ICML 2025 论文列表

We introduce a family of algorithms for online conformal prediction with coverage guarantees for both adversarial and stochastic data. In the adversarial setting, we establish the standard guarantee: over time, a pre-specified target fraction of confidence sets cover the ground truth. For stochastic data, we provide a guarantee at every time instead of just on average over time: the probability that a confidence set covers the ground truth—conditioned on past observations—converges to a pre-specified target when the conditional quantiles of the errors are a linear function of past data. Complementary to our theory, our experiments spanning over $15$ datasets suggest that the performance improvement of our methods over baselines grows with the magnitude of the data’s dependence, even when baselines are tuned on the test set. We put these findings to the test by pre-registering an experiment for electricity demand forecasting in Texas, where our algorithms achieve over a $10$\% reduction in confidence set sizes, a more than a $30$\% improvement in quantile and absolute losses with respect to the observed errors, and significant outcomes on all $78$ out of $78$ pre-registered hypotheses. We provide documentation for the pypi package implementing our algorithms here: \url{https://conformalopt.readthedocs.io/}.

Deep neural networks trained as image denoisers are widely used as priors for solving imaging inverse problems. We introduce Stochastic deep Restoration Priors (ShaRP), a novel framework that stochastically leverages an ensemble of deep restoration models beyond denoisers to regularize inverse problems. By using generalized restoration models trained on a broad range of degradations beyond simple Gaussian noise, ShaRP effectively addresses structured artifacts and enables self-supervised training without fully sampled data. We prove that ShaRP minimizes an objective function involving a regularizer derived from the score functions of minimum mean square error (MMSE) restoration operators. We also provide theoretical guarantees for learning restoration operators from incomplete measurements. ShaRP achieves state-of-the-art performance on tasks such as magnetic resonance imaging reconstruction and single-image super-resolution, surpassing both denoiser- and diffusion-model-based methods without requiring retraining.

Deep reinforcement learning (DRL) has been widely used for dynamic algorithm configuration, particularly in evolutionary computation, which benefits from the adaptive update of parameters during the algorithmic execution. However, applying DRL to algorithm configuration for multi-objective combinatorial optimization (MOCO) problems remains relatively unexplored. This paper presents a novel graph neural network (GNN) based DRL to configure multi-objective evolutionary algorithms. We model the dynamic algorithm configuration as a Markov decision process, representing the convergence of solutions in the objective space by a graph, with their embeddings learned by a GNN to enhance the state representation. Experiments on diverse MOCO challenges indicate that our method outperforms traditional and DRL-based algorithm configuration methods in terms of efficacy and adaptability. It also exhibits advantageous generalizability across objective types and problem sizes, and applicability to different evolutionary computation methods.

This paper investigates decentralized unlearning, aiming to eliminate the impact of a specific client on the whole decentralized system. However, decentralized communication characterizations pose new challenges for effective unlearning: the indirect connections make it difficult to trace the specific client's impact, while the dynamic topology limits the scalability of retraining-based unlearning methods. In this paper, we propose the first **P**rovable **D**ecentralized **U**nlearning algorithm under **D**ynamic **T**opologies called PDUDT. It allows clients to eliminate the influence of a specific client without additional communication or retraining. We provide rigorous theoretical guarantees for PDUDT, showing it is statistically indistinguishable from perturbed retraining. Additionally, it achieves an efficient convergence rate of $\mathcal{O}(\frac{1}{T})$ in subsequent learning, where $T$ is the total communication rounds. This rate matches state-of-the-art results. Experimental results show that compared with the Retrain method, PDUDT saves more than 99\% of unlearning time while achieving comparable unlearning performance.

This paper studies zeroth-order optimization for stochastic convex minimization problems. We propose a parameter-free stochastic zeroth-order method (POEM), which introduces a step-size scheme based on the distance over finite difference and an adaptive smoothing parameter. Our theoretical analysis shows that POEM achieves near-optimal stochastic zeroth-order oracle complexity. Furthermore, numerical experiments demonstrate that POEM outperforms existing zeroth-order methods in practice.

Nash equilibrium (NE) plays an important role in game theory. How to efficiently compute an NE in NFGs is challenging due to its complexity and non-convex optimization property. Machine Learning (ML), the cornerstone of modern artificial intelligence, has demonstrated remarkable empirical performance across various applications including non-convex optimization. To leverage non-convex stochastic optimization techniques from ML for approximating an NE, various loss functions have been proposed. Among these, only one loss function is unbiased, allowing for unbiased estimation under the sampled play. Unfortunately, this loss function suffers from high variance, which degrades the convergence rate. To improve the convergence rate by mitigating the high variance associated with the existing unbiased loss function, we propose a novel surrogate loss function named Nash Advantage Loss (NAL). NAL is theoretically proved unbiased and exhibits significantly lower variance than the existing unbiased loss function. Experimental results demonstrate that the algorithm minimizing NAL achieves a significantly faster empirical convergence rates compared to other algorithms, while also reducing the variance of estimated loss value by several orders of magnitude.

Distribution matching is a key technique in machine learning, with applications in generative models, domain adaptation, and algorithmic fairness. A related but less explored challenge is generating a distribution that aligns with multiple underlying distributions, often with conflicting objectives, known as a Pareto optimal distribution. In this paper, we develop a general theory based on information geometry to construct the Pareto set and front for the entire exponential family under KL and inverse KL divergences. This formulation allows explicit derivation of the Pareto set and front for multivariate normal distributions, enabling applications like multiobjective variational autoencoders (MOVAEs) to generate interpolated image distributions. Experimental results on real-world images demonstrate that both algorithms can generate high-quality interpolated images across multiple distributions.

We present a novel unified analysis for a broad class of adaptive optimization algorithms with structured (e.g., layerwise, diagonal, and kronecker-factored) preconditioners for both online regret minimization and offline convex optimization. Our analysis not only provides matching rate to several important structured preconditioned algorithms including diagonal AdaGrad, full-matrix AdaGrad, and AdaGrad-Norm, but also gives an improved convergence rate for a one-sided variant of Shampoo over that of original Shampoo. Interestingly, more structured preconditioners (e.g., diagonal Adagrad, AdaGrad-Norm which use less space and compute) are often presented as computationally efficient approximations to full-matrix Adagrad, aiming for improved optimization performance through better approximations. Our unified analysis challenges this prevailing view and reveals, perhaps surprisingly, that more structured preconditioners, despite using less space and computation per step, can outperform their less structured counterparts. To demonstrate this, we show that one-sided Shampoo, which is relatively much cheaper than full-matrix AdaGrad could outperform it both theoretically and experimentally.

We study the role of contextual information in the online learning problem of brokerage between traders. In this sequential problem, at each time step, two traders arrive with secret valuations about an asset they wish to trade. The learner (a broker) suggests a trading (or brokerage) price based on contextual data about the asset and the market conditions. Then, the traders reveal their willingness to buy or sell based on whether their valuations are higher or lower than the brokerage price. A trade occurs if one of the two traders decides to buy and the other to sell, i.e., if the broker's proposed price falls between the smallest and the largest of their two valuations. We design algorithms for this problem and prove optimal theoretical regret guarantees under various standard assumptions.

Understanding neural network training dynamics at scale is an important open problem. Although realistic model architectures, optimizers, and data interact in complex ways that make predictive theory challenging, we show that compute-optimally trained models exhibit remarkably precise collective regularities. Specifically, loss curves from models of varying sizes collapse onto a single universal curve when training compute and loss are normalized to unity at the end of training. With learning rate decay, discrepancies between normalized curves fall below the noise floor of individual models' loss curves across random seeds, yielding an exceptionally tight collapse we term "supercollapse." We observe supercollapse across learning rate schedules, datasets, and architectures, including transformers trained on next-token prediction. This collapse breaks down when hyperparameters are scaled suboptimally, providing a practical indicator of proper scaling. We explain these phenomena by connecting collapse to the power-law structure in typical neural scaling laws, and analyzing a simple but effective model of SGD noise dynamics that accurately captures how learning rate schedules deform loss curves away from power laws while preserving universality, and why learning rate decay suppresses variance to enable supercollapse.

We study online finite-horizon Markov Decision Processes with adversarially changing loss and aggregate bandit feedback (a.k.a full-bandit). Under this type of feedback, the agent observes only the total loss incurred over the entire trajectory, rather than the individual losses at each intermediate step within the trajectory. We introduce the first Policy Optimization algorithms for this setting. In the known-dynamics case, we achieve the first *optimal* regret bound of $\tilde \Theta(H^2\sqrt{SAK})$, where $K$ is the number of episodes, $H$ is the episode horizon, $S$ is the number of states, and $A$ is the number of actions. In the unknown dynamics case we establish regret bound of $\tilde O(H^3 S \sqrt{AK})$, significantly improving the best known result by a factor of $H^2 S^5 A^2$.

Hierarchical clustering (HC) is an important data analysis technique in which the goal is to recursively partition a dataset into a tree-like structure while grouping together similar data points at each level of granularity. Unfortunately, for many of the proposed HC objectives, there exist strong barriers to approximation algorithms with the hardness of approximation. We consider the problem of hierarchical clustering given auxiliary information from natural oracles in the learning-augmented framework. Our main results are algorithms that, given learning-augmented oracles, compute efficient approximate HC trees for the celebrated Dasgupta's and Moseley-Wang objectives that overcome known hardness barriers.

Deep latent variable models learn condensed representations of data that, hopefully, reflect the inner workings of the studied phenomena. Unfortunately, these latent representations are not statistically identifiable, meaning they cannot be uniquely determined. Domain experts, therefore, need to tread carefully when interpreting these. Current solutions limit the lack of identifiability through additional constraints on the latent variable model, e.g. by requiring labeled training data, or by restricting the expressivity of the model. We change the goal: instead of identifying the latent variables, we identify relationships between them such as meaningful distances, angles, and volumes. We prove this is feasible under very mild model conditions and without additional labeled data. We empirically demonstrate that our theory results in more reliable latent distances, offering a principled path forward in extracting trustworthy conclusions from deep latent variable models.

Self-Supervised Learning (SSL) powers many current AI systems. As research interest and investment grow, the SSL design space continues to expand. The Platonic view of SSL, following the Platonic Representation Hypothesis (PRH), suggests that despite different methods and engineering approaches, all representations converge to the same Platonic ideal. However, this phenomenon lacks precise theoretical explanation. By synthesizing evidence from Identifiability Theory (IT), we show that the PRH can emerge in SSL. There is a gap between SSL theory and practice: Current IT cannot explain SSL's empirical success, though it has practically relevant insights. Our work formulates a blueprint for SSL research to bridge this gap: we propose expanding IT into what we term Singular Identifiability Theory (SITh), a broader theoretical framework encompassing the entire SSL pipeline. SITh would allow deeper insights into the implicit data assumptions in SSL and advance the field towards learning more interpretable and generalizable representations. We highlight three critical directions for future research: 1) training dynamics and convergence properties of SSL; 2) the impact of finite samples, batch size, and data diversity; and 3) the role of inductive biases in architecture, augmentations, initialization schemes, and optimizers.

In this work, we study online convex optimization with a fixed constraint function $g : \mathbb{R}^d \rightarrow \mathbb{R}$. Prior work on this problem has shown $O(\sqrt{T})$ regret and cumulative constraint satisfaction $\sum_{t=1}^{T} g(x_t) \leq 0$, while only accessing the constraint value and subgradient at the played actions $g(x_t), \partial g(x_t)$. Using the same constraint information, we show a stronger guarantee of anytime constraint satisfaction $g(x_t) \leq 0 \ \forall t \in [T]$, and matching $O(\sqrt{T})$ regret guarantees. These contributions are thanks to our approach of using Polyak feasibility steps to ensure constraint satisfaction, without sacrificing regret. Specifically, after each step of online gradient descent, our algorithm applies a subgradient descent step on the constraint function where the step-size is chosen according to the celebrated Polyak step-size. We further validate this approach with numerical experiments.

Although Artificial Neural Networks (ANNs) have achieved remarkable success across various tasks, they still suffer from limited generalization. We hypothesize that this limitation arises from the traditional sample-based (0--dimensionnal) regularization used in ANNs. To overcome this, we introduce Deep Sturm-Liouville (DSL), a novel function approximator that enables continuous 1D regularization along field lines in the input space by integrating the Sturm-Liouville Theorem (SLT) into the deep learning framework. DSL defines field lines traversing the input space, along which a Sturm-Liouville problem is solved to generate orthogonal basis functions, enforcing implicit regularization thanks to the desirable properties of SLT. These basis functions are linearly combined to construct the DSL approximator. Both the vector field and basis functions are parameterized by neural networks and learned jointly. We demonstrate that the DSL formulation naturally arises when solving a Rank-1 Parabolic Eigenvalue Problem. DSL is trained efficiently using stochastic gradient descent via implicit differentiation and achieves competitive performance on diverse multivariate datasets, including high-dimensional image datasets such as MNIST and CIFAR-10.

Ensemble clustering has demonstrated great success in practice; however, its theoretical foundations remain underexplored. This paper examines the generalization performance of ensemble clustering, focusing on generalization error, excess risk and consistency. We derive a convergence rate of generalization error bound and excess risk bound both of $\mathcal{O}(\sqrt{\frac{\log n}{m}}+\frac{1}{\sqrt{n}})$, with $n$ and $m$ being the numbers of samples and base clusterings. Based on this, we prove that when $m$ and $n$ approach infinity and $m$ is significantly larger than log $n$, i.e., $m,n\to \infty, m\gg \log n$, ensemble clustering is consistent. Furthermore, recognizing that $n$ and $m$ are finite in practice, the generalization error cannot be reduced to zero. Thus, by assigning varying weights to finite clusterings, we minimize the error between the empirical average clusterings and their expectation. From this, we theoretically demonstrate that to achieve better clustering performance, we should minimize the deviation (bias) of base clustering from its expectation and maximize the differences (diversity) among various base clusterings. Additionally, we derive that maximizing diversity is nearly equivalent to a robust (min-max) optimization model. Finally, we instantiate our theory to develop a new ensemble clustering algorithm. Compared with SOTA methods, our approach achieves average improvements of 6.1\%, 7.3\%, and 6.0\% on 10 datasets w.r.t. NMI, ARI, and Purity. The code is available at https://github.com/xuz2019/GPEC.

The Lottery Ticket Hypothesis (LTH) suggests there exists a sparse LTH mask and weights that achieve the same generalization performance as the dense model while using significantly fewer parameters. However, finding a LTH solution is computationally expensive, and a LTH sparsity mask does not generalize to other random weight initializations. Recent work has suggested that neural networks trained from random initialization find solutions within the same basin modulo permutation, and proposes a method to align trained models within the same loss basin. We hypothesize that misalignment of basins is the reason why LTH masks do not generalize to new random initializations and propose permuting the LTH mask to align with the new optimization basin when performing sparse training from a different random init. We empirically show a significant increase in generalization when sparse training from random initialization with the permuted mask as compared to using the non-permuted LTH mask, on multiple datasets (CIFAR-10/100 & ImageNet) and models (VGG11 & ResNet20/50).

We study the convergence of the shuffling gradient method, a popular algorithm employed to minimize the finite-sum function with regularization, in which functions are passed to apply (Proximal) Gradient Descent (GD) one by one whose order is determined by a permutation on the indices of functions. In contrast to its easy implementation and effective performance in practice, the theoretical understanding remains limited. A recent advance by (Liu & Zhou, 2024b) establishes the first last-iterate convergence results under various settings, especially proving the optimal rates for smooth (strongly) convex optimization. However, their bounds for nonsmooth (strongly) convex functions are only as fast as Proximal GD. In this work, we provide the first improved last-iterate analysis for the nonsmooth case demonstrating that the widely used Random Reshuffle ($\textsf{RR}$) and Single Shuffle ($\textsf{SS}$) strategies are both provably faster than Proximal GD, reflecting the benefit of randomness. As an important implication, we give the first (nearly) optimal convergence result for the suffix average under the $\textsf{RR}$ sampling scheme in the general convex case, matching the lower bound shown by (Koren et al., 2022).