NeurIPS 2026 Papers

Predictive models on structured tabular data often face imbalanced targets: training emphasizes common values while rare outcomes stay underrepresented. Distributionally robust optimization hedges against shift, but standard ambiguity sets use a single radius over the entire distribution, so adversarial mass concentrates on dense regions and rare target ranges remain weakly protected; worst-case statements then track bulk behavior rather than tails. We introduce target-conditional distributionally robust optimization (TC-DRO), which defines ambiguity per target region with radii that grow where data are scarce. We establish coverage, per-region excess risk that tightens with local sample size when standard DRO yields vacuous tail guarantees, and a dual as weighted empirical risk with theory-derived density-adaptive weights. Experiments on seven tabular benchmarks show that Wasserstein DRO collapses to empirical risk minimization under uniform weights, while global $\chi^2$-DRO can remain close to ERM in practice; TC-DRO improves tail MSE and SERA relative to both standard training and recent imbalanced-regression methods.

While optimal transport (OT) enforces a rigid constraint by requiring two measures to be matched exactly, partial optimal transport relaxes this requirement by allowing mass to remain unmatched through a global budget, scalar rebate, or uniform rejection rule. However, many applications call for more structured, pointwise rejection mechanisms, where the decision to leave mass unmatched depends on side-specific reliability, support geometry, or external information about which components should participate in the comparison. We introduce \emph{intent-controlled partial optimal transport} (IC-POT), a targeted generalization of partial transport that replaces the global rejection paradigm with pointwise rejection costs over both measures. We show that the resulting optimization problem admits a dual interpretation in terms of local acceptance thresholds and can be solved by recasting it as a balanced Kantorovich OT problem on an augmented support. Beyond theoretical analysis, we demonstrate the practical relevance of IC-POT in settings where rejection is driven by side information. In positive-unlabeled learning and open-partial domain adaptation, incorporating pointwise rejection rules that encode statistical structure improves fixed baseline pipelines. Finally, we motivate the use of IC-POT with a geophysical practical case: multi-modal satellite ocean measurements, for which physical and instrumental priors naturally inform the rejection mechanism and define the retrieved comparable signal information.

We study mixed-variable optimization in scientific discovery, where the key challenge is to efficiently explore the search space under expensive experimental evaluations. Traditional Bayesian optimization (BO) methods typically rely on structural descriptors (e.g., molecular fingerprints) to measure similarity among categorical variables. However, such task-agnostic similarity often fails to reflect task-specific objectives, leading to biased generalization. To address this limitation, we propose \textbf{TagBO} (\textbf{T}ask-\textbf{a}ware \textbf{G}raph \textbf{B}ayesian \textbf{O}ptimization), a method that integrates LLM-derived relational priors with descriptor-based structural information for mixed-variable Bayesian optimization. Rather than directly using LLM outputs as predictive scores, TagBO treats LLM outputs as a potentially noisy source of task-aware relational priors and extracts coarse ordinal relational signals from LLM reasoning to construct task-aware similarity structures for scientific optimization. TagBO then performs constrained Gaussian process Bayesian optimization over the resulting joint discrete-continuous representation space. Experiments on diverse chemistry and materials formulation tasks demonstrate that TagBO consistently improves sample efficiency under fixed evaluation budgets across LLMs of varying capabilities.

*Discrete text-trigger optimization*—searching for text sequences that, when ingested by a model, steer it toward a specified objective—underpins model red-teaming (e.g., LLM jailbreaks), as well as auditing and interpretability. However, the current state of discrete optimizers hinders their adoption and progress. First, existing optimizers, when open-sourced at all, are scattered across research codebases tied to specific problem domains. Second, optimizer variants proliferate, each requiring engineering overhead to use or extend, and hard to compare head-to-head. Together, these raise the bar to *adopting* optimizers in existing or new domains, and to *advancing* them via new strategies. We address these gaps with TROPT, the first open-source framework that unifies discrete optimizers' execution and standardizes their development under a single interface. TROPT currently ships with 30+ end-to-end optimization recipes—covering applications such as jailbreaking and probing model internals—built from 15+ optimizers (spanning white-box to black-box access) and 15+ losses, from foundational to state-of-the-art methods. Beyond democratizing established methods, TROPT makes it easy to *customize* optimization recipes by swapping any component—models, objectives, and optimizers—extending its reach across domains and new applications. Demonstrating its utility, we leverage TROPT in several controlled studies: *(i)* novel large-scale experiments comparing and enhancing optimization strategies for LLM jailbreaks, revealing potent-yet-underadopted techniques; and *(ii)* cross-domain demonstrations (e.g., benign prompt recovery and corpus poisoning). In all, TROPT significantly lowers the barrier to adopting and advancing discrete text optimization.

Direct Preference Optimization (DPO) minimizes empirical risk over observed preference comparisons, implicitly assuming that the training preference distribution matches the deployment preference distribution. In practice, this i.i.d. assumption often fails, as preference distribution shift exhibits a natural hierarchical structure across three levels: group-level shift, prompt-level shift, and conditional preference-level shift. Such multi-level distributional mismatch poses a critical challenge for safe LLM deployment, yet existing robust DPO methods typically model either overall distributional uncertainty or a single robustness level, leaving the hierarchical structure of OOD preference shifts underexplored. We propose TPO, a tri-level distributionally robust framework for OOD preference optimization, which jointly models all three levels of distributional uncertainty through a hierarchical rectangular ambiguity set. By instantiating it with Wasserstein distance, we derive a tractable and interpretable objective that combines a closed-form preference-level margin penalty, prompt-level adversarial embedding perturbation, and worst-case group reweighting, each governed by an independent radius. We establish finite-sample convergence guarantees and empirically validate the effectiveness of \method{} over existing robust DPO methods.

Learning control policies for complex, long-horizon tasks is a central challenge in autonomous systems. Signal Temporal Logic (STL) offers an expressive language for specifying such tasks, but its non-Markovian nature and inherent sparse reward make it hard for standard Reinforcement Learning (RL) to solve. Prior RL approaches focus only on limited STL fragments or use robustness scores as sparse rewards. Our new method TGPO (Temporal Grounded Policy Optimization) decomposes STL into timed subgoals and invariant constraints and tackles the problem in a hierarchical fashion. Its high-level module proposes time allocations for subgoals, and the low-level time-conditioned policy learns to achieve the sequenced subgoals using a dense, stage-wise reward. In inference, we use the critic to efficiently sample time allocations and select the most promising assignment for the policy to rollout. We evaluate in five environments, from low-dimensional navigation to manipulation, drone, and quadrupedal locomotion, and TGPO significantly outperforms baselines (especially for high-dimensional and long-horizon cases), with 31.6% higher success rate compared to the best method.

Backtesting large language models on historical events requires reasoning exclusively from information available before a specified cutoff date. Yet models routinely leak post-cutoff knowledge from pre-training into their reasoning, inflating apparent accuracy and undermining evaluation validity. Prompt-based constraints fail when suppressed content is causally related to the prediction, and knowledge unlearning cannot address this problem because temporal compliance is instance-specific: the same fact may be legitimate evidence for one cutoff date and a violation for another. Rather than erasing knowledge, the model must learn **temporal discipline**: selecting evidence conditioned on each instance's cutoff date. We propose **TEMPO** (**T**emporal **E**nforcement via **M**ode-separated **P**olicy **O**ptimization), which trains this discipline via two contributions: (1) a two-mode reward where a leakage mode drives post-cutoff claims to zero as a hard prerequisite before a performance mode optimizes task performance; and (2) a GRPO-based training pipeline that enables the model to discover temporally valid reasoning strategies. We prove that training monotonically decreases leakage, converges to the leak-free optimum, and improves task performance once compliance is achieved. On three prediction tasks and two models, TEMPO reduces leakage from 2$\sim$13\% to 0.6$\sim$3.7\% across all conditions, with task performance improving 6$\sim$13\% where strong pre-cutoff signals exist and maintained where the prediction task is inherently difficult from valid information alone.

Large language models (LLMs) deployed as agents remain vulnerable to prompt-based instruction injection, where user inputs induce the model to violate higher-priority system directives. Existing methods often treat violations as a coherent class or rely on surface text patterns, which can limit robustness as attack strategies evolve. In this paper, we investigate LLM hidden-state dynamics under attack and uncover a phenomenon we term Asymmetric Logic: the model's response generations concentrate in a relatively low-variability region of latent representation space when it's compliant to the system prompt, while compromised behaviors exhibit diverse deviations. Based on this observation, we propose Asymmetric Entropic Optimization (AEO), a novel framework that monitors the internal shifts in latent representations to detect and proactively rectify anomalous behaviors. Our method effectively identifies logic deviations by quantifying the entropic divergence between the compliant manifold and the chaotic violation space. Across a range of state-of-the-art LLM backbones, AEO demonstrates strong robustness to diverse instruction injection attacks. For instance, on Qwen2.5-14B-Instruct, AEO attains a detection AUC of 97.28% with FPR95 of only 10.38%. The same chaos score also gates a lightweight post-hoc correction module that lifts overall instruction-following accuracy from 63.94% to 76.00% on IHEval, without any model fine-tuning. The code is available at https://anonymous.4open.science/r/AEO-code-56D2/.

We study stochastic zeroth-order (ZO) optimization of smooth nonconvex objectives under heavy-tailed sample-gradient noise, a regime motivated by empirical evidence that gradient noise in modern machine learning can violate the bounded-variance assumption underlying classical ZO theory. While the first-order literature has established optimal rates under bounded $p$-th moment noise for $p \in (1,2]$, analogous high-probability guarantees for nonconvex ZO optimization remain largely unexplored. The ZO setting is not a direct corollary of first-order theory: first-order methods update using $\nabla F(x;\xi)$, the same object on which the noise assumption is imposed, whereas derivative-free methods only observe noisy function values and construct directional finite-difference estimates. Thus, weak-$L_p$ control of $\nabla F(x;\xi)-\nabla f(x)$ must first be transferred to scalar two-point directional estimates, a concentration step absent from standard first-order analyses. We propose the Robust Scalar-Clipped Zeroth-Order method (\textbf{RSC-ZO}), a two-point method that clips each scalar directional derivative before aggregation. Under sample-wise smoothness and a weak-$L_p$ tail bound on the sample-gradient noise, RSC-ZO finds an $\varepsilon$-stationary point with high probability using $ \widetilde{O}\\left( \frac{d^{\frac{p}{2(p-1)}}} {\varepsilon^{\frac{3p-2}{p-1}}} \right) $ noisy function evaluations, matching the optimal first-order $\varepsilon$-dependence. At $p=2$, our bound becomes $\widetilde{O}(d\varepsilon^{-4})$, matching the classical dimension-accuracy dependence for stochastic ZO methods under bounded-variance noise, which is typically established only in expectation. In contrast, our guarantee holds with high probability and under the strictly weaker weak-$L_2$ tail condition, which can allow infinite gradient-noise variance. We further extend the analysis to a momentum variant and quantify the resulting batch-size/stepsize tradeoff.

We study stochastic random search for nonconvex optimization with only noisy function evaluations. We propose Mi2P, a two-point variant of stochastic three-point methods, and analyze it under generalized $(L_0,L_1)$-smoothness. Two regimes are considered. When the mean objective $f$ is $(L_0,L_1)$-smooth and component variance is bounded, Mi2P achieves $\widetilde{O}(d^3\sigma_0^2/\varepsilon^{6})$, matching the rate of \citet{boucherouite2024mistp} under a strictly weaker assumption (they require $f$ to be $L$-smooth, i.e., $L_1=0$). When an $L^1$-average $(L_0,L_1)$-smoothness holds across $\xi$, Mi2P attains the optimal $\widetilde{O}(d\sigma^2/\varepsilon^{4})$ rate; the per-sample $L$-smoothness used by gradient-estimation methods such as RSGF \citep{ghadimi2013stochastic} (i.e., each $f_\xi$ is $L$-smooth, $L_1 = 0$ pointwise in $\xi$) is a special case of this condition. For finite sums with $G$-Lipschitz components, a translation-symmetric variance-reduction scheme yields $\widetilde{O}(\min\{d^{4/3}n^{2/3}/\varepsilon^{8/3},\, dn/\varepsilon^2\})$ without storing snapshots. We also extend the framework to $\delta$-inexact comparison feedback (e.g., RLHF, A/B testing), giving an $O(\sqrt{d\delta})$ accuracy floor. Our analysis is presented for directional distributions with bounded support; the same rates hold for any rotation-invariant distribution with sub-Gaussian tails on the norm of $s$ (including Gaussian) under a step-size restriction that does not affect the asymptotic complexity.

We study stochastic simple bilevel optimization with smooth, possibly nonconvex upper- and lower-level objectives accessed only through stochastic gradient oracles. A key challenge is that the dual multiplier induced by the lower-level constraint may become unbounded near lower-level stationary points, invalidating bounded-dual analyses and destabilizing stochastic gradient estimates. To address this, we propose \emph{Stochastic Dynamic Barrier Perturbed Gradient} (SDBPG), a single-loop method that adaptively perturbs the dual formulation to regularize this degeneracy. The perturbation stabilizes the multiplier and yields controlled bias and variance even near the lower-level stationarity region. Under a mild rare-visit assumption, SDBPG finds an $(\epsilon_f,\epsilon_g)$-stationary point in $\mathcal{O}(\max\{\epsilon_f^{-2},\epsilon_g^{-2}\})$ iterations, with sample gradient complexities $\mathcal{O}(\epsilon^{-4})$ and $\mathcal{O}(\epsilon^{-6})$ for the upper- and lower-level objectives where $\epsilon=\max(\epsilon_f,\epsilon_g)$. We further develop PR-SDBPG, a penalty-regularized variant that eliminates the rare-visit assumption, and VR-PR-SDBPG, which improves the resulting sample complexities entirely through variance reduction. To our knowledge, these are the first explicit $(\epsilon_f,\epsilon_g)$-stationarity guarantees for stochastic nonconvex-nonconvex simple bilevel optimization.

This paper initiates the study of a stochastic approximation approach with the Fully Stochastic Primal Dual Algorithm (FSPDA) framework for decentralized optimization on random and time varying topologies. Our framework relies on a novel observation that randomnesses in time varying topology can be incorporated into a stochastic equality constrained optimization formulation. We derived two new algorithms supporting sparsified communication on time varying topologies --- FSPDA-SA allows agents to execute multiple local gradient steps to accelerate convergence, and FSPDA-STORM further incorporates variance reduction to improve sample complexity. For problems with smooth (possibly non-convex) objective function, within $T$ iterations, FSPDA-SA (resp. FSPDA-STORM) finds an $\mathcal{O}( 1/\sqrt{T} )$-stationary (resp. $\mathcal{O}( 1/T^{2/3} )$) solution. The latter shows the first near-optimal convergence rate over time varying topology.

Generative recommendation (GR), which directly generates sequential semantic IDs for items, has recently attracted increasing attention in recommender systems. Given that core recommendation metrics are inherently evaluated at the sequence level, reinforcement learning (RL) serves as a natural optimization framework. However, adapting recent group-based RL algorithms to GR presents notable challenges: token-level methods such as GRPO exhibit much more severe training instability, while sequence-level methods such as GSPO enforce uniform token weighting and thus ignore the heterogeneous roles of tokens. To address this dilemma, we propose Stable and Granular Policy Optimization (SGPO), a group-based RL algorithm tailored for GR. SGPO maintains a sequence-level ratio to promote optimization stability while injecting fine-grained token-wise advantages. By incorporating token log-probabilities and reward signs, SGPO explicitly upweights high-confidence tokens in positive trajectories to reinforce successful retrieval, while strictly penalizing them in negative trajectories to encourage exploration, and uses an adaptive scaling factor to bound the variance of reshaped advantages. Experiments on two public benchmarks and a billion-scale industrial dataset show that SGPO consistently outperforms six strong RL baselines and, when deployed on a commercial platform, achieves a 2.36% lift in click-through rate (CTR) and a 1.95% increase in advertising revenue in online A/B testing.

While reinforcement learning (RL) has been central to the recent success of large language models (LLMs), RL optimization is notoriously unstable, especially when compared to supervised fine-tuning (SFT). In this work, we investigate the stability gap between SFT and RL from a gradient-based perspective, and show that the convexity of the SFT loss with respect to model logits plays a key role in enabling stable training. Our theoretical analysis demonstrates that this property induces favorable gradient directionality during optimization. In contrast, Proximal Policy Optimization (PPO), a widely adopted policy gradient algorithm utilizing a clipped surrogate objective, lacks this stabilizing property. Motivated by this observation, we propose Logits Convex Optimization (LCO), a simple yet effective policy optimization framework that aligns the learned policy with an optimal target derived from the original RL objective, thereby emulating the stabilizing effects of logits-level convexity. Extensive experiments across multiple model families show that our LCO framework consistently improves training stability and outperforms conventional RL methods on a broad range of benchmarks.

Large-scale Ising optimization underlies critical optimization and learning applications, including correlation clustering, MAP inference, and energy-based models. Spectral relaxation methods run in polynomial time but yield solutions with significant optimality gaps while metaheuristics close those gaps but scale poorly to large instances. In particular, spectral methods are inherently single-shot as they solve exactly one eigenvalue problem. We introduce $\textit{Spectral Annealing}$ (SpecAnn), a new spectral optimization approach that transforms traditional spectral methods from single-shot approximations into exploration-based optimization, by sweeping a parametrized normalization path from the raw adjacency to the signed normalized Laplacian, with an $O(n)$ diagonal predictor that warm-starts successive eigensolves and GPU-batched local search refining candidates in parallel. Experiments on general Ising problems demonstrate that SpecAnn achieves competitive to near-optimal solutions depending on instance structure, with runtimes less than 7 minutes for instances of 8.4M variables. SpecAnn delivers up to 83$\times$ speedup over recent GPU-accelerated methods while maintaining superior solution quality, and scales successfully beyond 524K variables where traditional metaheuristics fail.

Speculative decoding accelerates LLM inference by drafting a tree of candidate continuations and verifying it in one target forward. Existing drafters fall into two camps with opposite weaknesses. Autoregressive drafters such as EAGLE-3 preserve dependence along each draft path but call the drafter once per tree depth, making drafting a non-trivial share of per-iteration latency. Parallel drafters cut drafter calls by predicting multiple future positions in one forward, but each position is predicted without seeing the others, producing paths the verifier rejects. In this paper, we propose SpecBlock, a block-iterative drafter that combines path dependence with cheap drafting. Each drafter forward produces $K$ dependent positions and we call this a block. The draft tree grows through repeated block expansions. Two mechanisms explicitly carry path dependence to keep later draft positions accurate. Within each block, a layer-wise shift carries the previous position's hidden state into every decoder layer. Across blocks, each new block can start from any position of the previous block, inheriting its hidden state to extend the path. To spend verifier budget where acceptance is likely, a co-trained rank head replaces the fixed top-$k$ tree by allocating per-position branching during drafting. To avoid training the drafter on prefixes it never produces at inference, a valid-prefix mask drops the loss at later positions once an earlier one is wrong. Beyond static drafting, a cost-aware bandit at deployment uses free verifier feedback to update the drafter selectively, only when the expected throughput gain exceeds the update cost. Experiments show that SpecBlock improves mean speedup by $8$--$13\%$ over EAGLE-3 at $44$--$52\%$ of its drafting cost, and cost-aware adaptation extends this lead to $11$--$19\%$.

Multiplicative motor and observation noise, along with internal noise corrupting computation, are central features of the sensorimotor system in biological and robotic agents. Yet, analytical solutions for stochastic optimal control are largely restricted to additive noise models and neglect internal noise. Here, we consider the problem of finding optimal control and filter laws for partially observable stochastic linear systems under quadratic costs with multiplicative control and observation noise, as well as internal noise. We provide an efficient, analytically derived coordinate-descent algorithm that computes mutually optimal linear control and filter laws by reformulating the problem as a constrained optimization. Our method provably guarantees monotonic decrease of the expected cost and convergence to a critical point, and overcomes the suboptimality and incompleteness of prior analytical approaches. Compared to state-of-the-art numerical methods, it achieves orders-of-magnitude computational speedups. Our solution also proves instrumental in revealing novel internal-noise-dependent, task-structured control strategies in a redundant arm control task.

Quantum state tomography of pure non-Gaussian states is fundamentally limited by scarce and noisy data due to measurement-induced collapse and experimental drift. We introduce a novel reconstruction framework that parameterizes the wavefunction directly via an overparameterized neural network, trained using rank-1 factored gradient descent. We rigorously prove that this formulation's loss landscape is devoid of spurious local minima and strict saddles, guaranteeing all critical points are global minima. By utilizing the max-sliced Wasserstein-1 distance, our loss perfectly maps to the structure of homodyne measurements, structurally preventing gradient vanishing in low-shot regimes. On noisy two-mode cat states, our method achieves continuous fidelity improvements, successfully bypassing the noise-floor plateaus that limit standard iterative maximum-likelihood estimation.

Second-order methods are provably faster than first-order methods, and their efficient implementations for large-scale optimization problems have attracted significant attention. Yet, optimization problems in ML often have nonsmooth derivatives, which makes the existing convergence rate theory of second-order methods inapplicable. In this paper, we propose a new semismooth Newton method (SSN) that enjoys both global convergence rates and asymptotic superlinear convergence without requiring second-order differentiability. Crucially, our method does not require (generalized) Hessians to be evaluated at each iteration but only periodically, and it reuses stale Hessians otherwise (i.e., it performs lazy Hessian updates), saving compute cost and often leading to significant speedups in time, whilst still maintaining strong global and local convergence rate guarantees. We develop our theory in an infinite-dimensional setting and illustrate it with numerical experiments on matrix factorization and neural networks with Lipschitz constraints.