ICLR 2026 论文列表

Graph-structured data are central to many scientific and industrial applications where the goal is to optimize expensive black-box objectives defined over graph structures or node configurations---as seen in molecular design, supply chains, and sensor placement. Bayesian optimization offers a principled approach for such settings, but existing methods largely focus on functions defined over nodes of a fixed graph. Moreover, graph optimization is often approached heuristically, and it remains unclear how to systematically incorporate structural constraints into BO. To address these gaps, we build on shortest-path graph kernels to develop a principled framework for acquisition optimization over unseen graph structures and associated node attributes. Through a novel formulation based on mixed-integer programming, we enable global exploration of the combinatorial graph domain and explicit embedding of problem-specific constraints. We demonstrate that our method, BoGrape, is competitive both on general synthetic benchmarks and representative molecular design case studies with application-specific constraints.

Neural Architecture Search (NAS), particularly gradient-based techniques, has proven highly effective in automating the design of neural networks. Recent work has extended NAS to hardware-aware settings, aiming to discover architectures that are both accurate and computationally efficient. Many existing methods integrate hardware metrics into the optimization objective as regularization terms, which introduces differentiability requirements and hyperparameter tuning challenges. This can either result in overly penalizing resource-intensive architectures or architectures failing to meet the hardware constraints of the target device. To address these challenges, we propose ConNAS, a novel gradient-based NAS framework that enforces hardware constraints directly through gradient modification. This approach eliminates the need for differentiable hardware metrics and regularization weights. The novelty in ConNAS lies in modifying gradients with respect to architectural choices, steering the search away from infeasible architectures while ensuring constraint satisfaction. Evaluations on the NATS-Bench benchmark demonstrate that ConNAS consistently discovers architectures that meet the imposed hardware constraints while achieving performance within just 0.14% of the optimal feasible architecture. Additionally, in a practical deployment scenario, ConNAS outperforms handcrafted architectures by up to 1.55% in accuracy under tight hardware budgets.

Hyperparameter tuning can dramatically impact training stability of large-scale models. Recent works on neural network parameterisations, such as μP, have shown that layer types and sizes should dictate how global hyperparameters should be rescaled in order to achieve efficient transfer across model sizes. On the other hand, the established practice for hyperparameter optimisation search is to look for optimal global base values that apply at some fixed model scale. We transfer hyperparameters across all scaling axes: width and depth, using an extension of CompleteP (Dey et al., 2025), training horizon, and batch size. Our study covers all optimisation hyperparameters of modern models: learning rates, Adam parameters, weight decay, initialisation scales, and residual block multipliers. Lastly, we demonstrate that hyperparameter transfer holds even in the per-layer hyperparameter regime. We characterise the empirical challenges of navigating the high-dimensional hyperparameter landscape, and propose practical guidelines for tackling this optimisation problem. We suggest a simplified parameterisation of the hyperparameter space that reduces the dimensionality of the search-space at no performance cost. Our experiments demonstrate training speed improvements when applying transferred hyperparameters to Large Language Models.

Fine-tuning Large Language Models (LLMs) with reinforcement learning (RL) has become a key technique for enhancing performance on a wide range of tasks, from user alignment to complex reasoning. However, this approach is often hindered by the difficulty of fine-grained credit assignment, as it typically relies on sparse rewards given only at the end of a completely generated sequence. Conventional solutions often require training an auxiliary value network known as critic, which introduces significant computational overhead and training instability. We present Group-Normalized Implicit Value Optimization (GN-IVO), a novel, critic-free algorithm that directly addresses this challenge. GN-IVO learns step-level values implicitly from the policy through a group-normalized distributional matching objective. This approach elegantly circumvents the need for an explicit critic and avoids the computation of the intractable partition function by normalizing values across a group of sampled model responses. Theoretically, we prove that our objective recovers the true value function up to a constant, guaranteeing that the optimal policy is preserved. We demonstrate the practical effectiveness of GN-IVO on a diverse set of text generation and reasoning tasks, showing that it consistently outperforms strong RL baselines for LLMs.

Speculative decoding accelerates large language model (LLM) inference by letting a lightweight draft model propose multiple tokens that the target model verifies in parallel. Yet existing training objectives optimize only a single greedy draft path, while decoding follows a tree policy that re-ranks and verifies multiple branches. This draft policy misalignment limits achievable speedups. We introduce Group Tree Optimization (GTO), which aligns training with the decoding-time tree policy through two components: (i) Draft Tree Reward, a sampling-free objective equal to the expected acceptance length of the draft tree under the target model, directly measuring decoding performance; (ii) Group-based Draft Policy Training, a stable optimization scheme that contrasts trees from the current and a frozen reference draft model, forming debiased group-standardized advantages and applying a PPO-style surrogate along the longest accepted sequence for robust updates. We further prove that increasing our Draft Tree Reward provably improves acceptance length and speedup. Across dialogue (MT-Bench), code (HumanEval), and math (GSM8K), and multiple LLMs (e.g., LLaMA-3.1-8B, LLaMA-3.3-70B, Vicuna-1.3-13B, DeepSeek-R1-Distill-LLaMA-8B), GTO increases acceptance length by 7.4\% and yields an additional 7.7\% speedup over prior state-of-the-art EAGLE-3. By bridging draft policy misalignment, GTO offers a practical, general solution for efficient LLM inference. Code and draft models are available at https://anonymous.4open.science/r/GTO-ICLR-348F/.

Modern optimization faces a fundamental challenge: local gradient-based methods provide no global information about the objective function $L$ landscape, often leading to suboptimal convergence and sensitivity to initialization. We introduce a novel optimization framework that leverages resurgence theory from complex analysis to extract global structural information from divergent asymptotic series. Our key insight is that the factorially divergent perturbative expansions of parameter space partition functions encode precise information about all critical objective function value in the landscape through their Borel transform singularities. The algorithm works by computing the statistical mechanical partition function $Z(g) = \int e^{-L(\theta)/g} d\theta$ for small coupling $g\ll 1$, extracting its asymptotic series coefficients, and identifying Borel plane singularities that correspond one-to-one with critical objective function values. These target values provide global guidance to local optimizers, enabling principled learning rate adaptation and escape from suboptimal regions. Unlike heuristic adaptive methods, targets are theoretically grounded in the geometry of the optimization landscape.

Bilevel optimization is a hierarchical framework where an upper-level optimization problem is constrained by a lower-level problem, commonly used in machine learning applications such as hyperparameter optimization. Existing bilevel optimization methods typically assume strong convexity or Polyak-Łojasiewicz (PL) conditions for the lower-level function to establish non-asymptotic convergence to a solution with a small hypergradient. However, these assumptions may not hold in practice, and recent work (Chen et al. 2024) has shown that bilevel optimization is inherently intractable for general convex lower-level functions with the goal of finding small hypergradients. In this paper, we identify a tractable class of bilevel optimization problems that interpolates between lower-level strong convexity and general convexity via lower-level uniform convexity. For uniformly convex lower-level functions with exponent $p\geq 2$, we establish a novel implicit differentiation theorem characterizing the hyperobjective's smoothness property. Building on this, we design a new stochastic algorithm, termed UniBiO, with provable convergence guarantees, based on an oracle that provides stochastic gradient and Hessian-vector product information for the bilevel problems. Our algorithm achieves $\widetilde{O}(\epsilon^{-5p+6})$ oracle complexity bound for finding $\epsilon$-stationary points. Notably, our complexity bounds match the optimal rates in terms of the $\epsilon$ dependency for strongly convex lower-level functions ($p=2$), up to logarithmic factors. Our theoretical findings are validated through experiments on synthetic tasks and data hyper-cleaning, demonstrating the effectiveness of our proposed algorithm.

Predicting relevance is a pervasive problem across digital platforms, covering social media, entertainment, and commerce. However, when optimized solely for relevance and engagement, many machine-learning models amplify data biases and produce homogeneous outputs, reinforcing filter bubbles and content uniformity. To address this issue, we introduce a pairwise top-k diversity objective with a differentiable smooth-ranking approximation, providing a model-agnostic way to incorporate diversity optimization directly into standard gradient-based learning. Building on this objective, we cast relevance and diversity as a joint optimization problem, we analyze the resulting gradient trade-offs, and propose two complementary strategies: direct optimization, which modifies the learning objective, and indirect optimization, which reweights training data. Both strategies can be applied either when training models from scratch or when fine-tuning existing relevance-optimized models. We use recommendation as a natural evaluation setting where scalability and diversity are critical, and show through extensive experiments that our methods consistently improve diversity with negligible accuracy loss. Notably, fine-tuning with our objective is especially efficient, requiring only a few gradient steps to encode diversity at scale.

Searching large and highly complex design spaces for a global optimum can be infeasible and unnecessary. A practical alternative is to iteratively refine the neighborhood of an initial design using local optimization methods such as gradient descent. We propose local entropy search (LES), a Bayesian optimization paradigm that explicitly targets the solutions reachable by the descent sequences of arbitrary iterative optimizers. The algorithm propagates the posterior belief over the objective through the optimizer, yielding a probability distribution over descent sequences. It then selects the next evaluation by maximizing mutual information with that distribution, using a practical combination of analytic entropy calculations and Monte-Carlo sampling of descent sequences. Empirical results on high-complexity synthetic objectives and benchmark problems show that LES achieves strong sample efficiency compared to existing local and global Bayesian optimization methods.

Aligning Large Language Models (LLMs) with human preferences is crucial for safe and effective AI interactions. While popular methods like Direct Preference Optimization (DPO) have simplified alignment, they remain sensitive to data noise and overlook the differential importance of individual tokens. Existing token-level approaches often rely on probability prediction or simplistic weighting schemes to obtain token importance, which still cannot fully address these issues. To solve this problem, we propose the Token-Importance Guided Direct Preference Optimization (TI-DPO), a framework that achieves fine-grained semantic control through two synergistic innovations. First, we propose a novel hybrid weighting mechanism that combines gradient attribution with a Gaussian prior, ensuring both the accuracy and robustness of token importance scores. Second, we employ a triplet loss to provide structured guidance for the optimization, explicitly guiding model outputs to approach preferred responses and diverge from non-preferred ones. Experimental results show that TI-DPO achieves higher accuracy and stronger generative diversity, providing more stable and computationally efficient solutions compared with DPO and other RLHF methods.

Kolmogorov-Arnold Networks (KANs) have emerged as a promising alternative to traditional neural networks, offering enhanced interpretability based on the Kolmogorov-Arnold representation theorem. While their empirical success is growing, a theoretical understanding of their training dynamics remains nascent. This paper investigates the optimization of a two-layer KAN in the overparameterized regime, focusing on a simplified yet insightful setting where only the first-layer coefficients are trained via gradient descent. Our main result establishes that, provided the network is sufficiently wide, this training method is guaranteed to converge to a global minimum and achieve zero training error. Furthermore, we derive a novel, fine-grained convergence rate that explicitly connects the optimization speed to the structure of the data labels through the eigenspectrum of the KAN Tangent Kernel (KAN-TK). Our analysis reveals a key advantage of this architecture: guaranteed convergence is achieved with a hidden layer width of $m=\mathcal{O}(n^2)$, a significant polynomial improvement over the $m=\mathcal{O}(n^6)$ requirement for classic two-layer neural networks using ReLU activation functions and analyzed within the same Tangent Kernel framework. We validate our theoretical findings with numerical experiments that corroborate our predictions on convergence speed and the impact of label structure.

Direct alignment algorithms such as Direct Preference Optimization (DPO) fine-tune models based on preference data, using only supervised learning instead of two-stage reinforcement learning with human feedback (RLHF). We show that DPO encodes a statistical estimation problem over reward functions induced by a parametric policy class. When the true reward function that generates preferences cannot be realized via the policy class, DPO becomes misspecified, resulting in failure modes such as preference order reversal, worsening of policy reward, and high sensitivity to the input preference data distribution. On the other hand, we study the local behavior of two-stage RLHF for a parametric class and relate it to a natural gradient step in policy space. Our fine-grained geometric characterization allows us to propose AuxDPO, which introduces additional auxiliary variables in the DPO loss function to help move towards the RLHF solution in a principled manner and mitigate the misspecification in DPO. We empirically demonstrate the superior performance of AuxDPO on didactic bandit settings as well as LLM alignment tasks.

Existing work on linear constrained Markov decision processes (CMDPs) has primarily focused on stochastic settings, where the losses and costs are either fixed or drawn from fixed distributions. However, such formulations are inherently vulnerable to adversarially changing environments. To overcome this limitation, we propose a primal-dual policy optimization algorithm for online finite-horizon {adversarial} linear CMDPs, where the losses are adversarially chosen under full-information feedback and the costs are stochastic under bandit feedback. Our algorithm is the \emph{first} to achieve sublinear regret and constraint violation bounds in this setting, both bounded by $\widetilde{\mathcal{O}}(K^{3/4})$, where $K$ denotes the number of episodes. The algorithm introduces and runs with a new class of policies, which we call weighted LogSumExp softmax policies, designed to adapt to adversarially chosen loss functions. Our main result stems from the following key contributions: (i) a new covering number argument for the weighted LogSumExp softmax policies, and (ii) two novel algorithmic components---periodic policy mixing and a regularized dual update---which allow us to effectively control both the covering number and the dual variable. We also report numerical results that validate our theoretical findings on the performance of the algorithm.

We revisit policy-gradient optimization for Large Language Models (LLMs) from a single-stream perspective. Prevailing group-based methods like GRPO reduce variance with on-the-fly baselines but suffer from critical flaws: frequent degenerate groups erase learning signals, and synchronization barriers hinder scalability. We introduce Single-stream Policy Optimization (SPO), which eliminates these issues by design. SPO replaces per-group baselines with a persistent, KL-adaptive value tracker and normalizes advantages globally across the batch, providing a stable, low-variance learning signal for every sample. Being group-free, SPO enables higher throughput and scales effectively in long-horizon or tool-integrated settings where generation times vary. Furthermore, the persistent value tracker naturally enables an adaptive curriculum via prioritized sampling. Experiments using Qwen3-8B show that SPO converges more smoothly and attains higher accuracy than GRPO, while eliminating computation wasted on degenerate groups. Ablation studies confirm that SPO's gains stem from its principled approach to baseline estimation and advantage normalization, offering a more robust and efficient path for LLM reasoning. Across five hard math benchmarks with Qwen3-8B, SPO improves the average maj@32 by $+3.4\ \text{percentage points} (\mathrm{pp})$ over GRPO, driven by substantial absolute point gains on challenging datasets, including $+7.3\ \mathrm{pp}$ on BRUMO 25, $+4.4\ \mathrm{pp}$ on AIME 25, $+3.3\ \mathrm{pp}$ on HMMT 25, and achieves consistent relative gain in pass@$k$ across the evaluated $k$ values. SPO's success challenges the prevailing trend of adding incidental complexity to RL algorithms, highlighting a path where fundamental principles, not architectural workarounds, drive the next wave of progress in LLM reasoning.

Deep reinforcement learning (RL) has achieved remarkable success, yet its deployment in real-world scenarios is often limited by vulnerability to environmental uncertainties. Distributionally robust RL (DR-RL) algorithms have been proposed to resolve this challenge, but existing approaches are largely restricted to value-based methods in tabular settings. In this work, we introduce Distributionally Robust Soft Actor-Critic (DR-SAC), the first actor–critic based DR-RL algorithm for offline learning in continuous action spaces. DR-SAC maximizes the entropy-regularized rewards against the worst possible transition models within an KL-divergence constrained uncertainty set. We derive the distributionally robust version of the soft policy iteration with a convergence guarantee and incorporate a generative modeling approach to estimate the unknown nominal transition models. Experiment results on five continuous RL tasks demonstrate our algorithm achieves up to $9.8\times$ higher average reward than the SAC baseline under common perturbations. Additionally, DR-SAC significantly improves computing efficiency and applicability to large-scale problems compared with existing DR-RL algorithms.

Algorithms with predictions leverage predictions for unknown inputs in online decision-making. These algorithms are analyzed by consistency, i.e., competitive ratio under perfect predictions, and robustness, i.e., competitive ratio under worst-case predictions. Smooth degrading performance with an increased prediction error is also desirable. This paper refines the notion of smoothness, a function of prediction error, defined as the competitive ratio over the problem instances where predictions are guaranteed to provide additional information. With our refined smoothness metric, we establish smoothness bounds for a few scheduling problems, including online total completion time minimization and makespan minimization. For a single machine to minimize the total completion time, we show a lower bound of $\eta$ and a $\eta^2$-smooth algorithm, where $\eta$ is the prediction error ($\eta \geq 1$); the bound holds for small errors. For parallel identical machines to minimize the makespan, we show a lower bound of $2 - O(\eta^{-2})$ and present an $O(\eta^2)$-smooth algorithm for small errors. Both bounds are tighter than the existing ones. For uniformly-related machines to minimize the makespan, we show a tight lower bound of $\lceil \log \eta \rceil$, matched by an $O(\log \eta)$-smooth algorithm.

Large language models deployed in sensitive applications increasingly require the ability to unlearn specific knowledge, such as user requests, copyrighted materi- als, or outdated information, without retraining from scratch to ensure regulatory compliance, user privacy, and safety. This task, known as machine unlearning, aims to remove the influence of targeted data (forgetting) while maintaining per- formance on the remaining data (retention). A common approach is to formu- late this as a multi-objective problem and reduce it to a single-objective prob- lem via scalarization, where forgetting and retention losses are combined using a weighted sum. However, this often results in unstable training dynamics and degraded model utility due to conflicting gradient directions. To address these challenges, we propose OFMU, a penalty-based bi-level optimization framework that explicitly prioritizes forgetting while preserving retention through a hierar- chical structure. Our method enforces forgetting via an inner maximization step that incorporates a similarity-aware penalty to decorrelate the gradients of the for- get and retention objectives, and restores utility through an outer minimization step. To ensure scalability, we develop a two-loop algorithm with provable conver- gence guarantees under both convex and non-convex regimes. We further provide a rigorous theoretical analysis of convergence rates and show that our approach achieves better trade-offs between forgetting efficacy and model utility compared to prior methods. Extensive experiments across vision and language benchmarks demonstrate that OFMU consistently outperforms existing unlearning methods in both forgetting efficacy and retained utility.

A recent breakthrough in nonconvex optimization is the online-to-nonconvex conversion framework of Cutkosky et al. (2023), which reformulates the task of finding an $\varepsilon$-first-order stationary point as an online learning problem. When both the gradient and the Hessian are Lipschitz continuous, instantiating this framework with two different online learners achieves a complexity of $ \mathcal{O}(\varepsilon^{-1.75}\log(1/\varepsilon)) $ in the deterministic case and a complexity of $ \mathcal{O}(\varepsilon^{-3.5}) $ in the stochastic case. However, this approach suffers from several limitations: (i) the deterministic method relies on a complex double-loop scheme that solves a fixed-point equation to construct hint vectors for an optimistic online learner, introducing an extra logarithmic factor; (ii) the stochastic method assumes a bounded second-order moment of the stochastic gradient, which is stronger than standard variance bounds; and (iii) different online learning algorithms are used in the two settings. In this paper, we address these issues by introducing an online optimistic gradient method based on a novel **doubly optimistic hint function**. Specifically, we use the gradient at an extrapolated point as the hint, motivated by two optimistic assumptions: that the difference between the hint and the target gradient remains near constant, and that consecutive update directions change slowly due to smoothness. Our method eliminates the need for a double loop and removes the logarithmic factor. Furthermore, by simply replacing full gradients with stochastic gradients and under the standard assumption that their variance is bounded by $\sigma^2$, we obtain a unified algorithm with complexity $\mathcal{O}(\varepsilon^{-1.75} + \sigma^2 \varepsilon^{-3.5})$, smoothly interpolating between the best-known deterministic rate and the optimal stochastic rate.

Modern neural networks exhibit a striking property: basins of attraction in the loss landscape are often connected by low-loss paths, yet optimization dynamics generally remain confined to a single convex basin and rarely explore intermediate points. We resolve this paradox by identifying entropic barriers arising from the interplay between curvature variations along these paths and noise in optimization dynamics. Empirically, we find that curvature systematically rises away from minima, producing effective forces that bias noisy dynamics back toward the endpoints — even when the loss remains nearly flat. These barriers persist longer than energetic barriers, shaping the late-time localization of solutions in parameter space. Our results highlight the role of curvature-induced entropic forces in governing both connectivity and confinement in deep learning landscapes.