ICLR 2025 论文列表

This paper studies stochastic contextual bandits with knapsack constraints (CBwK), where a learner observes a context, takes an action, receives a reward, and incurs a vector of costs at every round. The learner aims to maximize the cumulative rewards across $T$ rounds under the knapsack constraints with an initial budget of $B$. We study CBwK in the small budget regime where the budget $B = \Omega(\sqrt{T})$ and propose an Adaptive and Universal Primal--Dual algorithm (AUPD) that achieves strong regret performance: i) AUPD achieves $\tilde{O}((1 + \frac{\nu^*}{\delta b})\sqrt{T})$ regret under the strict feasibility assumption without any prior information, matching the best-known bounds; ii) AUPD achieves $\tilde{O}(\sqrt{T}+ \frac{\nu^*}{\sqrt{b}}T^{\frac{3}{4}})$ regret without strict feasibility assumption, which, to the best of our knowledge, is the first result in the literature. Here, the parameter $\nu^*$ represents the optimal average reward; $b=B/T$ is the average budget and $\delta b$ is the feasibility/safety margin. We establish these strong results through the adaptive budget-aware design, which effectively balances reward maximization and budget consumption. We provide a new perspective on analyzing budget consumption using the Lyapunov drift method, along with a refined analysis of its cumulative variance. Our theory is further supported by experiments conducted on a large-scale dataset.

Sparse Principal Component Analysis (Sparse PCA) is a pivotal tool in data analysis and dimensionality reduction. However, Sparse PCA is a challenging problem in both theory and practice: it is known to be NP-hard and current exact methods generally require exponential runtime. In this paper, we propose a novel framework to efficiently approximate Sparse PCA by (i) approximating the general input covariance matrix with a re-sorted block-diagonal matrix, (ii) solving the Sparse PCA sub-problem in each block, and (iii) reconstructing the solution to the original problem. Our framework is simple and powerful: it can leverage any off-the-shelf Sparse PCA algorithm and achieve significant computational speedups, with a minor additive error that is linear in the approximation error of the block-diagonal matrix. Suppose $g(k, d)$ is the runtime of an algorithm (approximately) solving Sparse PCA in dimension $d$ and with sparsity constant $k$. Our framework, when integrated with this algorithm, reduces the runtime to $\mathcal{O}\left(\frac{d}{d^\star} \cdot g(k, d^\star) + d^2\right)$, where $d^\star \leq d$ is the largest block size of the block-diagonal matrix. For instance, integrating our framework with the Branch-and-Bound algorithm reduces the complexity from $g(k, d) = \mathcal{O}(k^3\cdot d^k)$ to $\mathcal{O}(k^3\cdot d \cdot (d^\star)^{k-1})$, demonstrating exponential speedups if $d^\star$ is small. We perform large-scale evaluations on many real-world datasets: for exact Sparse PCA algorithm, our method achieves an average speedup factor of 100.50, while maintaining an average approximation error of 0.61%; for approximate Sparse PCA algorithm, our method achieves an average speedup factor of 6.00 and an average approximation error of -0.91%, meaning that our method oftentimes finds better solutions.

We investigate a generalized form of submodular maximization, referred to as $k$-submodular maximization, with applications across the domains of social networks and machine learning. In this work, we propose the multilinear extension of $k$-submodular functions and unified Frank-Wolfe-type frameworks based on that. This continuous framework accommodates 1) monotone or non-monotone functions, and 2) various constraint types including matroid constraints, knapsack constraints, and their combinations. Notably, we attain an asymptotically optimal $1/2$-approximation for monotone $k$-submodular maximization problems with knapsack constraints, surpassing previous $1/3$-approximation results, and a factor-$1/3$ approximation for non-monotone $k$-submodular maximization problems with knapsack constraints and matroid constraints which outperforms previous $0.245$-approximation results. The foundation for our analysis stems from new insights into specific linear and monotone properties pertaining to the multilinear extension.

Recent research in Meta-Black-Box-Optimization (MetaBBO) have shown that meta-trained neural networks can effectively guide the design of black-box optimizers, significantly reducing the need for expert tuning and delivering robust performance across complex problem distributions. Despite their success, a paradox remains: MetaBBO still rely on human-crafted Exploratory Landscape Analysis features to inform the meta-level agent about the low-level optimization progress. To address the gap, this paper proposes Neural Exploratory Landscape Analysis (NeurELA), a novel framework that dynamically profiles landscape features through a two-stage, attention-based neural network, executed in an entirely end-to-end fashion. NeurELA is pre-trained over a variety of MetaBBO algorithms using a multi-task neuroevolution strategy. Extensive experiments show that NeurELA achieves consistently superior performance when integrated into different and even unseen MetaBBO tasks and can be efficiently fine-tuned for further performance boost. This advancement marks a pivotal step in making MetaBBO algorithms more autonomous and broadly applicable. The source code of NeurELA can be accessed at https://anonymous.4open.science/r/Neur-ELA-303C.

We train, for the first time, large language models using FP8 precision on datasets up to 2 trillion tokens --- a 20-fold increase over previous limits. Through these extended training runs, we uncover critical instabilities in FP8 training that were not observable in earlier works with shorter durations. We trace these instabilities to outlier amplification by the SwiGLU activation function. Interestingly, we show, both analytically and empirically, that this amplification happens only over prolonged training periods, and link it to a SwiGLU weight alignment process. To address this newly identified issue, we introduce Smooth-SwiGLU, a novel modification that ensures stable FP8 training without altering function behavior. We also demonstrate, for the first time, FP8 quantization of both Adam optimizer moments. Combining these innovations, we successfully train a 7B parameter model using FP8 precision on 256 Intel Gaudi2 accelerators, achieving on-par results with the BF16 baseline while delivering up to a $\sim$ 34 % throughput improvement. A reference implementation is supplied in https://github.com/Anonymous1252022/Megatron-DeepSpeed

This paper considers a class of structured fractional minimization problems. The numerator consists of a differentiable function, a simple nonconvex nonsmooth function, a concave nonsmooth function, and a convex nonsmooth function composed with a linear operator. The denominator is a continuous function that is either weakly convex or has a weakly convex square root. These problems are prevalent in various important applications in machine learning and data science. Existing methods, primarily based on subgradient methods and smoothing proximal gradient methods, often suffer from slow convergence and numerical stability issues. In this paper, we introduce {\sf FADMM}, the first Alternating Direction Method of Multipliers tailored for this class of problems. {\sf FADMM} decouples the original problem into linearized proximal subproblems, featuring two variants: one using Dinkelbach's parametric method ({\sf FADMM-D}) and the other using the quadratic transform method ({\sf FADMM-Q}). By introducing a novel Lyapunov function, we establish that {\sf FADMM} converges to $\epsilon$-approximate critical points of the problem within an oracle complexity of $\mathcal{O}(1/\epsilon^{3})$. Extensive experiments on synthetic and real-world datasets, including sparse Fisher discriminant analysis, robust Sharpe ratio minimization, and robust sparse recovery, demonstrate the effectiveness of our approach.

Attention-based models, such as Transformer, excel across various tasks but lack a comprehensive theoretical understanding, especially regarding token-wise sparsity and internal linear representations. To address this gap, we introduce the single-location regression task, where only one token in a sequence determines the output, and its position is a latent random variable, retrievable via a linear projection of the input. To solve this task, we propose a dedicated predictor, which turns out to be a simplified version of a non-linear self-attention layer. We study its theoretical properties, by showing its asymptotic Bayes optimality and analyzing its training dynamics. In particular, despite the non-convex nature of the problem, the predictor effectively learns the underlying structure. This work highlights the capacity of attention mechanisms to handle sparse token information and internal linear structures.

Quadratic programming is a ubiquitous prototype in convex programming. Many machine learning problems can be formulated as quadratic programming, including the famous Support Vector Machines (SVMs). Linear and kernel SVMs have been among the most popular models in machine learning over the past three decades, prior to the deep learning era. Generally, a quadratic program has an input size of $\Theta(n^2)$, where $n$ is the number of variables. Assuming the Strong Exponential Time Hypothesis ($\textsf{SETH}$), it is known that no $O(n^{2-o(1)})$ time algorithm exists when the quadratic objective matrix is positive semidefinite (Backurs, Indyk, and Schmidt, NeurIPS'17). However, problems such as SVMs usually admit much smaller input sizes: one is given $n$ data points, each of dimension $d$, and $d$ is oftentimes much smaller than $n$. Furthermore, the SVM program has only $O(1)$ equality linear constraints. This suggests that faster algorithms are feasible, provided the program exhibits certain structures. In this work, we design the first nearly-linear time algorithm for solving quadratic programs whenever the quadratic objective admits a low-rank factorization, and the number of linear constraints is small. Consequently, we obtain results for SVMs: * For linear SVM when the input data is $d$-dimensional, our algorithm runs in time $\widetilde O(nd^{(\omega+1)/2}\log(1/\epsilon))$ where $\omega\approx 2.37$ is the fast matrix multiplication exponent; * For Gaussian kernel SVM, when the data dimension $d = O(\log n)$ and the squared dataset radius is sub-logarithmic in $n$, our algorithm runs in time $O(n^{1+o(1)}\log(1/\epsilon))$. We also prove that when the squared dataset radius is at least $\Omega(\log^2 n)$, then $\Omega(n^{2-o(1)})$ time is required. This improves upon the prior best lower bound in both the dimension $d$ and the squared dataset radius.

Second-order methods for convex optimization outperform first-order methods in terms of theoretical iteration convergence, achieving rates up to $O(k^{-5})$ for highly-smooth functions. However, their practical performance and applications are limited due to their multi-level structure and implementation complexity. In this paper, we present new results on high-order optimization methods, supported by their practical performance. First, we show that the basic high-order methods, such as the Cubic Regularized Newton Method, exhibit global superlinear convergence for $\mu$-strongly star-convex functions, a class that includes $\mu$-strongly convex functions and some non-convex functions. Theoretical convergence results are both inspired and supported by the practical performance of these methods. Secondly, we propose a practical version of the Nesterov Accelerated Tensor method, called NATA. It significantly outperforms the classical variant and other high-order acceleration techniques in practice. The convergence of NATA is also supported by theoretical results. Finally, we introduce an open-source computational library for high-order methods, called OPTAMI. This library includes various methods, acceleration techniques, and subproblem solvers, all implemented as PyTorch optimizers, thereby facilitating the practical application of high-order methods to a wide range of optimization problems. We hope this library will simplify research and practical comparison of methods beyond first-order.

Classification tasks play a fundamental role in various applications, spanning domains such as healthcare, natural language processing and computer vision. With the growing popularity and capacity of machine learning models, people can easily access trained classifiers as a service online or offline. However, model use comes with a cost and classifiers of higher capacity (such as large foundation models) usually incur higher inference costs. To harness the respective strengths of different classifiers, we propose a principled approach, OCCAM, to compute the best classifier assignment strategy over classification queries (termed as the optimal model portfolio) so that the aggregated accuracy is maximized, under user-specified cost budgets. Our approach uses an unbiased and low-variance accuracy estimator and effectively computes the optimal solution by solving an integer linear programming problem. On a variety of real-world datasets, OCCAM achieves 40% cost reduction with little to no accuracy drop.

Communication efficiency has garnered significant attention as it is considered the main bottleneck for large-scale decentralized Machine Learning applications in distributed and federated settings. In this regime, clients are restricted to transmitting small amounts of compressed information to their neighbors over a communication graph. Numerous endeavors have been made to address this challenging problem by developing algorithms with compressed communication for decentralized non-convex optimization problems. Despite considerable efforts, current theoretical understandings of the problem are still very limited, and existing algorithms all suffer from various limitations. In particular, these algorithms typically rely on strong, and often infeasible assumptions such as bounded data heterogeneity or require large batch access while failing to achieve linear speedup with the number of clients. In this paper, we introduce MoTEF, a novel approach that integrates communication compression with $\textbf{Mo}$mentum $\textbf{T}$racking and $\textbf{E}$rror $\textbf{F}$eedback. MoTEF is the first algorithm to achieve an asymptotic rate matching that of distributed SGD under arbitrary data heterogeneity, hence resolving a long-standing theoretical obstacle in decentralized optimization with compressed communication. We provide numerical experiments to validate our theoretical findings and confirm the practical superiority of MoTEF.

In modern deep neural networks, the learning dynamics of individual neurons are often obscure, as the networks are trained via global optimization. Conversely, biological systems build on self-organized, local learning, achieving robustness and efficiency with limited global information. Here, we show how self-organization between individual artificial neurons can be achieved by designing abstract bio-inspired local learning goals. These goals are parameterized using a recent extension of information theory, Partial Information Decomposition (PID), which decomposes the information that a set of information sources holds about an outcome into unique, redundant and synergistic contributions. Our framework enables neurons to locally shape the integration of information from various input classes, i.e., feedforward, feedback, and lateral, by selecting which of the three inputs should contribute uniquely, redundantly or synergistically to the output. This selection is expressed as a weighted sum of PID terms, which, for a given problem, can be directly derived from intuitive reasoning or via numerical optimization, offering a window into understanding task-relevant local information processing. Achieving neuron-level interpretability while enabling strong performance using local learning, our work advances a principled information-theoretic foundation for local learning strategies.

Two-stage adaptive robust optimization (ARO) is a powerful approach for planning under uncertainty, balancing first-stage decisions with recourse decisions made after uncertainty is realized. To account for uncertainty, modelers typically define a simple uncertainty set over which potential outcomes are considered. However, classical methods for defining these sets unintentionally capture a wide range of unrealistic outcomes, resulting in overly-conservative and costly planning in anticipation of unlikely contingencies. In this work, we introduce AGRO, a solution algorithm that performs adversarial generation for two-stage adaptive robust optimization using a variational autoencoder. AGRO generates high-dimensional contingencies that are simultaneously adversarial and realistic, improving the robustness of first-stage decisions at a lower planning cost than standard methods. To ensure generated contingencies lie in high-density regions of the uncertainty distribution, AGRO defines a tight uncertainty set as the image of "latent" uncertainty sets under the VAE decoding transformation. Projected gradient ascent is then used to maximize recourse costs over the latent uncertainty sets by leveraging differentiable optimization methods. We demonstrate the cost-efficiency of AGRO by applying it to both a synthetic production-distribution problem and a real-world power system expansion setting. We show that AGRO outperforms the standard column-and-constraint algorithm by up to 1.8% in production-distribution planning and up to 8% in power system expansion.

We propose a general framework for a hybrid continuous-discrete algorithm that integrates continuous-time deterministic dynamics with Metropolis-Hastings (MH) steps to combine search dynamics that either preserve or break detailed balance. Our purpose is to study the non-equilibrium dynamics that leads to the ground state of rugged energy landscapes in this general setting. Our results show that MH-driven dynamics reach ``easy'' ground states more quickly, indicating a stronger bias toward these solutions in algorithms using reversible transition probabilities. To validate this, we construct a set of Ising problem instances with a controllable bias in the energy landscape that makes certain degenerate solutions more accessible than others. The constructed hybrid algorithm demonstrates significant improvements in convergence and ground-state sampling accuracy, achieving a 100x speedup on GPU compared to simulated annealing, making it well-suited for large-scale applications.

Gradient-based multi-objective optimization (MOO) is essential in modern machine learning, with applications in e.g., multi-task learning, federated learning, algorithmic fairness and reinforcement learning. In this work, we first reveal some limitations of Pareto stationarity, a widely accepted first-order condition for Pareto optimality, in the presence of sparse function-variable structures. Next, to account for such sparsity, we propose a novel solution concept termed Refined Pareto Stationarity (RPS), which we prove is always sandwiched between Pareto optimality and Pareto stationarity. We give an efficient partitioning algorithm to automatically mine the function-variable dependency and substantially trim non-optimal Pareto stationary solutions. Then, we show that gradient-based descent algorithms in MOO can be enhanced with our refined partitioning. In particular, we propose Multiple Gradient Descent Algorithm with Refined Partition (RP-MGDA) as an example method that converges to RPS, while still enjoying a similar per-step complexity and convergence rate. Lastly, we validate our approach through experiments on both synthetic examples and realistic application scenarios where distinct function-variable dependency structures appear. Our results highlight the importance of exploiting function-variable structure in gradient-based MOO, and provide a seamless enhancement to existing approaches.

Adam is a widely used optimizer in neural network training due to its adaptive learning rate. However, because different data samples influence model updates to varying degrees, treating them equally can lead to inefficient convergence. To address this, a prior work proposed adapting the sampling distribution using a bandit framework to select samples adaptively. While promising, the bandit-based variant of Adam suffers from limited theoretical guarantees. In this paper, we introduce \textit{Adam with Combinatorial Bandit Sampling} (AdamCB), which integrates combinatorial bandit techniques into Adam to resolve these issues. AdamCB is able to fully utilize feedback from multiple samples at once, enhancing both theoretical guarantees and practical performance. Our regret analysis shows that AdamCB achieves faster convergence than Adam-based methods including the previous bandit-based variant. Numerical experiments demonstrate that AdamCB consistently outperforms existing methods.

Bilevel optimization, which addresses challenges in hierarchical learning tasks, has gained significant interest in machine learning. Implementing gradient descent for bilevel optimization presents computational hurdles, notably the need to compute the exact lower-level solution and the inverse Hessian of the lower-level objective. While these two aspects are inherently connected, existing methods typically handle them separately by solving the lower-level problem and a linear system for the inverse Hessian-vector product. In this paper, we introduce a general framework to tackle these computational challenges in a coordinated manner. Specifically, we leverage quasi-Newton algorithms to accelerate the solution of the lower-level problem while efficiently approximating the inverse Hessian-vector product. Furthermore, by leveraging the superlinear convergence properties of BFGS, we establish a non-asymptotic convergence analysis for the BFGS adaptation within our framework. Numerical experiments demonstrate the comparable or superior performance of our proposed algorithms in real-world learning tasks, including hyperparameter optimization, data hyper-cleaning, and few-shot meta-learning.

We study the implicit bias of the family of steepest descent algorithms with infinitesimal learning rate, including gradient descent, sign gradient descent and coordinate descent, in deep homogeneous neural networks. We prove that an algorithm-dependent geometric margin increases during training and characterize the late-stage bias of the algorithms. In particular, we define a generalized notion of stationarity for optimization problems and show that the algorithms progressively reduce a (generalized) Bregman divergence, which quantifies proximity to such stationary points of a margin-maximization problem. We then experimentally zoom into the trajectories of neural networks optimized with various steepest descent algorithms, highlighting connections to the implicit bias of Adam.

The Gromov–Wasserstein (GW) problem, a variant of the classical optimal transport (OT) problem, has attracted growing interest in the machine learning and data science communities due to its ability to quantify similarity between measures in different metric spaces. However, like the classical OT problem, GW imposes an equal mass constraint between measures, which restricts its application in many machine learning tasks. To address this limitation, the partial Gromov-Wasserstein (PGW) problem has been introduced. It relaxes the equal mass constraint, allowing the comparison of general positive Radon measures. Despite this, both GW and PGW face significant computational challenges due to their non-convex nature. To overcome these challenges, we propose the linear partial Gromov-Wasserstein (LPGW) embedding, a linearized embedding technique for the PGW problem. For $K$ different metric measure spaces, the pairwise computation of the PGW distance requires solving the PGW problem $\mathcal{O}(K^2)$ times. In contrast, the proposed linearization technique reduces this to $\mathcal{O}(K)$ times. Similar to the linearization technique for the classical OT problem, we prove that LPGW defines a valid metric for metric measure spaces. Finally, we demonstrate the effectiveness of LPGW in practical applications such as shape retrieval and learning with transport-based embeddings, showing that LPGW preserves the advantages of PGW in partial matching while significantly enhancing computational efficiency. The code is available at https://github.com/mint-vu/Linearized_Partial_Gromov_Wasserstein.