论文检索

Optimization

Guner Dilsad ER, Sebastian Trimpe, Michael Muehlebach

We consider a distributed learning problem, where agents minimize a global objective function by exchanging information over a network. Our approach has two distinct features: (i) It substantially reduces communication by triggering communication only when necessary, and (ii) it is agnostic to the data-distribution among the different agents. We can therefore guarantee convergence even if the local data-distributions of the agents are arbitrarily distinct. We analyze the convergence rate of the algorithm both in convex and nonconvex settings and derive accelerated convergence rates in a convex setting. We also characterize the effect of communication failures and demonstrate that our algorithm is robust to communication failures. The article concludes by presenting numerical results from distributed learning tasks on the MNIST and CIFAR-10 datasets. The experiments underline communication savings of 35\% or more due to the event-based communication strategy, show resilience towards heterogeneous data-distributions, and highlight that our approach outperforms common baselines such as FedAvg, FedProx, SCAFFOLD and FedADMM.

General Machine Learning · Representation Learning

Nikita Zozoulenko, Thomas Cass, Lukas Gonon

We introduce Random Feature Representation Boosting (RFRBoost), a novel method for constructing deep residual random feature neural networks (RFNNs) using boosting theory. RFRBoost uses random features at each layer to learn the functional gradient of the network representation, enhancing performance while preserving the convex optimization benefits of RFNNs. In the case of MSE loss, we obtain closed-form solutions to greedy layer-wise boosting with random features. For general loss functions, we show that fitting random feature residual blocks reduces to solving a quadratically constrained least squares problem. Through extensive numerical experiments on tabular datasets for both regression and classification, we show that RFRBoost significantly outperforms RFNNs and end-to-end trained MLP ResNets in the small- to medium-scale regime where RFNNs are typically applied. Moreover, RFRBoost offers substantial computational benefits, and theoretical guarantees stemming from boosting theory.

Theory · Learning Theory

Yannis Montreuil, Axel Carlier, Lai Xing Ng, Wei Tsang Ooi

Two-stage Learning-to-Defer (L2D) enables optimal task delegation by assigning each input to either a fixed main model or one of several offline experts, supporting reliable decision-making in complex, multi-agent environments. However, existing L2D frameworks assume clean inputs and are vulnerable to adversarial perturbations that can manipulate query allocation—causing costly misrouting or expert overload. We present the first comprehensive study of adversarial robustness in two-stage L2D systems. We introduce two novel attack strategies—untargeted and targeted—which respectively disrupt optimal allocations or force queries to specific agents. To defend against such threats, we propose SARD, a convex learning algorithm built on a family of surrogate losses that are provably Bayes-consistent and $(\mathcal{R}, \mathcal{G})$-consistent. These guarantees hold across classification, regression, and multi-task settings. Empirical results demonstrate that SARD significantly improves robustness under adversarial attacks while maintaining strong clean performance, marking a critical step toward secure and trustworthy L2D deployment.

Optimization · Zero-order and Black-box Optimization

Yuya Hikima, Hiroshi Sawada, Akinori Fujino

In this study, we tackle an optimization problem with a known function and an unknown decision-dependent distribution, which arises in a variety of applications and is often referred to as a performative prediction problem.To solve the problem, several zeroth-order methods have been developed because the gradient of the objective function cannot be obtained explicitly due to the unknown distribution.Although these methods have theoretical convergence, they cannot utilize the information on the known function, which limits their efficiency in reducing the objective value.To overcome this issue, we propose new zeroth-order methods that generate effective update directions by utilizing information on the known function.As theoretical results, we show the convergence of our methods to stationary points and provide the worst-case sample complexity analysis, which improves the state of the arts when the maximum objective value dominates the cube root of the decision variable's dimensionality in order.Our simulation experiments on multiple applications show that our methods output solutions with lower objective values than the existing zeroth-order methods do.

General Machine Learning · Everything Else

Zihan Zhou, Yang Zhou, Zijie Zhang, Lingjuan Lyu, Da Yan, Ruoming Jin, Dejing Dou

Machine unlearning (MU) aims to remove the influence of specific data points from trained models, enhancing compliance with privacy regulations. However, the vulnerability of basic MU models to malicious unlearning requests in adversarial learning environments has been largely overlooked. Existing adversarial MU attacks suffer from three key limitations: inflexibility due to pre-defined attack targets, inefficiency in handling multiple attack requests, and instability caused by non-convex loss functions. To address these challenges, we propose a Flexible, Efficient, and Stable Attack (DDPA). First, leveraging Carathéodory's theorem, we introduce a convex polyhedral approximation to identify points in the loss landscape where convexity approximately holds, ensuring stable attack performance. Second, inspired by simplex theory and John's theorem, we develop a regular simplex detection technique that maximizes coverage over the parameter space, improving attack flexibility and efficiency. We theoretically derive the proportion of the effective parameter space occupied by the constructed simplex. We evaluate the attack success rate of our DDPA method on real datasets against state-of-the-art machine unlearning attack methods. Our source code is available at https://github.com/zzz0134/DDPA.

Reinforcement Learning

Liyao Lyu, Jingrun Chen

We propose a *gradient-free* deep reinforcement learning algorithm to solve *high-dimensional*, finite-horizon stochastic control problems. Although the recently developed deep reinforcement learning framework has achieved great success in solving these problems, direct estimation of policy gradients from Monte Carlo sampling often suffers from high variance. To address this, we introduce the Momentum Consensus-Based Optimization (M-CBO) and Adaptive Momentum Consensus-Based Optimization (Adam-CBO) frameworks. These methods optimize policies using Monte Carlo estimates of the value function, rather than its gradients. Adjustable Gaussian noise supports efficient exploration, helping the algorithm converge to optimal policies in complex, nonconvex environments. Numerical results confirm the accuracy and scalability of our approach across various problem dimensions and show the potential for extension to mean-field control problems. Theoretically, we prove that M-CBO can converge to the optimal policy under some assumptions.

General Machine Learning · Everything Else

Xinyi Lu, Hao Zhang, Chenglin Li, Weijia Lu, ZHIFEI YANG, Wenrui Dai, xiaodong Zhang, Xiaofeng Ma, Can Zhang, Junni Zou 等

The significant communication overhead and client data heterogeneity have posed an important challenge to current federated learning (FL) paradigm. Existing compression-based and optimization-based FL algorithms typically focus on addressing either the model compression challenge or the data heterogeneity issue individually, rather than tackling both of them. In this paper, we observe that by symbolizing the client model updates to be uploaded (i.e., normalizing the magnitude for each model parameter at local clients), the model heterogeneity, essentially stemmed from data heterogeneity, can be mitigated, and thereby helping improve the overall generalization performance of the globally aggregated model at the server. Inspired with this observation, and further motivated by the success of Lion optimizer in achieving the optimal performance on most tasks in the centralized learning, we propose a new FL algorithm, called FedSMU, which simultaneously reduces the communication overhead and alleviates the data heterogeneity issue. Specifically, FedSMU splits the standard Lion optimizer into the local updates and global execution, where only the symbol of client model updates commutes between the client and server. We theoretically prove the convergence of FedSMU for the general non-convex settings. Through extensive experimental evaluations on several benchmark datasets, we demonstrate that our FedSMU algorithm not only reduces the communication overhead, but also achieves a better generalization performance than the other compression-based and optimization-based baselines.

Social Aspects · Privacy

Roie Reshef, Kfir Levy

This paper addresses the challenge of achieving Differential Privacy (DP) in Federated Learning (FL) under the partial-participation setting, where each machine participates in only some of training rounds.While earlier work achieved optimal performance and efficiency in full-participation scenarios, these methods could not extend effectively to cases with partial-participation.Our approach addresses this gap by introducing a novel noise-cancellation mechanism that ensures privacy without compromising convergence rates or computational efficiency.We analyze our method within the Stochastic Convex Optimization (SCO) framework and demonstrate that it achieves optimal performance for both homogeneous and heterogeneous data distributions.This work broadens the applicability of DP in FL, providing a practical and efficient solution for privacy-preserving learning in distributed systems with partial participation.

Deep Learning · Theory

Davide Sartor, Alberto Sinigaglia, Gian Antonio Susto

Imposing input-output constraints in multi-layer perceptrons (MLPs) plays a pivotal role in many real world applications. Monotonicity in particular is a common requirement in applications that need transparent and robust machine learning models. Conventional techniques for imposing monotonicity in MLPs by construction involve the use of non-negative weight constraints and bounded activation functions, which poses well known optimization challenges. In this work, we generalize previous theoretical results, showing that MLPs with non-negative weight constraint and activations that saturate on alternating sides are universal approximators for monotonic functions. Additionally, we show an equivalence between saturation side in the activations and sign of the weight constraint. This connection allows us to prove that MLPs with convex monotone activations and non-positive constrained weights also qualify as universal approximators, in contrast to their non-negative constrained counterparts. This results provide theoretical grounding to the empirical effectiveness observed in previous works, while leading to possible architectural simplification. Moreover, to further alleviate the optimization difficulties, we propose an alternative formulation that allows the network to adjust its activations according to the sign of the weights. This eliminates the requirement for weight reparameterization, easing initialization and improving training stability. Experimental evaluation reinforce the validity of the theoretical results, showing that our novel approach compares favorably to traditional monotonic architectures.

Theory · Optimization

Michael Sucker, Peter Ochs

Learning-to-optimize leverages machine learning to accelerate optimization algorithms. While empirical results show tremendous improvements compared to classical optimization algorithms, theoretical guarantees are mostly lacking, such that the outcome cannot be reliably assured. Especially, convergence is hardly studied in learning-to-optimize, because conventional convergence guarantees in optimization are based on geometric arguments, which cannot be applied easily to learned algorithms. Thus, we develop a probabilistic framework that resembles classical optimization and allows for transferring geometric arguments into learning-to-optimize. Based on our new proof-strategy, our main theorem is a generalization result for parametric classes of potentially non-smooth, non-convex loss functions and establishes the convergence of learned optimization algorithms to critical points with high probability. This effectively generalizes the results of a worst-case analysis into a probabilistic framework, and frees the design of the learned algorithm from using safeguards.

Optimization · Non-Convex

Kaheon Kim, Rentian Yao, Changbo Zhu, Xiaohui Chen

The optimal transport barycenter (a.k.a. Wasserstein barycenter) is a fundamental notion of averaging that extends from the Euclidean space to the Wasserstein space of probability distributions. Computation of the *unregularized* barycenter for discretized probability distributions on point clouds is a challenging task when the domain dimension $d > 1$. Most practical algorithms for approximating the barycenter problem are based on entropic regularization. In this paper, we introduce a nearly linear time $O(m \log{m})$ and linear space complexity $O(m)$ primal-dual algorithm, the *Wasserstein-Descent $\dot{\mathbb{H}}^1$-Ascent* (WDHA) algorithm, for computing the *exact* barycenter when the input probability density functions are discretized on an $m$-point grid. The key success of the WDHA algorithm hinges on alternating between two different yet closely related Wasserstein and Sobolev optimization geometries for the primal barycenter and dual Kantorovich potential subproblems. Under reasonable assumptions, we establish the convergence rate and iteration complexity of WDHA to its stationary point when the step size is appropriately chosen. Superior computational efficacy, scalability, and accuracy over the existing Sinkhorn-type algorithms are demonstrated on high-resolution (e.g., $1024 \times 1024$ images) 2D synthetic and real data.

Theory · Domain Adaptation and Transfer Learning

Tyler Ingebrand, Adam Thorpe, Ufuk Topcu

A central challenge in transfer learning is designing algorithms that can quickly adapt and generalize to new tasks without retraining. Yet, the conditions of when and how algorithms can effectively transfer to new tasks is poorly characterized. We introduce a geometric characterization of transfer in Hilbert spaces and define three types of inductive transfer: interpolation within the convex hull, extrapolation to the linear span, and extrapolation outside the span. We propose a method grounded in the theory of function encoders to achieve all three types of transfer. Specifically, we introduce a novel training scheme for function encoders using least-squares optimization, prove a universal approximation theorem for function encoders, and provide a comprehensive comparison with existing approaches such as transformers and meta-learning on four diverse benchmarks. Our experiments demonstrate that the function encoder outperforms state-of-the-art methods on four benchmark tasks and on all three types of transfer.

Optimization · Non-Convex

Siqi Zhang, Xing Huang, Feihu Huang

Bilevel optimization is widely applied in many machine learning tasks such as hyper-parameter learning and meta learning. Recently, many algorithms have been proposed to solve these bilevel optimization problems, which rely on the smoothness condition of objective functions of the bilevel optimization. In fact, some machine learning tasks such as learning language model do not satisfy the smoothness condition of objective functions. More recently, some methods have begun to study generalized smooth bilevel optimization. However, these proposed methods for generalized smooth bilevel optimization only focus on the (strongly) convex lower objective function. Meanwhile, these methods only consider the generalized-smooth upper-level objective, but still require the standard smooth lower-level objective in the bilevel optimization. To fill this gap, in the paper, thus we study the generalized-smooth bilevel optimization with the nonconvex lower-level objective function, where both upper-level and lower-level objectives are generalized-smooth. We propose an efficient single-loop Hessian/Jacobian-free penalty normalized gradient (i.e., PNGBiO) method. Moreover, we prove that our PNGBiO obtains a fast convergence rate of $O(\frac{1}{T^{1/4}})$ for finding a stationary solution, where $T$ denotes the iteration number. Meanwhile, we also propose a stochastic version of our PNGBiO (i.e., S-PNGBiO) method to solve stochastic bilevel problems, and prove that our S-PNGBiO has a fast convergence rate of $O(\frac{1}{T^{1/6}})$. Some experimental results on hyper-parameter learning and meta learning demonstrate efficiency of our proposed methods.

Optimization · Stochastic

Savelii Chezhegov, Klyukin Yaroslav, Andrei Semenov, Aleksandr Beznosikov, Alexander Gasnikov, Samuel Horváth, Martin Takac, Eduard Gorbunov

Methods with adaptive stepsizes, such as AdaGrad and Adam, are essential for training modern Deep Learning models, especially Large Language Models. Typically, the noise in the stochastic gradients is heavy-tailed for the later ones. Gradient clipping provably helps to achieve good high-probability convergence for such noises. However, despite the similarity between AdaGrad/Adam and Clip-SGD, the current understanding of the high-probability convergence of AdaGrad/Adam-type methods is limited in this case. In this work, we prove that AdaGrad/Adam (and their delayed version) can have provably bad high-probability convergence if the noise is heavy-tailed. We also show that gradient clipping fixes this issue, i.e., we derive new high-probability convergence bounds with polylogarithmic dependence on the confidence level for AdaGrad-Norm and Adam-Norm with clipping and with/without delay for smooth convex/non-convex stochastic optimization with heavy-tailed noise. We extend our results to the case of AdaGrad/Adam with delayed stepsizes. Our empirical evaluations highlight the superiority of clipped versions of AdaGrad/Adam in handling the heavy-tailed noise.

Optimization · Non-Convex

Han Zhou, dr. Jordy Van Landeghem, Teodora Popordanoska, Matthew B Blaschko

The selective classifier (SC) has been proposed for rank based uncertainty thresholding, which could have applications in safety critical areas such as medical diagnostics, autonomous driving, and the justice system. The Area Under the Risk-Coverage Curve (AURC) has emerged as the foremost evaluation metric for assessing the performance of SC systems. In this work, we present a formal statistical formulation of population AURC, presenting an equivalent expression that can be interpreted as a reweighted risk function. Through Monte Carlo methods, we derive empirical AURC plug-in estimators for finite sample scenarios. The weight estimators associated with these plug-in estimators are shown to be consistent, with low bias and tightly bounded mean squared error (MSE). The plug-in estimators are proven to converge at a rate of $\mathcal{O}(\sqrt{\ln(n)/n})$ demonstrating statistical consistency. We empirically validate the effectiveness of our estimators through experiments across multiple datasets, model architectures, and confidence score functions (CSFs), demonstrating consistency and effectiveness in fine-tuning AURC performance.

Theory · Online Learning and Bandits

Spencer Hutchinson, Mahnoosh Alizadeh

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.

Optimization · Non-Convex

Andi Han, Pierre-Louis Poirion, Akiko Takeda

Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian manifold structure and performing optimization intrinsically on the manifold. This approach typically involves computing a search direction in the tangent space and updating variables via a retraction operation. However, as the size of the variables increases, the computational cost of the retraction can become prohibitively high, limiting the applicability of Riemannian optimization to large-scale problems. To address this challenge and enhance scalability, we propose a novel approach that restricts each update on a random submanifold, thereby significantly reducing the per-iteration complexity. We introduce two sampling strategies for selecting the random submanifolds and theoretically analyze the convergence of the proposed methods. We provide convergence results for general nonconvex functions and functions that satisfy Riemannian Polyak–Łojasiewicz condition as well as for stochastic optimization settings. Additionally, we demonstrate how our approach can be generalized to quotient manifolds derived from the orthogonal manifold. Extensive experiments verify the benefits of the proposed method, across a wide variety of problems.

Deep Learning · Theory

Max Milkert, David Hyde, Forrest Laine

In a neural network with ReLU activations, the number of piecewise linear regions in the output can grow exponentially with depth.However, this is highly unlikely to happen when the initial parameters are sampled randomly, which therefore often leads to the use of networks that are unnecessarily large.To address this problem, we introduce a novel parameterization of the network that restricts its weights so that a depth $d$ network produces exactly $2^d$ linear regions at initialization and maintains those regions throughout training under the parameterization.This approach allows us to learn approximations of convex, one-dimensional functions that are several orders of magnitude more accurate than their randomly initialized counterparts.We further demonstrate a preliminary extension of our construction to multidimensional and non-convex functions, allowing the technique to replace traditional dense layers in various architectures.

Theory · Optimization

Martin Van Waerebeke, Marco Lorenzi, Giovanni Neglia, Kevin Scaman

Machine Unlearning (MU) aims at removing the influence of specific data points from a trained model, striving to achieve this at a fraction of the cost of full model retraining. In this paper, we analyze the efficiency of unlearning methods and establish the first upper and lower bounds on minimax computation times for this problem, characterizing the performance of the most efficient algorithm against the most difficult objective function. Specifically, for strongly convex objective functions and under the assumption that the forget data is inaccessible to the unlearning method, we provide a phase diagram for the *unlearning complexity ratio*---a novel metric that compares the computational cost of the best unlearning method to full model retraining. The phase diagram reveals three distinct regimes: one where unlearning at a reduced cost is infeasible, another where unlearning is trivial because adding noise suffices, and a third where unlearning achieves significant computational advantages over retraining. These findings highlight the critical role of factors such as data dimensionality, the number of samples to forget, and privacy constraints in determining the practical feasibility of unlearning.

General Machine Learning · Online Learning, Active Learning and Bandits

Yuxiao Wen

In combinatorial semi-bandits, a learner repeatedly selects from a combinatorial decision set of arms, receives the realized sum of rewards, and observes the rewards of the individual selected arms as feedback. In this paper, we extend this framework to include \emph{graph feedback}, where the learner observes the rewards of all neighboring arms of the selected arms in a feedback graph $G$. We establish that the optimal regret over a time horizon $T$ scales as $\widetilde{\Theta}(S\sqrt{T}+\sqrt{\alpha ST})$, where $S$ is the size of the combinatorial decisions and $\alpha$ is the independence number of $G$. This result interpolates between the known regrets $\widetilde\Theta(S\sqrt{T})$ under full information (i.e., $G$ is complete) and $\widetilde\Theta(\sqrt{KST})$ under the semi-bandit feedback (i.e., $G$ has only self-loops), where $K$ is the total number of arms. A key technical ingredient is to realize a convexified action using a random decision vector with negative correlations. We also show that online stochastic mirror descent (OSMD) that only realizes convexified actions in expectation is suboptimal.