NeurIPS 2026 论文列表

Optimization under heavy-tailed stochastic noise remains a major challenge in modern machine learning, where classical moment assumptions often fail to capture realistic gradient distributions. In this work, we revisit robust estimation techniques and provide a systematic analysis of the Median-of-Means (MoM) estimator under a structured noise model that interpolates between a symmetric heavy-tailed distribution with bounded $\beta$-th moment ($\beta \in (0, 1]$) and a mean-zero distribution with bounded $\alpha$-th moment ($\alpha \in (1, 2]$). We derive new upper bounds on the variance and bias of MoM in this setting, thereby extending the applicability of existing results beyond purely symmetric or bounded-moment settings. Building on these properties, we study clipped stochastic optimization methods with MoM gradient estimation and establish high-probability convergence guarantees that hold for general $\beta \in (0, 1]$ and $\alpha \in (1, 2]$. Our bounds match or improve upon prior complexity guarantees while requiring weaker distributional assumptions, and they reveal that bias only affects the final neighborhood of convergence. Overall, this work advances the theoretical foundations for robust stochastic optimization in the presence of extreme gradient noise.

Low-budget molecular optimization is often framed as Bayesian optimization in a learned latent space, but standard benchmarks typically allow hundreds or thousands of evaluations, whereas a realistic wet-lab round may allow only a few dozen. We revisit this regime using a SELFIES molecular variational autoencoder and GuacaMol objectives at $N=30$ oracle calls. The main finding is not a new surrogate model, but a geometric mismatch in candidate generation. The training latents of the VAE concentrate near a narrow spherical shell, while many high-dimensional optimizers propose candidates from boxes or box-shaped trust regions. Such candidates can leave the decoder's training distribution even when their coordinates look individually plausible. We study a simple geometric constraint, the on-sphere scaffold, that restricts candidate generation to the empirical shell occupied by the VAE training latents. Uniform random search on this shell already outperforms most of the classical box-supported Bayesian optimization baselines. We then introduce two minimal optimizers to probe what remains useful once the support is fixed. GeoWalk performs geodesic local search on the empirical sphere and outperforms every published Bayesian optimization baseline tested. GeoCMA keeps the scaffold but adds covariance learning in a random subspace, becoming preferable when the search representation contains learnable directional or semantic structure, as in LassoBench, NAS-Bench-101 graph-VAE optimization, and GSM8K text-latent prompt optimization. A controlled ablation of three recent Gaussian-process recipes, changing only whether candidates are proposed on the empirical sphere or on the published box-supported domain, shows that the scaffold rather than the surrogate is the load-bearing component. The practical lesson is simple: first match the empirical search support; add a surrogate or covariance learner only when the remaining search space contains directional structure that can be learned from the available budget.

Optimization proxies amortize parametric constrained optimization by learning fast approximations of solution maps. Because these maps are smooth only within active-set regimes, the parameter space may split into combinatorially many critical regions, making finite-sample generalization and reliable constraint behavior central challenges. To address this challenge, this paper develops sparse stochastic masked Sobolev training for optimization proxies, augmenting value supervision with randomly selected solver-sensitivity targets rather than dense Jacobian matching. The mask acts as an algorithmic control: it exposes the proxy to local derivative information while avoiding overconstraint from conflicting active constraint set signals. We provide approximation bounds showing that, under coverage and regularity, joint value-and-Jacobian matching improves finite-sample generalization. Experiments characterize when and how this benefit appears. In smooth optimal-control distillation, where feasibility is guaranteed by construction, and only a few active-set regimes arise, Sobolev supervision reaches 95\% of teacher performance about $2.5\times$ faster than value-only training. In AC optimal power flow, masked Sobolev training keeps optimality gaps below 0.22\% across three PGLib networks while reducing the median worst-case constraint violation by up to $4\times$. A mean--variance portfolio study identifies the complementary limitation: when sensitivities are highly local or vanish across active-set regimes, derivative supervision can be less useful than value-only training.

Preference optimization is a standard alignment method for generative models, yet extending it to continuous-time dynamics remains non-trivial. In flow matching, reward-driven updates modify the transport trajectories but lack inherent constraints to pretrained data manifold, often pushing generated (terminal) samples off the pretrained support. We formalize this failure mode as ``manifold drift``, a phenomenon where preference-aligned trajectories diverge from the pretrained support. Theoretically, we prove that while optimal flow matching exactly preserves the terminal manifold, existing methods like FlowDPO fail to do so whenever reward-driven updates contain components normal to the manifold surface. As a remedy, we propose **ThermoDPO**, a temperature-controlled objective that anchors pairwise preference optimization on preferred samples. Across temperature regimes, this objective connects rejection sampling fine-tuning and FlowDPO while upper-bounding a reconstruction-based surrogate for manifold drift. To counteract diminished signals at low temperatures, we further introduce a weighted variant, **ThermoDPO-weighted**, which we evaluate across all experiments for its superior trade-off between preference alignment and manifold preservation. Empirically, **ThermoDPO-weighted** demonstrates a better trade-off on synthetic manifolds than FlowDPO variants. On real-world image benchmarks, it improves OCR-oriented alignment over the pretrained model and FlowDPO variants while remaining competitive with strong baselines in held-out model-based and human evaluations without visible sample degradation.

As the era of large language models (LLMs) unfolds, Preference Optimization (PO) methods have become a central approach to aligning LLMs with human preferences and improving performance. We propose Maximum a Posteriori Preference Optimization (MaPPO), a methodology for learning from preferences that explicitly incorporates prior reward knowledge into the optimization objective. Building on the paradigm employed by Direct Preference Optimization (DPO) and its variants of treating preference learning as a Maximum Likelihood Estimation (MLE) problem, MaPPO integrates prior reward estimates into a principled Maximum a Posteriori (MaP) objective. This not only generalizes DPO and its variants, but also enhances alignment by mitigating the oversimplified binary classification of responses. Additionally, MaPPO introduces no additional hyperparameters, and supports preference optimization in both offline and online settings. In addition, MaPPO can be used as a plugin for DPO variants, including widely used SimPO, IPO and CPO, and produce consistent improvements. Extensive empirical evaluations of different model sizes and model series on three standard benchmarks (MT-Bench, AlpacaEval 2.0, and Arena-Hard) demonstrate consistent improvements in alignment performance without sacrificing computational efficiency.

Multi-objective Bayesian optimization (MOBO) traditionally aims to approximate the entire Pareto front, but real-world deployment is often limited to a small, representative subset of solutions due to resource constraints. Current two-stage methods first approximate the full front before selecting solutions, wasting evaluation budget. We formalize this problem as Multi-objective Bayesian Optimization with Cardinality-aware Pareto Selection (MOBO-CAPS), where the goal is to identify a set of exactly $M$ solutions with high hypervolume. We propose two practical cardinality-aware acquisition strategies: REHVI, a replacement-aware approximation to expected hypervolume improvement, and CHO-UCB, which constructs an optimistic $M$-point set by optimizing a collective UCB-based hypervolume objective. We prove a sublinear simple regret bound for the batched version of CHO-UCB, and empirically show that cardinality-aware acquisition design improves over standard MOBO followed by post-hoc subset selection across nine benchmarks.

Optimization modeling translates real decision-making problems into mathematical optimization models and solver-executable implementations. Although language models are increasingly used to generate optimization formulations and solver code, existing benchmarks for this capability are almost entirely text-only. This omits many optimization-modeling tasks that arise in operational practice, where requirements are described in text but essential instance information is often conveyed through visual artifacts such as tables, graphs, maps, schedules, and planning dashboards. We introduce \emph{multimodal optimization modeling}, a benchmark setting in which models must construct both a mathematical formulation and executable solver code from a text-and-visual problem specification. To evaluate this setting, we develop a solver-grounded framework that generates structured optimization instances, verifies each instance with an exact solver, and builds both the model-facing inputs and the hidden reference files from the same verified source. We instantiate the framework as MM-OptBench, a benchmark of 780 solver-verified instances spanning 6 optimization families, 26 subcategories, and 3 structural difficulty levels. We then evaluate 9 multimodal large language models (MLLMs), including 6 frontier general-purpose models and 3 math-specialized models, with aggregate, family-level, difficulty-level, and failure-mode analyses. The results show that the task remains far from solved: the best two models reach 52.1\% and 51.3\% pass@1, while on average across the six general-purpose MLLMs, pass@1 is 43.4\% on easy instances and 15.9\% on hard instances. All three math-specialized MLLMs solve 0/780 instances. Failure attribution shows that errors arise both when extracting instance data from text and visuals and when turning extracted data into solver-correct formulations and code. MM-OptBench provides a concrete testbed for solver-grounded, decision-oriented multimodal intelligence.

Close-up rendering, zooming into a scene well beyond any training camera, is important for virtual production and interactive 3D content, yet remains an open challenge. 3D Gaussian splatting (3DGS) enables high-fidelity, real-time novel view synthesis, but its rendering quality degrades at close range. Recent diffusion-based methods that enhance the rendering by conditioning on reference images from the training set produce significant artifacts in this setting. We analyze this failure and identify its root cause: the scale gap between the close-up and reference views. We show that the features in reference-conditioned enhancement models are not scale-invariant, causing cross-view attention to retrieve incorrect correspondences when the same content appears at different scales, and that this mismatch cannot be corrected in latent space because the VAE encoder is not scale-equivariant. Building on this analysis we introduce MACRO, Multi-plane Attention for Closeup Render Optimization, a training-free method for high-quality close-up novel view synthesis from 3DGS. MACRO resolves the scale gap by leveraging the scene's known 3D structure: it decomposes the close-up into depth planes, crops and resizes references in image space to match the scale of each plane before encoding, and applies a depth-aware attention mask so each token attends only to scale-matched references. The method requires no architectural changes or additional training. We further contribute two new close-up novel view synthesis benchmarks, the first standardized evaluation protocol for this setting, and demonstrate state-of-the-art results on both, outperforming existing 3DGS and diffusion-based methods on both reconstruction and perceptual metrics.

We study bandit convex optimization (BCO) when feedback is adversarially delayed and the comparator sequence is also adversarially non-stationary. This setting arises in online advertising, recommender systems, and adaptive dosing, but existing algorithms either absorb one of the two axes into a black-box global penalty or pay a worst-case cost that ignores the local interaction between delay and drift. We propose Oracle-DARS-DBCO, a delay-aware blocking algorithm whose block length $K$ and one-point smoothing radius $\delta$ satisfy the single identity $K\delta^{2}\asymp n^{2}$. This identity cancels the multiplicative coupling between delay deviation and one-point estimator variance, so the regret of each segment is paid only on that segment. We prove matching upper and lower bounds on the expected dynamic regret: $\widetilde{O}\bigl(\sqrt{n}\,m^{1/4}T^{3/4}+\sqrt{d_{\max}\,mT}\bigr)$ for convex losses and $\widetilde{O}\bigl(n^{2/3}m^{1/3}T^{2/3}+d_{\max}\,m\log(eT/m)\bigr)$ for $\alpha$-strongly convex losses, where $m=S_{T}+1$ is the number of stationary segments and $d_{\max}$ is the worst-case delay. The matching Rademacher-sign lower bounds $\Omega\bigl(\sqrt{d(S_{T}+1)\,T}\bigr)$ and $\Omega\bigl(d(S_{T}+1)\bigr)$ show that the delay price is segment-local. On fourteen scaling experiments, the fitted log--log exponents agree with the predicted ones within $0.04$, and Oracle-DARS-DBCO reduces regret by up to $9.17\times$ relative to the strongest non-restarting baseline on a piecewise-stationary benchmark.

Decision trees are prized for their interpretability and strong performance on tabular data, but popular greedy top-down induction algorithms can yield suboptimal and unnecessarily complex structures. Optimal decision tree methods address this through global optimization, yet remain restricted to axis-aligned threshold splits, which limit the expressivity of each node and often force deep, complex trees to capture non-linear feature effects. Shape Generalized Trees (SGTs) generalize threshold splits to learnable univariate shape functions, improving expressivity and enabling more compact trees. However, existing SGT induction algorithms are greedy and offer no optimality guarantees. In this work, we introduce Literati, the first algorithm for optimal SGT induction. We propose a novel AND/OR graph formulation of the problem that jointly optimizes tree structure and shape function complexity. To solve this AND/OR graph, we develop an AO*-based algorithm with two enhancements that improve anytime performance while preserving optimality: a secondary heuristic for OR-node selection and a round-robin policy for AND-node exploration. Across 24 real-world datasets, Literati achieves higher training and test accuracy than state-of-the-art tree approaches.

Diffusion and flow policies have become promising tools for robotic and sequential decision-making systems. Many stable and effective policy optimization methods require evaluating the likelihood or likelihood ratio of an action under the current policy. However, these quantities are generally intractable for diffusion and flow models, which prevents widely used policy update algorithms from being applied to generative policies. We propose Likelihood-Free Generative Policy Optimization (LFGPO), a framework that avoids exact likelihood evaluation by separating policy improvement from generative model training. In the first stage, LFGPO uses a lightweight neural network to represent the likelihood ratio that carries the policy improvement signal. In the second stage, it distills the ratio into diffusion or flow policies through a weighted score- or velocity-matching objective. Our framework incorporates a large family of Reinforcement Learning (RL) algorithms, including PPO and GRPO, to be applied to diffusion and flow policy optimization. We show that the solution to the weighted score matching objective solves a stochastic optimal control problem. Across MuJoCo continuous-control benchmarks, LFGPO delivers strong and stable improvements over competitive diffusion- and flow-policy baselines, showing a practical route to RL fine-tuning for generative policies.

Scaling neural solvers to large Vehicle Routing Problems (VRPs) runs into two recurring difficulties. To stay within compute budgets, scalable solvers tend to rely on partitioning, local candidate restriction, or staged decisions, which limit the global structure that ultimately drives solution quality. To improve the final solution, many neural pipelines fall back on a classical search, but use it as a one-shot post-processor. The model predicts, search repairs, and no sustained feedback is formed between them. We propose $\textit{LSSL}$ (Learning to Search, Searching to Learn), a closed-loop learning-search framework for large-scale VRP that addresses both difficulties in one framework. LSSL predicts a search-friendly guidance heatmap on a sparse candidate graph. A classical heuristic backend then uses this heatmap to refine the incumbent solution, and the structural state returned by the backend is fed back to recondition the model. As a result, learning and search interact within a closed loop, rather than operating as two detached stages. Built on a sparse diffusion transformer over an O($\textit{NK}$) candidate graph, the loop scales to ultra-large instances on a single consumer-grade GPU without hard decomposition. Experiments on large-scale TSP and CVRP benchmarks demonstrate that LSSL achieves superior scalability, efficiency, and solution quality. Ablation studies further reveal that the closed learning–search loop accounts for a substantial portion of the observed performance gains.

Reasoning traces improve vision-language models on complex multimodal tasks, but forcing every input to follow a long reasoning process leads to overthinking and unnecessary inference cost. We study adaptive fast/slow thinking for VLMs, where a single model should answer directly for simple inputs and reason step by step only when needed. The key observation is that offline adaptive thinking is not merely a length-control problem: fast direct answers and slow reasoning traces are typically generated by distinct behavior policies. This dual-reference structure makes standard offline reward optimization, such as Decoupled Generation and Optimization (DGO), mismatched because it assumes a single reference policy and can misweight one mode. We propose \textsc{Dual-Reference DGO}, which models fast and slow responses under a fast/slow mixture reference and derives a reward-weighted offline objective for adaptive VLM reasoning. Our formulation shows that router-free fast/slow switching emerges from competition between fast and slow partition functions, and yields an efficient mode-wise correction for behavior-reference mismatch. Experiments on multiple datasets show that \textsc{Dual-Reference DGO} improves the accuracy--length trade-off over baselines. Ablations show that single-reference DGO tends to collapse to almost always-fast or always-slow behavior, while our dual-reference formulation preserves both modes and learns difficulty-dependent routing.

Stochastic Gradient Descent (SGD) is a workhorse algorithm for continuous optimization. It is a folklore belief among deep learning practitioners that learning rate decay in SGD substantially improves performance. However, it has remained unclear whether learning rate decay offers an asymptotic advantage for \emph{global} nonconvex optimization. We answer this question in the affirmative by demonstrating a natural class of nonconvex functions for which we prove that SGD with learning rate decay requires \emph{exponentially fewer} gradient queries for global optimization than SGD with any fixed learning rate. To the best of our knowledge, this is the first exponential advantage that has been demonstrated for learning rate decay. The class of functions we consider includes many popular benchmark nonconvex functions. Our results provide a robust explanatory theory for the empirically observed benefits of learning rate decay. Our technical results are built upon a new discretization analysis of SGD with decaying step size, that allows us to establish a clean correspondence with continuous-time annealing of Langevin diffusions. We then show that this annealed diffusion performs the non-logconcave sampling task associated to the optimization problem in polynomial time, via a novel application of weak Poincar\'{e} inequalities.

Robust optimization is a widely used framework for decision-making under uncertainty, particularly in high-stakes applications where reliability is critical. A key challenge in this paradigm lies in constructing uncertainty sets that balance robustness and performance: overly conservative sets lead to pessimistic decisions, while insufficient coverage risks failure in practice. Recent approaches based on conformal prediction provide finite-sample, distribution-free guarantees for uncertainty sets, but remain largely task-agnostic and disconnected from downstream decision objectives. In this paper, we propose a decision-aware conformal prediction framework that directly learns the geometry of uncertainty sets to improve robust decision-making. Our approach introduces a polyhedral nonconformity score that induces feature-dependent uncertainty sets, and a three-step procedure that integrates conformal calibration, robust-decision-aware learning, and re-calibration to correct for post-selection bias. We establish finite-sample coverage guarantees for the final, data-dependent uncertainty set, while achieving improved decision performance by reducing unnecessary conservativeness. This work bridges the gap between statistical validity and decision optimality, providing a principled framework for data-driven robust optimization.

GraphRAG enhances Large Language Model reasoning by organizing retrieved knowledge into structured evidence graphs, enabling inference over connected evidence rather than isolated text fragments. Yet, existing GraphRAG methods often either miss query-critical links or introduce noisy or conflicting evidence that distracts reasoning. We propose CONSIST, a Conflict-aware Nash-optimized Minimal Sufficient graph learning algorithm that regulates evidence graphs to resolve conflicts during reasoning. Specifically, we cast graph learning as an exploration–editing process, where a candidate graph is expanded via structural and semantic connections and then refined by pruning unreliable edges. We further introduce Gumbel-based edge editing, framing it as a Nash-guided bargaining process, where current and future players negotiate over a customized utility to determine reliable edits that improve both immediate answer support and long-term graph quality. Experiments on multi-hop question answering and conflict-aware benchmarks demonstrate that CONSIST consistently outperforms recent state-of-the-art baselines, achieving average performance gains up to 7.0% EM and 6.3% F1. Moreover, CONSIST also produces substantially more compact evidence graphs, reducing retained nodes by 42.9% and edges by 54.7% on average.

Forward-Forward (FF) training allows each layer to learn from a local goodness criterion. In cumulative-goodness variants, however, later layers can inherit a task that earlier layers have already partially separated. We formalize this phenomenon as layer free-riding: under the softplus FF criterion, the class-discrimination gradient reaching block $d$ decays exponentially with the positive margin accumulated by preceding blocks. We then study three local remedies---per-block, hardness-gated, and depth-scaled---that recover current-layer separation measures without relying on backpropagated gradients. On CIFAR-10 and CIFAR-100, these remedies dramatically improve layer-separation statistics, with $4\times$--$45\times$ gains in deeper layers, while changing accuracy by less than one percentage point for non-degenerate training procedures. Tiny ImageNet provides a tougher cross-dataset check for our selected block-wise configuration and reveals the same qualitative gap between layer-health diagnostics and final accuracy. Calibration experiments further show that architecture and augmentation choices have a larger effect on final accuracy than the training-rule modifications studied here. Cumulative free-riding is therefore a real and repairable optimization pathology. Nonetheless, for the FF training rules, architectures, and datasets we study, it is not the dominant factor limiting achievable accuracy.

In this paper, we study last-iterate convergence in stochastic constrained convex--concave minimax optimization. A key difficulty is that the last iterates of vanilla stochastic extragradient (S-EG) and stochastic optimistic gradient descent--ascent (S-OGDA) can fail to converge in the presence of gradient noise, even for simple bilinear problems. To address this issue, we regularize the original convex--concave problem into a strongly convex--strongly concave one. Applying S-EG and S-OGDA to the regularized problem gives two simple single-loop first-order methods, which we call perturbed S-EG and perturbed S-OGDA. By carefully choosing the regularization parameter and balancing the resulting regularization bias, stochastic error, and optimization error, we prove that both methods achieve a last-iterate convergence rate of $\mathcal{O}(T^{-1/4+\varepsilon})$ for any $\varepsilon>0$ in terms of the primal--dual gap. This improves upon the best-known $\tilde{\mathcal{O}}(T^{-1/7})$ rate under comparable constrained settings. Moreover, for unconstrained problems, we establish almost sure convergence under a single-timescale stepsize scheme, whereas prior almost sure convergence results typically rely on two-timescale stepsizes and are limited to S-EG.

Optimizing neural networks for quantized objectives is fundamentally challenging because the quantizer is piece-wise constant, yielding zero gradients everywhere except at quantization thresholds where the derivative is undefined. Most existing methods deal with this issue by relaxing gradient computations with techniques like Straight Through Estimators (STE) and do not provide any guarantees of convergence. In this work, taking inspiration from Nesterov smoothing, we approximate the quantized loss surface with a continuous loss surface. In particular, we introduce LOTION, **L**ow-precision **O**ptimization via s**T**ochastic-no**I**se sm**O**othi**N**g, a principled smoothing framework that replaces the raw quantized loss with its expectation under unbiased randomized-rounding noise. In this framework, standard optimizers are guaranteed to converge to a local minimum of the loss surface. Moreover, when using noise derived from stochastic rounding, we show that the global minima of the original quantized loss are preserved. We empirically demonstrate that this method outperforms standard QAT on synthetic testbeds and on 150M-, 300M-, and 600M- parameter language models. On the 150M INT4 benchmark with modern QAT baselines, LOTION further achieves the best quantized validation loss.