ICML 2026 论文列表

In batch multi-objective Bayesian optimization (MOBO), it is often desirable to identify the whole Pareto optimal set, especially when considering the complicated interplay between different design criteria and constraints. This poses unique challenges in acquiring batches of both high quality and diversity to cover the Pareto front. We propose a novel acquisition strategy, Probability of Matching (POM), which evaluates both batch candidate quality and diversity by explicitly capturing the likelihood that all batch points are Pareto optimal, and the probability that they collectively cover the full Pareto set. To estimate the coverage probability and promote diversity, we incorporate non-replacement sampling principles, resulting in our new POM-guided batch MOBO method. Across synthetic benchmarks and real-world tasks, our method consistently outperforms state-of-the-art baselines on standard MOBO metrics as well as a new design-space coverage metric, Expected Minimum Distance (EMD), with comparable computational efficiency.

Dictionary learning has recently emerged as a promising approach for mechanistic interpretability of large transformer models. Disentangling high-dimensional transformer embeddings requires algorithms that scale to high-dimensional data with large sample sizes. Recent work has explored sparse autoencoders (SAEs) for this problem. However, SAEs use a simple linear encoder to solve the sparse encoding subproblem, which is known to be NP-hard. It is therefore interesting to understand whether this approach is sufficient to find good solutions to the dictionary learning problem or if a more sophisticated algorithm could find better solutions. In this work, we propose Double-Batch KSVD (DB-KSVD), a scalable dictionary learning algorithm that adapts the classic KSVD algorithm. DB-KSVD is informed by the rich theoretical foundations of KSVD but scales to datasets with millions of samples and thousands of dimensions. We demonstrate the efficacy of DB-KSVD by disentangling text embeddings of the Gemma-2-2B and Pythia-160M models and evaluating on six metrics from the SAEBench benchmark, where we achieve competitive results when compared to established approaches based on SAEs. We further show similar results when disentangling image embeddings obtained from the DINOv2-S and DINOv2-B models, solidifying our findings. By matching SAE performance with an entirely different optimization approach, our results suggest that (i) SAEs do find strong solutions to the dictionary learning problem and (ii) traditional optimization approaches can be scaled to the required problem sizes, offering a promising avenue for further research. We make an implementation of DB-KSVD available.

Automatic differentiation (AD) frameworks such as JAX and PyTorch have enabled gradient-based optimization for a wide range of scientific fields. Yet, many ''hard'' primitives in these libraries such as thresholding, Boolean logic, discrete indexing, and sorting operations yield zero or undefined gradients that are not useful for optimization. While numerous ''soft'' relaxations have been proposed that provide informative gradients, the respective implementations are fragmented across projects, making them difficult to combine and compare. This work introduces **SoftJAX** and **SoftTorch**, open-source, feature-complete libraries for *soft differentiable programming*. These libraries provide a variety of soft functions as drop-in replacements for their hard JAX and PyTorch counterparts. This includes (i) elementwise operators such as *clip* or *abs*, (ii) utility methods for manipulating Booleans and indices via fuzzy logic, (iii) axiswise operators such as *sort* or *rank* -- based on optimal transport or permutahedron projections, and (iv) offer full support for straight-through gradient estimation. Overall, SoftJAX and SoftTorch make the toolbox of soft relaxations easily accessible to differentiable programming, as demonstrated through benchmarking and a practical case study. Code is available at github.com/a-paulus/softjax and github.com/a-paulus/softtorch.

Analog in-memory computing (AIMC) performs computation directly within resistive crossbar arrays, offering an energy-efficient platform to scale large vision and language models. However, non-ideal analog device properties make the training on AIMC devices challenging. In particular, its update asymmetry can induce a systematic drift of weight updates towards a device-specific symmetric point (SP), which typically does not align with the optimum of the training objective. To mitigate this bias, most existing works assume the SP is known and pre-calibrate it to zero before training by setting the reference point as the SP. Nevertheless, calibrating AIMC devices requires costly pulse updates, and residual calibration error can directly degrade training performance. In this work, we present the first theoretical characterization of the pulse complexity of SP calibration and the resulting estimation error. We further propose a dynamic SP estimation method that tracks the SP during model training, and establishes its convergence guarantees. In addition, we develop an enhanced variant based on chopping and filtering techniques from digital signal processing. Numerical experiments demonstrate both the efficiency and effectiveness of the proposed method.

We study multi-objective optimization over probability distributions in Wasserstein space. Recently, Nguyen et al. (2025) introduced Multiple Wasserstein Gradient Descent (MWGraD) algorithm, which exploits the geometric structure of Wasserstein space to jointly optimize multiple objectives. Building on this approach, we propose an accelerated variant, A-MWGraD, inspired by Nesterov's acceleration. We analyze the continuous-time dynamics and establish convergence to weakly Pareto optimal points in probability space. Our theoretical results show that A-MWGraD achieves a convergence rate of $\mathcal{O}(1/t^2)$ for geodesically convex objectives and $\mathcal{O}(e^{-\sqrt{\beta}t})$ for $\beta$-strongly geodesically convex objectives, improving upon the $\mathcal{O}(1/t)$ rate of MWGraD in the geodesically convex setting. We further introduce a practical kernel-based discretization for A-MWGraD and demonstrate through numerical experiments that it consistently outperforms MWGraD in convergence speed and sampling efficiency on multi-target sampling tasks.

Forward-mode automatic differentiation (FmAD) and zero-order (ZO) optimization are increasingly proposed as memory-efficient, backpropagation-free alternatives for large language model (LLM) fine-tuning, yet their benefits are typically evaluated only against standard backpropagation (BP), omitting memory-efficient variants such as activation checkpointing. We present a unified theoretical and empirical comparison of BP, checkpointed BP, FmAD, and ZO for LLM and vision-language model training, showing that while FmAD and ZO reduce activation memory, they trade memory for higher computational cost and longer wall-clock time to convergence, resulting in lower accuracy and slower training, especially under constrained perturbation budgets. Across models, BP with checkpointing outperforms FmAD and ZO variants, including variance-reduced methods, achieving up to 31.1% higher accuracy, 34.8% faster convergence, and 3.8$\times$ fewer computations at comparable memory usage, while also revealing instability-related failure modes in FmAD and ZO. Overall, our results correct a one-sided benchmarking narrative by showing that memory-efficient methods entail fundamentally different trade-offs, and that ignoring these distinctions has led to misleading conclusions about LLM optimization in prior work.

We propose a mathematically principled PDE gradient flow framework for distributionally robust optimization (DRO). Exploiting the recent advances in the intersection of Monte Carlo sampling and statistical optimal transport, we show that our theoretical framework can be implemented as practical algorithms for sampling from worst-case distributions and, consequently, DRO. While numerous previous works have relied on dual reformulation techniques, we contribute a sound and complete gradient flow view based on SDEs or PDEs that can be used to construct new algorithms for general, potentially non-convex, losses. Without loss of generality, we solve a class of Wasserstein and entropy-regularized DRO problems using the recently-discovered Wasserstein Fisher-Rao and Stein variational gradient flows. Notably, we also show some simple reductions of our framework recover exactly previously proposed popular DRO methods, and provide new insights into their theoretical limits and optimization dynamics of DRO. Numerical studies based on stochastic gradient descent on machine learning tasks provide empirical backing for our theoretical findings.

In recent years, bilevel optimization (BLO) has attracted significant attention for its broad applications in machine learning. However, most existing works on BLO remain confined to the single-task setting and rely on the lower-level strong convexity assumption, which significantly restricts their applicability to modern machine learning problems of growing complexity. In this paper, we make the first attempt to extend BLO to the multi-task setting under a relaxed lower-level general convexity (LLGC) assumption. To this end, we reformulate the multi-task bilevel learning (MTBL) problem with LLGC into an equality constrained multi-objective optimization (ECMO) problem. However, ECMO itself is a new problem that has not yet been studied in the literature. To address this gap, we first establish a new Karush–Kuhn–Tucker (KKT)-based Pareto stationarity as the convergence criterion for ECMO algorithm design. Based on this foundation, we propose a weighted Chebyshev (WC)-penalty algorithm that achieves a finite-time convergence rate of $\mathcal{O}(ST^{-\frac{1}{2}})$ to KKT-based Pareto stationarity in both deterministic and stochastic settings, where $S$ denotes the number of objectives, and $T$ is the total iterations. Moreover, by varying the preference vector over the $S$-dimensional simplex, our WC-penalty method systematically explores the Pareto front. Finally, solutions to the ECMO problem translate directly into solutions for the original MTBL problem, thereby closing the loop between these two foundational optimization frameworks.

Federated stochastic multi-level compositional minimax optimization supports a growing number of machine learning applications. However, the interplay of multi-level compositional structure and minimax formulation in federated learning setting poses significant optimization challenges, resulting in slow convergence rates for existing algorithms. In this paper, we propose a novel federated learning algorithm, LS$^2$MC-GDA, that leverages smoothing techniques and variance-reduced stochastic compositional gradients. To support our theoretical analysis, we introduce a stage-wise extension of LS$^2$MC-GDA, which serves to bridge the gap between different stationarity measures. We establish that our algorithm achieves a sample complexity of $O(\kappa^{3/2}/N\epsilon^3)$ and a communication complexity of $O(\kappa/\epsilon^2)$, substantially improving existing theoretical results in terms of the condition number $\kappa$ and the solution accuracy $\epsilon$ and achieving a linear speedup with respect to the number of workers $N$. Finally, experimental results validate the effectiveness of our algorithm.

Deep Reinforcement Learning (DRL) has emerged as a promising approach for solving Combinatorial Optimization (CO) problems, such as the 3D Bin Packing Problem (3D-BPP), Traveling Salesman Problem (TSP), or Vehicle Routing Problem (VRP), but these neural solvers often exhibit brittleness when facing distribution shifts. To address this issue, we uncover the Satisficing Generalization Edge, which we validate both theoretically and experimentally: identifying a set of promising actions is inherently more generalizable than selecting the single optimal action. To exploit this property, we propose Adaptive Selection After Proposal (ASAP), a generic framework that decomposes the decision-making process into two distinct phases: a proposal policy that acts as a robust filter, and a selection policy as an adaptable decision maker. This architecture enables a highly effective online adaptation strategy where the selection policy can be rapidly fine-tuned on a new distribution. Concretely, we introduce a two-phase training framework enhanced by Model-Agnostic Meta-Learning (MAML) to prime the model for fast adaptation. Extensive experiments on 3D-BPP, TSP, and CVRP demonstrate that ASAP improves the generalization capability of state-of-the-art baselines and achieves superior online adaptation on out-of-distribution instances.

Post-training with reinforcement learning (RL) has recently shown strong promise for advancing multimodal agents beyond supervised imitation. However, RL remains limited by poor data efficiency, particularly in settings where interaction data are scarce and quickly become outdated. To address this challenge, GIPO (Gaussian Importance sampling Policy Optimization) is proposed as a policy optimization objective based on truncated importance sampling, replacing hard clipping with a log-ratio-based Gaussian trust weight to softly damp extreme importance ratios while maintaining non-zero gradients. Theoretical analysis shows that GIPO introduces an implicit, tunable constraint on the update magnitude, while concentration bounds guarantee robustness and stability under finite-sample estimation. Experimental results show that GIPO achieves state-of-the-art performance among clipping-based baselines across a wide range of replay buffer sizes, from near on-policy to highly stale data, while exhibiting superior bias--variance trade-off, high training stability and improved sample efficiency. Code is available at https://github.com/distanceLu/GIPO.

Recently, many empirical work has shown that, in machine learning, the noise distribution of stochastic gradients often exhibits heavy tails when stochastic optimization methods are employed. Most existing theoretical analyses of heavy-tailed stochastic methods rely on various convexity and smoothness assumptions and our knowledge of how heavy-tailed stochastic methods behave in the setting of weakly convex optimization is still limited. In the weakly convex setting, this paper derives new upper bounds on the convergence of the stochastic gradient method (SGD) under heavy-tailed noises. In particular, for vanilla SGD, we establish an in-expectation convergence guarantee on the bounded constrained domain under the assumption of bounded $p$-th central moment ($p$-BCM) of the gradient noise, and a high-probability guarantee on the unbounded domain when the noise follows a heavy-tailed sub-Weibull distribution. By equipping SGD with the gradient clipping (Clip-SGD), we demonstrate that it achieves high-probability convergence in the unbounded domain under the $p$-BCM gradient noise. All of our high-probability convergence bounds depend on the failure probability only through polynomial-logarithmic factors. Finally, we present experiments to validate our theoretical findings.

We propose an OT-guided sampling framework for solving graph combinatorial optimization through exact multilinear relaxation. Graph combinatorial optimization problems can be written as quadratic unconstrained binary optimization(QUBO). Leveraging a classical result in combinatorial optimization, we obtain a continuous multi-linear relaxation of QUBO that is exact, in the sense that it preserves the optimal binary solutions. The challenge is that the resulting energy landscape is highly nonconvex. We address this by treating the objective as an energy function and optimizing via sampling from the induced Boltzmann distribution to escape poor local optima. Viewing sampling as transporting a simple reference distribution to the target distribution, we use optimal transport to characterize more efficient probability flow and derive a stochastic optimal control problem whose solution yields an optimal sampling dynamics. We parameterize the control policy with graph neural networks to approximate the optimal control. Experiments show improved solution quality and efficiency over strong combinatorial and learning-based baselines.

A key challenge in deriving unified neural solvers for combinatorial optimization (CO) is efficient generalization of models between one set of tasks to new tasks not used during the initial training process. To address it, we first establish a new GNN encoder, which uses a GCON module as a form of expressive message passing together with energy-based unsupervised loss functions. This model achieves high performance (often comparable with state-of-the-art results) across multiple CO tasks when trained individually on each task. We then leverage knowledge from the computational reducibility literature to propose pretraining and fine-tuning strategies to transfer effectively (a) between MVC, MIS and MaxClique, and (b) in a multi-task learning setting that additionally incorporates MaxCut, MDS and graph coloring. Additionally, in a leave-one-out, multi-task learning setting, we observe that pretraining on all but one task almost always leads to faster convergence on the remaining task when fine-tuning while avoiding negative transfer. Our findings indicate that learning common representations across multiple graph CO problems is viable through the use of expressive message passing coupled with pretraining strategies that are informed by the polynomial reduction literature, thereby taking an important step towards enabling the development of foundational models for neural CO.

The Gromov-Wasserstein (GW) distance enables comparison across different spaces but remains fragile to structural noise due to its global quadratic coupling. Existing robust extensions primarily rely on node-centric mass relaxation. However, we argue that this strategy is far from sufficient: it only addresses node-induced structural noise (outliers) while neglecting edge-induced distortions where spurious connections exist between valid nodes. To overcome this limitation, we propose the Structurally Robust Gromov-Wasserstein (SRGW) distance, a novel formulation that adaptively filters geometric distortions during optimization. By introducing a structure-aware dual-mask mechanism, our method effectively isolates these stubborn structural outliers while preserving strict marginal constraints for balanced transport. We solve this objective using a Mask-Guided GW Algorithm, which jointly optimizes the transport plan and the structural noise filters. We provide a rigorous theoretical analysis proving that our algorithm converges to a critical point under the Kurdyka-Łojasiewicz framework. Extensive experiments on synthetic geometric matching and real-world subgraph alignment benchmarks demonstrate that Mask-Guided GW achieves superior alignment quality, particularly under severe structural noise.

Diffusion probabilistic models (DPMs)’ sampling process is often inefficient, requiring hundreds to thousands of iterative steps to accurately approximate the diffusion trajectory. This inefficiency limits their practical applicability. Although recent advances in sampling efficiency—such as numerical solvers for diffusion ordinary differential equations (ODEs)—have made progress, significant challenges remain: training-free numerical solvers suffer from the suboptimality of manually designed timestep selection rules and the inherent inconsistency between the forward diffusion process (typically involving thousands of steps) and the reverse denoising process (usually limited to tens of steps). Since timestep selection is inherently a discrete problem and cannot be optimized via gradients, we propose an innovative approach—reparameterizing the timestep scheduling through probabilistic masking, thereby enabling gradient-based optimization of sampling timesteps. To circumvent backpropagation, we employ policy gradient methods. Furthermore, to address the inconsistency between forward diffusion (training) and reverse denoising (inference), we extend this framework into a bilevel optimization paradigm: the inner loop performs additional lightweight training on the model at specific timesteps determined by the outer mask to align forward and reverse processes, while the outer loop optimizes the timestep distribution via probabilistic masking and policy gradient based on generation quality. Under mild assumptions, we theoretically analyze the convergence of the proposed algorithm. Extensive experiments across diverse datasets and samplers demonstrate that this framework effectively enhances sampling efficiency and generation quality while maintaining compatibility with various DPM architectures and advanced ODE solvers.

Bayesian optimization (BO) has traditionally solved black-box problems where function evaluation is expensive and, therefore, observations are few. Recently, however, there has been growing interest in applying BO to problems where function evaluation is cheaper and observations are more plentiful. In this regime, scaling to many observations $N$ is impeded by Gaussian-process (GP) surrogates: GP hyperparameter fitting scales as $\mathcal{O}(N^3)$ (reduced to roughly $\mathcal{O}(N^2)$ in modern implementations), and it is repeated at every BO iteration. Many methods improve scaling at acquisition time, but hyperparameter fitting still scales poorly, making it the bottleneck. We propose Epistemic Nearest Neighbors (ENN), a lightweight alternative to GPs that estimates function values and uncertainty (epistemic and aleatoric) from $K$-nearest-neighbor observations. ENN scales as $\mathcal{O}(N)$ for both fitting and acquisition. Our BO method, TuRBO-ENN, replaces the GP surrogate in TuRBO with ENN and its Thompson-sampling acquisition with $\mathrm{UCB} = \mu(x) + \sigma(x)$. For the special case of noise-free problems, we can omit fitting altogether by replacing $\mathrm{UCB}$ with a non-dominated sort over $\mu(x)$ and $\sigma(x)$. We show empirically that TuRBO-ENN reduces proposal time (i.e., fitting time + acquisition time) by one to two orders of magnitude compared to TuRBO at up to 50,000 observations without sacrificing solution quality.

Decentralized stochastic bi-level optimization has been actively studied in recent years. However, existing studies assume that the lower-level loss function is strongly convex, which limits their applicability to many machine learning models. To address this limitation, in this paper, we propose a novel decentralized stochastic first-order optimization algorithm, which does not require second-order Hessian or Jacobian matrices, for the setting where the lower-level loss function is nonconvex but satisfies the Polyak–Łojasiewicz (PL) condition. Additionally, unlike existing single-agent methods that introduce a regularization term to the lower-level loss function to artificially enforce strong convexity, our algorithm does not require such modification. Moreover, our algorithm employs a constant single-timescale learning rate for updating variables, which is different from the time-dependent and two-timescale learning rate schedules used in prior work. To establish the convergence rate, we develop a new convergence analysis framework for the pure PL condition, rather than relying on the artificial strong convexity introduced through regularization in existing single-agent methods. To the best of our knowledge, this is the first algorithm for nonconvex decentralized bi-level optimization that offers theoretical convergence guarantees under mild conditions. Finally, our extensive experimental results on hyperparameter optimization and model pruning applications validate the efficacy of the proposed algorithm.

Sharpness-Aware Minimization (SAM) has established itself as a powerful and widely adopted optimizer for training machine learning models. By explicitly minimizing the sharpness of the loss landscape, SAM often improves generalization while delivering strong empirical performance. However, SAM and its variants, like most training algorithms, are sensitive to the choice of learning rate, which is typically selected through extensive hyperparameter tuning or predefined schedulers. In this work, motivated by recent advances on the effectiveness of stochastic Polyak step sizes for Stochastic Gradient Descent (SGD), we derive Polyak schedulers tailored to SAM-style updates, yielding novel adaptive algorithms in both deterministic and stochastic settings. In the smooth setting, we prove linear convergence for strongly convex objectives and an $\mathcal{O}(1/T)$ convergence rate for convex objectives in the deterministic case. In the stochastic setting, we establish analogous convergence guarantees up to a neighborhood of the optimum. Numerical experiments demonstrate that the proposed Polyak schedulers achieve performance comparable to or better than carefully tuned SAM baselines, while substantially reducing the need for learning-rate tuning.