of reduced returns. Furthermore, we attribute this tradeoff to the *reshaping effect of the strongest adversaries* in ARPO, which significantly complicates the global landscape by inducing *deceptive sticky FOSPs*. This improves robustness but makes navigation more challenging. To alleviate this, we develop the *BARPO*, a bilevel framework unifying SPO and ARPO by modulating adversary strength, thereby facilitating navigability while preserving global optima. Extensive empirical results demonstrate that BARPO consistently outperforms vanilla ARPO, providing a practical approach to reconcile theoretical and empirical performance.

Variance reduction (VR) is a crucial tool for solving finite-sum optimization problems, including the composite general convex setting, which is the focus of this work. On the one hand, denoting the number of component functions as n and the target accuracy as ε, some VR methods achieve the near-optimal complexity 𝒪(n+√(n)/), but they all have nested structure and fail to provide convergence guarantee for the iterate sequence itself. On the other hand, single-loop VR methods, being free from the aforementioned disadvantages, have complexity no better than 𝒪(n+n/) which is the complexity of the deterministic method FISTA, thus leaving a critical gap unaddressed. In this work, we propose the Harmonia technique which relates checkpoint update probabilities to momentum parameters in single-loop VR methods. Based on this technique, we further propose to vary the growth rate of the momentum parameter, creating a novel continuous trade-off between acceleration and variance reduction, controlled by the key parameter α∈[0,1]. The proposed techniques lead to following favourable consequences. First, several known complexity of quite different algorithms are re-discovered under the proposed unifying algorithmic framework Katyusha-H. Second, under an extra mild condition, Katyusha-H achieves the near-optimal complexity for α belonging to a certain interval, highlighting the effectiveness of the acceleration-variance reduction trade-off. Last, without extra conditions, Katyusha-H achieves the complexity 𝒪(n+√(n)/) with α=1 and proper mini-batch sizes. The proposed idea and techniques may be of general interest beyond the considered problem in this work.

Diffusion bridge models offer a powerful framework for connecting two data distributions, such as in image restoration and translation. Many existing methods learn this bridge by mimicking the score-matching formulation of standard diffusion models. In this work, we find that this way leads to an anomalous underfitting phenomenon near the target endpoint, as the process approaches the target distribution (t → 0). This underfitting, characterized by significant drift in the predicted variance and direction, results from an excessively large discrepancy in noise levels between the network's input and its regression target.To resolve this issue, we propose the Noise-Aligned Diffusion Bridge (NADB).Our approach reformulates the diffusion bridge by first employing a mean network to provide a cleaner conditional target, and then introducing a novel, noise-aligned mapping relationship. This new formulation resolves the noise mismatch and corrects the underfitting near the target endpoint. Experimental validation across multiple image restoration and image translation tasks demonstrates the effectiveness of our approach. Code is available at https://github.com/gyr02/NADB.

Offline reinforcement learning agents face significant deployment challenges due to the synthetic-to-real distribution mismatch. While most prior research has focused on improving the fidelity of synthetic sampling and incorporating off-policy mechanisms, the directly integrated paradigm often fails to ensure consistent policy behavior in biased models and underlying environmental dynamics, which inherently arise from discrepancies between behavior and learning policies. In this paper, we first shift the focus from model reliability to policy discrepancies while optimizing for expected returns, and then self-consistently incorporate synthetic data, deriving a novel actor-critic paradigm, Dual Alignment Maximin Optimization (DAMO). It is a unified framework to ensure both model-environment policy consistency and synthetic and offline data compatibility. The inner minimization performs dual conservative value estimation, aligning policies and trajectories to avoid out-of-distribution states and actions, while the outer maximization ensures that policy improvements remain consistent with inner value estimates. Empirical evaluations demonstrate that DAMO effectively ensures model and policy alignments, achieving competitive performance across diverse benchmark tasks.

In machine learning, it is common to encounter a class of nonconvex, nonsmooth composite optimization problems where the objective function may not possess a globally Lipschitz continuous gradient. To address such issues, we investigate stochastic Bregman proximal gradient methods with recursive momentum, and propose SBPG-STORM, whose convergence in expectation is established under bounded variance assumption. Although this assumption is widely used, it is often not satisfied in many practical applications. One possible method to solve this problem is to use variance reduction estimators, which we have integrated with recursive momentum to propose SBPG-SVRRM and SBPG-SVRRM+. Without assuming bounded variance, we prove the convergence in expectation by establishing their descent Lyapunov functions. Furthermore, under the expectation KŁ property, we demonstrate the global convergence of the iteration points as well as the convergence speed under different Łojasiewicz exponents. The preliminary numerical results indicate that our proposed methods exhibit comparable performance to the state-of-the-art methods.

Solving the Traveling Salesman Problem (TSP) efficiently holds significant value across multiple domains, yet traditional algorithms and learning-based methods struggle to maintain efficiency while achieving high accuracy as the problem scales expand. Despite efficient inferring without any iterative search, neural constructive approaches, commonly starting solvers from a sequence of vertex embeddings for the entire instance, cause terrible computation complexity for large-scale problems due to global and meticulous spatial capture. In this paper, we introduce the General Decomposition and Merging Framework (GDMF), a novel approach enhancing the efficiency of solving large-scale TSP through parallel processes and multi-level representation. GDMF comprises two key steps: First, GDMF decomposes input instances into more tractable sub-units which are then processed in parallel to construct sub-paths, substantially accelerating computational throughput. To effectively generate tours, we integrate the neural network with multi-level features from individual vertices, local grids, and global graph topology, leading to comprehensive perception and potent decisions. Extensive experiments underscore the effectiveness of GDMF in time-critical settings. Notably, GDMF attains a superior computational efficiency, approximately 3–9 times speedup with a comparable optimality gap than the prior efficient method for large-scale TSP. This innovation showcases its potential for real-time decision support in practical applications such as dynamic routing in logistics and crisis management.

Solving the Nash equilibrium in normal-form games with large-scale strategy spaces presents significant challenges. Open-ended learning frameworks, such as PSRO and its variants, have emerged as effective solutions. However, these methods often lack an efficient metric for evaluating strategy improvement, which limits their effectiveness in approximating equilibria.In this paper, we introduce a novel evaluative metric called Advantage, which possesses desirable properties inherently connected to the Nash equilibrium, ensuring that each strategy update approaches equilibrium. Building upon this, we propose the Advantage Policy Space Response Oracle (A-PSRO), an innovative unified open-ended learning framework applicable to both zero-sum and general-sum games. A-PSRO leverages the Advantage as a refined evaluation metric, leading to a consistent learning objective for agents in normal-form games. Experiments showcase that A-PSRO significantly reduces exploitability in zero-sum games and improves rewards in general-sum games, outperforming existing algorithms and validating its practical effectiveness.

In this paper, we focus on a class of two block nonconvex nonsmooth optimization problem with linear constraints. Firstly, we propose a Bregman-type improved alternating direction method of multiplie (ADMM) by combining the extrapolation technique. Subsequently, to reduce the difficulty of solving the subproblem, we generalize it to the linear variant by linearizing the smooth component. By assuming the merit function satisfies Kurdyka-Łojasiewicz (KŁ) property, we prove that the whole sequence generated by each proposed algorithm converges to a unique critical point of the augmented Lagrangian function (ALF). The convergence rates for the iteration sequence and the merit function value sequence are also provided. Eventually, we perform experiments on Lasso model and verify the effciency of our proposed algorithms.

In this study, we propose a novel splitting algorithm designed to address a class of nonconvex composite optimization problems with linear constraints, characterized by a difference-of-functions structure. Our approach incorporates a relaxation step, linear modification, an inertial technique, and Bregman distance-based updates. This problem framework covers many important nonsmooth and nonconvex optimization problems in the literature, including difference-of-convex problems with linear constraints. Under mild assumptions, we prove that the sequence generated by our algorithm is bounded. Leveraging the Kurdyka-Lojasiewicz (KL) property, we further establish global convergence and derive the convergence rate. Finally, numerical experiments on the robust principal component analysis (PCA) problem demonstrate the efficiency of our method.

The alternating direction method of multipliers (ADMM) is a widely employed first-order method due to its efficiency and simplicity. Nonetheless, like other splitting methods, ADMM's performance degrades substantially as the scale of the optimization problems it addresses increases. This work is devoted to studying an accelerated stochastic generalized ADMM framework with a class of variance-reduced gradient estimators for solving large-scale nonconvex nonsmooth optimization problems with linear constraints, in which we combine inertial technique and Bregman distance. Under the assumption that the objective functions are semi-algebraic which satisfies the Kurdyka-& Lstrok;ojasiewicz (KL) property, we establish the global convergence and convergence rate of the sequence generated by our proposed algorithm. Finally, numerical experiments on conducting a graph-guided fused lasso illustrates the efficiency of the proposed method.

Ensuring the robustness of deep reinforcement learning (DRL) agents against adversarial attacks is critical for their trustworthy deployment. Recent research highlights the challenges of achieving state-adversarial robustness and suggests that an optimal robust policy (ORP) does not always exist, complicating the enforcement of strict robustness constraints. In this paper, we further explore the concept of ORP. We first introduce the Intrinsic State-adversarial Markov Decision Process (ISA-MDP), a novel formulation where adversaries cannot fundamentally alter the intrinsic nature of state observations. ISA-MDP, supported by empirical and theoretical evidence, universally characterizes decision-making under state-adversarial paradigms. We rigorously prove that within ISA-MDP, a deterministic and stationary ORP exists, aligning with the Bellman optimal policy. Our findings theoretically reveal that improving DRL robustness does not necessarily compromise performance in natural environments. Furthermore, we demonstrate the necessity of infinity measurement error (IME) in both Q-function and probability spaces to achieve ORP, unveiling vulnerabilities of previous DRL algorithms that rely on 1-measurement errors. Motivated by these insights, we develop the Consistent Adversarial Robust Reinforcement Learning (CAR-RL) framework, which optimizes surrogates of IME. We apply CAR-RL to both value-based and policy-based DRL algorithms, achieving superior performance and validating our theoretical analysis.

We propose several modifications of the Barzilai–Borwein (BB) step size in the variance reduction (VR) methods for finite-sum optimization problems. Our first approach relies on a scalar function, which we call the TaiL Function (TLF). The TLF maps the computed BB step size to some positive real number, which will be used as the step size instead. The computational overhead is almost negligible and the functional forms of TLFs in this work don’t involve any problem-dependent parameters. In the strongly convex setting, due to the undesirable appearance of the condition number κ in the linear convergence rate, the IFO complexity of VR methods with BB step size has the form 𝒪((n+κ ^a)κlog (1/ϵ )) , a∈ℝ_+ . With the utilization of the TLF, the aforementioned complexity is improved to 𝒪((n+κ ^ã)log (1/ϵ )) , ã∈ℝ_+, ã

Multi-view Diffusion has greatly advanced the development of 3D content creation by generating multiple images from distinct views, achieving remarkable photorealistic results. However, existing works are still vulnerable to inconsistent 3D geometric structures (commonly known as Janus Problem) and severe artifacts. In this paper, we introduce MIRROR, a versatile plug-and-play method that rectifies such inconsistencies in a training-free manner, enabling the acquisition of high-fidelity, realistic structures without compromising diversity. Our key idea focuses on tracing the motion trajectory of physical points across adjacent viewpoints, enabling rectifications based on neighboring observations of the same region. Technically, MIRROR comprises two core modules: Trajectory Tracking Module (TTM) for pixel-wise trajectory tracking that labels identical points across views, and Feature Rectification Module (FRM) for explicitly adjustment of each pixel embedding on noisy synthesized images by minimizing the distance to corresponding block features in neighboring views, thereby achieving consistent outputs. Extensive evaluations demonstrate that MIRROR can seamlessly integrate with a diverse range of off-the-shelf object-level multi-view diffusion models, significantly enhancing both the consistency and the fidelity in an efficient way.

This paper focuses on face stylization with a single artistic target. Existing works for this task often fail to retain the source content while achieving geometry variation. Here, we present a novel StyO model, i.e., Stylize the face in only One-shot, to solve the above problem. In particular, StyO exploits a disentanglement and recombination strategy. It first disentangles the content and style of source and target images into identifiers, which are then recombined in a cross manner to derive the stylized face image. In this way, StyO decomposes complex images into independent and specific attributes, and simplifies one-shot face stylization as the combination of different attributes from input images, thus producing results better matching face geometry of target image and content of source one. StyO is implemented with latent diffusion models (LDM) and composed of two key modules: 1) Identifier Disentanglement Learner (IDL) for disentanglement phase. It represents identifiers as contrastive text prompts, i.e. positive and negative descriptions. And it introduces a novel triple reconstruction loss to fine-tune the pre-trained LDM for encoding style and content into corresponding identifiers; 2) Fine-graind Content Controller (FCC) for recombination phase. It recombines disentangled identifiers from IDL to form an augmented text prompt for generating stylized faces. In addition, FCC also constrains the cross-attention maps of latent and text features to preserve source face details in results. The extensive evaluation shows that StyO produces high-quality images on numerous paintings of various styles and outperforms the current state-of-the-art.