NeurIPS 2025 论文列表

Offline multi-objective optimization aims to identify Pareto-optimal solutions given a dataset of designs and their objective values. In this work, we propose a preference-guided diffusion model that generates Pareto-optimal designs by leveraging a classifier-based guidance mechanism. Our guidance classifier is a preference model trained to predict the probability that one design dominates another, directing the diffusion model toward optimal regions of the design space. Crucially, this preference model generalizes beyond the training distribution, enabling the discovery of Pareto-optimal solutions outside the observed dataset. We introduce a novel diversity-aware preference guidance, augmenting Pareto dominance preference with diversity criteria. This ensures that generated solutions are optimal and well-distributed across the objective space, a capability absent in prior generative methods for offline multi-objective optimization. We evaluate our approach on various continuous offline multi-objective optimization tasks and find that it consistently outperforms other inverse/generative approaches while remaining competitive with forward/ surrogate-based optimization methods. Our results highlight the effectiveness of classifier-guided diffusion models in generating diverse and high-quality solutions that approximate the Pareto front well.

We aim to provide a unified convergence analysis for permutation-based Stochastic Gradient Descent (SGD), where data examples are permuted before each epoch. By examining the relations among permutations, we categorize existing permutation-based SGD algorithms into three categories: Arbitrary Permutations, Independent Permutations (including Random Reshuffling and FlipFlop Rajput et al., 2022), Dependent Permutations (including GraBs Lu et al., 2022a; Cooper et al., 2023). Existing unified analyses failed to encompass the Dependent Permutations category due to the inter-epoch permutation dependency. In this work, we propose a generalized assumption that explicitly characterizes the dependence of permutations across epochs. Building upon this assumption, we develop a unified framework for permutation-based SGD with arbitrary permutations of examples, incorporating all the existing permutation-based SGD algorithms. Furthermore, we adapt our framework for Federated Learning (FL), developing a unified framework for regularized client participation FL with arbitrary permutations of clients.

Smoothness is known to be crucial for acceleration in offline optimization, and for gradient-variation regret minimization in online learning. Interestingly, these two problems are actually closely connected --- accelerated optimization can be understood through the lens of gradient-variation online learning. In this paper, we investigate online learning with *Hölder* functions, a general class encompassing both smooth and non-smooth (Lipschitz) functions, and explore its implications for offline optimization. For (strongly) convex online functions, we design the corresponding gradient-variation online learning algorithm whose regret smoothly interpolates between the optimal guarantees in smooth and non-smooth regimes. Notably, our algorithms do not require prior knowledge of the Hölder smoothness parameter, exhibiting strong adaptivity over existing methods. Through online-to-batch conversion, this gradient-variation online adaptivity yields an optimal universal method for stochastic convex optimization under Hölder smoothness. However, achieving universality in offline strongly convex optimization is more challenging. We address this by integrating online adaptivity with a detection-based guess-and-check procedure, which, for the first time, yields a universal offline method that achieves accelerated convergence in the smooth regime while maintaining near-optimal convergence in the non-smooth one.

Neural Architecture Search (NAS) aims to identify high-performance networks within a defined search space. Training-free metrics have been proposed to estimate network performance without actual training, reducing NAS deployment costs. However, individual training-free metrics often capture only partial architectural features, and their estimation capabilities are different in various tasks. Combining multiple training-free metrics has been explored to enhance scalability across tasks. Yet, these methods typically optimize global metric combinations over the entire search space, overlooking the varying sensitivities of different architectures to specific metrics, which may limit the final architectures' performance. To address these challenges, we propose the Per-Architecture Training-Free Metric Optimization NAS (PO-NAS) algorithm. This algorithm: (a) Integrates multiple training-free metrics as auxiliary scores, dynamically optimizing their combinations using limited real-time training data, without relying on benchmarks; (b) Individually optimizes metric combinations for each architecture; (c) Integrates an evolutionary algorithm that leverages efficient predictions from surrogate models, enhancing search efficiency in large search spaces. Notably, PO-NAS combines the efficiency of training-free search with the robust performance of training-based evaluations. Extensive experiments demonstrate the effectiveness of our approach. Our code has been made publicly available at https://anonymous.4open.science/r/PO-NAS-2953.

Recently, Direct Alignment Algorithms (DAAs) such as Direct Preference Optimization (DPO) have emerged as alternatives to the standard Reinforcement Learning from Human Feedback (RLHF) for aligning large language models (LLMs) with human values. Surprisingly, while DAAs do not use a separate proxy reward model as in RLHF, their performance can still deteriorate over the course of training -- an over-optimization phenomenon found in RLHF where the learning policy exploits the overfitting to inaccuracies of the reward model to achieve high rewards. One attributed source of over-optimization in DAAs is the under-constrained nature of their offline optimization, which can gradually shift probability mass toward non-preferred responses not presented in the preference dataset. This paper proposes a novel importance-sampling approach to mitigate the distribution shift problem of offline DAAs. This approach, called (IS-DAAs), multiplies the DAA objective with an importance ratio that accounts for the reference policy distribution. IS-DAAs additionally avoid the high variance issue associated with importance sampling by clipping the importance ratio to a maximum value. Our extensive experiments demonstrate that IS-DAAs can effectively mitigate over-optimization, especially under low regularization strength, and achieve better performance than other methods designed to address this problem.

We study the problem of minimizing the sum of a smooth function and a nonsmooth convex regularizer over a compact Riemannian submanifold embedded in Euclidean space. By introducing an auxiliary splitting variable, we propose an adaptive Riemannian alternating direction method of multipliers (ARADMM), which, for the first time, achieves convergence without requiring smoothing of the nonsmooth term. In contrast to conventional Riemannian ADMM methods that require exactly solving a nested subproblem at each iteration, our approach involves only one Riemannian gradient evaluation and one proximal update per iteration. Through careful and adaptive coordination of the stepsizes and penalty parameters, we establish an optimal iteration complexity of order $\mathcal{O}(\epsilon^{-3})$ for finding an $\epsilon$-approximate KKT point, matching the complexity of existing smoothing technique-based Riemannian ADMM methods. Extensive numerical experiments on sparse PCA and robust subspace recovery demonstrate that our ARADMM consistently outperforms state-of-the-art Riemannian ADMM variants in convergence speed and solution quality.

Conformal Prediction (CP) is a powerful statistical machine learning tool to construct uncertainty sets with coverage guarantees, which has fueled its extensive adoption in generating prediction regions for decision-making tasks, e.g., Trajectory Optimization (TO) in uncertain environments. However, existing methods predominantly employ a sequential scheme, where decisions rely unidirectionally on the prediction regions, and consequently the information from decision-making fails to be fed back to instruct CP. In this paper, we propose a novel Feedback-Based CP (Fb-CP) framework for shrinking-horizon TO with a joint risk constraint over the entire mission time. Specifically, a CP-based posterior risk calculation method is developed by fully leveraging the realized trajectories to adjust the posterior allowable risk, which is then allocated to future times to update prediction regions. In this way, the information in the realized trajectories is continuously fed back to the CP, enabling attractive feedback-based adjustments of the prediction regions and a provable online improvement in trajectory performance. Furthermore, we theoretically prove that such adjustments consistently maintain the coverage guarantees of the prediction regions, thereby ensuring provable safety. Additionally, we develop a decision-focused iterative risk allocation algorithm with theoretical convergence analysis for allocating the posterior allowable risk which closely aligns with Fb-CP. Furthermore, we extend the proposed method to handle distribution shift. The effectiveness and superiority of the proposed method are demonstrated through benchmark experiments.

Hyperbolic deep learning has become a growing research direction in computer vision due to the unique properties afforded by the alternate embedding space. The negative curvature and exponentially growing distance metric provide a natural framework for capturing hierarchical relationships between datapoints and allowing for finer separability between their embeddings. However, current hyperbolic learning approaches are still prone to overfitting, computationally expensive, and prone to instability, especially when attempting to learn the manifold curvature to adapt to tasks and different datasets. To address these issues, our paper presents a derivation for Riemannian AdamW that helps increase hyperbolic generalization ability. For improved stability, we introduce a novel fine-tunable hyperbolic scaling approach to constrain hyperbolic embeddings and reduce approximation errors. Using this along with our curvature-aware learning schema for Riemannian Optimizers enables the combination of curvature and non-trivialized hyperbolic parameter learning. Our approach demonstrates consistent performance improvements across Computer Vision, EEG classification, and hierarchical metric learning tasks while greatly reducing runtime.

Adversarial learning is a widely used paradigm in machine learning, often formulated as a min-max optimization problem where the inner maximization imposes adversarial constraints to guide the outer learner toward more robust solutions. This framework underlies methods such as Sharpness-Aware Minimization (SAM) and Generative Adversarial Networks (GANs). However, traditional gradient-based approaches to such problems often face challenges in balancing accuracy and efficiency due to second-order complexities. In this paper, we propose a bilevel optimization framework that reformulates these adversarial learning problems by leveraging the tractability of the lower-level problem. The bilevel framework introduces no additional complexity and enables the use of advanced bilevel tools. We further develop a provably convergent single-loop stochastic algorithm that effectively balances learning accuracy and computational cost. Extensive experiments show that our method improves generation quality in terms of FID and JS scores for GANs, and consistently achieves higher accuracy for SAM under label noise and across various backbones, while promoting flatter loss landscapes. Overall, this work provides a practical and theoretically grounded framework for solving adversarial learning tasks through bilevel optimization.

The recent success of Shampoo in the AlgoPerf contest has sparked renewed interest in Kronecker-factorization-based optimization algorithms for training neural networks. Despite its success, Shampoo relies heavily on several heuristics such as learning rate grafting and stale preconditioning to achieve performance at-scale. These heuristics increase algorithmic complexity, necessitate further hyperparameter tuning, and lack theoretical justification. This paper investigates these heuristics from the angle of Frobenius norm approximation to full-matrix Adam and decouples the preconditioner's eigenvalues and eigenbasis updates. We show that grafting from Adam mitigates the staleness and mis-scaling of the preconditioner's *eigenvalues* and how correcting the eigenvalues directly eliminates the need for learning rate grafting. To manage the error induced by infrequent *eigenbasis* computations, we propose an adaptive criterion for determining the eigenbasis computation frequency motivated by terminating a warm-started QR algorithm. This criterion decouples the update frequency of different preconditioner matrices and enables us to investigate the impact of approximation error on convergence. These practical techniques offer a principled angle towards removing Shampoo's heuristics and developing improved Kronecker-factorization-based training algorithms.

Finding an $\epsilon$-stationary point of a nonconvex function with a Lipschitz continuous Hessian is a central problem in optimization. Regularized Newton methods are a classical tool and have been studied extensively, yet they still face a trade‑off between global and local convergence. Whether a parameter-free algorithm of this type can simultaneously achieve optimal global complexity and quadratic local convergence remains an open question. To bridge this long-standing gap, we propose a new class of regularizers constructed from the current and previous gradients, and leverage the conjugate gradient approach with a negative curvature monitor to solve the regularized Newton equation. The proposed algorithm is adaptive, requiring no prior knowledge of the Hessian Lipschitz constant, and achieves a global complexity of $O(\epsilon^{-\frac{3}{2}})$ in terms of the second-order oracle calls, and $\tilde O(\epsilon^{-\frac{7}{4}})$ for Hessian-vector products, respectively. When the iterates converge to a point where the Hessian is positive definite, the method exhibits quadratic local convergence. Preliminary numerical results, including training the physics-informed neural networks, illustrate the competitiveness of our algorithm.

Finite-sum Coupled Compositional Optimization (FCCO), characterized by its coupled compositional objective structure, emerges as an important optimization paradigm for addressing a wide range of machine learning problems. In this paper, we focus on a challenging class of non-convex non-smooth FCCO, where the outer functions are non-smooth weakly convex or convex and the inner functions are smooth or weakly convex. Existing state-of-the-art result face two key limitations: (1) a high iteration complexity of $O(1/\epsilon^6)$ under the assumption that the stochastic inner functions are Lipschitz continuous in expectation; (2) reliance on vanilla SGD-type updates, which are not suitable for deep learning applications. Our main contributions are two fold: (i) We propose stochastic momentum methods tailored for non-smooth FCCO that come with provable convergence guarantees; (ii) We establish a **new state-of-the-art** iteration complexity of $O(1/\epsilon^5)$. Moreover, we apply our algorithms to multiple inequality constrained non-convex optimization problems involving smooth or weakly convex functional inequality constraints. By optimizing a smoothed hinge penalty based formulation, we achieve a **new state-of-the-art** complexity of $O(1/\epsilon^5)$ for finding an (nearly) $\epsilon$-level KKT solution. Experiments on three tasks demonstrate the effectiveness of the proposed algorithms.

Many real-world black-box optimization problems have multiple conflicting objectives. Rather than attempting to approximate the entire set of Pareto-optimal solutions, interactive preference learning, i.e., optimization with a decision maker in the loop, allows to focus the search on the most relevant subset. However, few previous studies have exploited the fact that utility functions are usually monotonic. In this paper, we address the Bayesian Optimization with Preference Exploration (BOPE) problem and propose using a neural network ensemble as a utility surrogate model. This approach naturally integrates monotonicity and allows to learn the decision maker's preferences from pairwise comparisons. Our experiments demonstrate that the proposed method outperforms state-of-the-art approaches and exhibits robustness to noise in utility evaluations. An ablation study highlights the critical role of monotonicity in enhancing performance.

Introduced by Korpelevich in 1976, the extragradient method (EG) has become a cornerstone technique for solving min-max optimization, root-finding problems, and variational inequalities (VIs). Despite its longstanding presence and significant attention within the optimization community, most works focusing on understanding its convergence guarantees assume the strong $L$-Lipschitz condition. In this work, building on the proposed assumptions by Zhang et al. [2019] for minimization and Vankov et al. [2024a] for VIs, we focus on the more relaxed $\alpha$-symmetric $(L_0, L_1)$-Lipschitz condition. This condition generalizes the standard Lipschitz assumption by allowing the Lipschitz constant to scale with the operator norm, providing a more refined characterization of problem structures in modern machine learning. Under the $\alpha$-symmetric $(L_0, L_1)$-Lipschitz condition, we propose a novel step size strategy for EG to solve root-finding problems and establish sublinear convergence rates for monotone operators and linear convergence rates for strongly monotone operators. Additionally, we prove local convergence guarantees for weak Minty operators. We supplement our analysis with experiments validating our theory and demonstrating the effectiveness and robustness of the proposed step sizes for EG.

Variational Quantum Algorithms (VQAs) are emerging as leading strategies with the potential to unlock practical applications and deliver significant advantages in the investigation of many-body quantum systems and quantum chemistry. A key challenge hindering the application of VQAs to large-scale problems is rooted in the no-cloning theorem in quantum mechanics, precluding standard backpropagation and leading to prohibitive quantum resource expenditure such as measurement cost. To address this challenge, we reformulate the training dynamics of VQAs as a non-linear partial differential equation and propose a novel protocol that leverages physics-informed neural networks (PINNs) to model this dynamical system efficiently. Given a small amount of training trajectory data collected from quantum devices, our protocol predicts the parameter updates of VQAs over multiple iterations on the classical side, dramatically reducing quantum resource costs. Through systematic numerical experiments, we demonstrate that our method achieves up to a 30x speedup compared to conventional methods and reduces quantum resource costs by as much as 90\% for tasks involving up to 40 qubits, including ground state preparation of different quantum systems, while maintaining competitive accuracy. Our approach complements existing techniques aimed at improving the efficiency of VQAs and further strengthens their potential for practical applications.

Mixture-of-Experts (MoE) models enable efficient scaling of large language models (LLMs) by activating only a subset of experts per input. However, we observe that the commonly used auxiliary load balancing loss often leads to expert overlap and overly uniform routing, which hinders expert specialization and degrades overall performance during post-training. To address this, we propose a simple yet effective solution that introduces two complementary objectives: (1) an orthogonality loss to encourage experts to process distinct types of tokens, and (2) a variance loss to encourage more discriminative routing decisions. Gradient-level analysis demonstrates that these objectives are compatible with the existing auxiliary loss and contribute to optimizing the training process. Experimental results over various model architectures and across multiple benchmarks show that our method significantly enhances expert specialization. Notably, our method improves classic MoE baselines with auxiliary loss by up to 23.79\%, while also maintaining load balancing in downstream tasks, without any architectural modifications or additional components. We will release our code to contribute to the community.

Physics-informed neural networks (PINNs) have shown significant promise in computational science and engineering, yet they often face optimization challenges and limited accuracy. In this work, we identify directional gradient conflicts during PINN training as a critical bottleneck. We introduce a novel gradient alignment score to systematically diagnose this issue through both theoretical analysis and empirical experiments. Building on these insights, we show that (quasi) second-order optimization methods inherently mitigate gradient conflicts, thereby consistently outperforming the widely used Adam optimizer. Among them, we highlight the effectiveness of SOAP \cite{vyas2024soap} by establishing its connection to Newton’s method. Empirically, SOAP achieves state-of-the-art results on 10 challenging PDE benchmarks, including the first successful application of PINNs to turbulent flows at Reynolds numbers up to 10,000. It yields 2–10x accuracy improvements over existing methods while maintaining computational scalability, advancing the frontier of neural PDE solvers for real-world, multi-scale physical systems. All code and datasets used in this work are publicly available at: \url{https://github.com/PredictiveIntelligenceLab/jaxpi/tree/pirate}. \end{abstract}

Model-free optimization methods typically rely on cost samples gathered by perturbing the current solution estimate along a finite and fixed set of directions. However, at each iteration, only the current cost samples are used, while potentially informative, previously collected samples are discarded. In this work, we challenge this conventional approach by introducing a simple yet effective memory mechanism that maintains an auxiliary vector of iteratively updated cost samples. By leveraging this stored information, our method estimates descent directions through an averaging of all perturbing directions weighted by the auxiliary vector components. This results in a faster convergence without increasing the number of function queries. By interpreting the resulting algorithm as a time-varying dynamical system, we are able to establish its convergence properties in the strongly convex case. In particular, by using tools from system theory based on timescale separation, we are able to guarantee a linear convergence rate toward an arbitrarily small neighborhood of the optimal solution. Numerical simulations on regression problems demonstrate that the proposed approach significantly outperforms existing model-free optimization methods.

We study population convergence guarantees of stochastic gradient descent (SGD) for smooth convex objectives in the interpolation regime, where the noise at optimum is zero or near zero. The behavior of the last iterate of SGD in this setting---particularly with large (constant) stepsizes---has received growing attention in recent years due to implications for the training of over-parameterized models, as well as to analyzing forgetting in continual learning and to understanding the convergence of the randomized Kaczmarz method for solving linear systems. We establish that after $T$ steps of SGD on $\beta$-smooth convex loss functions with stepsize $0 < \eta < 2/\beta$, the last iterate exhibits expected excess risk $\widetilde{O}(\tfrac{1}{\eta (2-\beta \eta) T^{1-\beta\eta/2}} + \tfrac{\eta}{(2-\beta\eta)^2} T^{\beta\eta/2} \sigma_\star^2)$, where $\sigma_\star^2$ denotes the variance of the stochastic gradients at the optimum. In particular, for a well-tuned stepsize we obtain a near optimal $\widetilde{O}(1/T + \sigma_\star/\sqrt T)$ rate for the last iterate, extending the results of Varre et al. (2021) beyond least squares regression; and when $\sigma_\star=0$ we obtain a rate of $O(1/\sqrt T)$ with $\eta=1/\beta$, improving upon the best-known $O(T^{-1/4})$ rate recently established by Evron et al. (2025) in the special case of realizable linear regression.