ICML 2024 Papers

We study the problem of obtaining optimal and realistic prescriptions when using ReLU networks for data-driven decision-making. In this setting, the network is used to predict a quantity of interest and then is optimized to retrieve the decisions that maximize the quantity (e.g. find the best prices that maximize revenue). However, optimizing over-parameterized models often produces unrealistic prescriptions, far from the data manifold. This phenomenon is known as the Optimizer's Curse. To tackle this problem, we model the requirement for the resulting decisions to align with the data manifold as a tractable optimization constraint. This is achieved by reformulating the highly nonlinear Local Outlier Factor (LOF) metric as a single linear or quadratic constraint. To solve the problem efficiently for large networks, we propose an adaptive sampling algorithm that reduces the initial hard-to-solve optimization problem into a small number of significantly easier-to-solve problems by restricting the decision space to realistic polytopes, i.e. polytopes of the decision space that contain at least one realistic data point. Experiments on publicly available networks demonstrate the efficacy and scalability of our approach.

Coreset selection is powerful in reducing computational costs and accelerating data processing for deep learning algorithms. It strives to identify a small subset from large-scale data, so that training only on the subset practically performs on par with full data. Practitioners regularly desire to identify the smallest possible coreset in realistic scenes while maintaining comparable model performance, to minimize costs and maximize acceleration. Motivated by this desideratum, for the first time, we pose the problem of refined coreset selection, in which the minimal coreset size under model performance constraints is explored. Moreover, to address this problem, we propose an innovative method, which maintains optimization priority order over the model performance and coreset size, and efficiently optimizes them in the coreset selection procedure. Theoretically, we provide the convergence guarantee of the proposed method. Empirically, extensive experiments confirm its superiority compared with previous strategies, often yielding better model performance with smaller coreset sizes. The implementation is available at https://github.com/xiaoboxia/LBCS.

Graph embeddings have emerged as a powerful tool for understanding the structure of graphs. Unlike classical spectral methods, recent methods such as DeepWalk, Node2Vec, etc. are based on solving nonlinear optimization problems on the graph, using local information obtained by performing random walks. These techniques have empirically been shown to produce ``better'' embeddings than their classical counterparts. However, due to their reliance on solving a nonconvex optimization problem, obtaining theoretical guarantees on the properties of the solution has remained a challenge, even for simple classes of graphs. In this work, we show convergence properties for the DeepWalk algorithm on graphs obtained from the Stochastic Block Model (SBM). Despite being simplistic, the SBM has proved to be a classic model for analyzing the behavior of algorithms on large graphs. Our results mirror the existing ones for spectral embeddings on SBMs, showing that even in the case of one-dimensional embeddings, the output of the DeepWalk algorithm provably recovers the cluster structure with high probability.

Large language models based on the Transformer architecture have demonstrated impressive capabilities to learn in context. However, existing theoretical studies on how this phenomenon arises are limited to the dynamics of a single layer of attention trained on linear regression tasks. In this paper, we study the optimization of a Transformer consisting of a fully connected layer followed by a linear attention layer. The MLP acts as a common nonlinear representation or feature map, greatly enhancing the power of in-context learning. We prove in the mean-field and two-timescale limit that the infinite-dimensional loss landscape for the distribution of parameters, while highly nonconvex, becomes quite benign. We also analyze the second-order stability of mean-field dynamics and show that Wasserstein gradient flow almost always avoids saddle points. Furthermore, we establish novel methods for obtaining concrete improvement rates both away from and near critical points. This represents the first saddle point analysis of mean-field dynamics in general and the techniques are of independent interest.

We design differentially private regret-minimizing algorithms in the online convex optimization (OCO) framework. Unlike recent results, our algorithms and analyses do not require smoothness, thus yielding the first private regret bounds with an optimal leading-order term for non-smooth loss functions. Additionally, even for smooth losses, the resulting regret guarantees improve upon previous results in terms their dependence of dimension. Our results provide the best known rates for DP-OCO in all practical regimes of the privacy parameter, barring when it is exceptionally small. The principal innovation in our algorithm design is the use of sampling from strongly log-concave densities which satisfy the Log-Sobolev Inequality. The resulting concentration of measure allows us to obtain a better trade-off for the dimension factors than prior work, leading to improved results. Following previous works on DP-OCO, the proposed algorithm explicitly limits the number of switches via rejection sampling. Thus, independently of privacy constraints, the algorithm also provides improved results for online convex optimization with a switching budget.

Bayesian Optimization (BO) is a technique for sample-efficient black-box optimization that employs probabilistic models to identify promising input for evaluation. When dealing with composite-structured functions, such as $f=g \circ h$, evaluating a specific location $x$ yields observations of both the final outcome $f(x) = g(h(x))$ as well as the intermediate output(s) $h(x)$. Previous research has shown that integrating information from these intermediate outputs can enhance BO performance substantially. However, existing methods struggle if the outputs $h(x)$ are high-dimensional. Many relevant problems fall into this setting, including in the context of generative AI, molecular design, or robotics. To effectively tackle these challenges, we introduce Joint Composite Latent Space Bayesian Optimization (JoCo), a novel framework that jointly trains neural network encoders and probabilistic models to adaptively compress high-dimensional input and output spaces into manageable latent representations. This enables effective BO on these compressed representations, allowing JoCo to outperform other state-of-the-art methods in high-dimensional BO on a wide variety of simulated and real-world problems.

We study nonconvex zeroth-order optimization (ZOO) in a high-dimensional space $\mathbb R^d$ for functions with approximately $s$-sparse gradients. To reduce the dependence on the dimensionality $d$ in the query complexity, high-dimensional ZOO methods seek to leverage gradient sparsity to design gradient estimators. The previous best method needs $O\big(s\log\frac ds\big)$ queries per step to achieve $O\big(\frac1T\big)$ rate of convergence w.r.t. the number T of steps. In this paper, we propose *Gradient Compressed Sensing* (GraCe), a query-efficient and accurate estimator for sparse gradients that uses only $O\big(s\log\log\frac ds\big)$ queries per step and still achieves $O\big(\frac1T\big)$ rate of convergence. To our best knowledge, we are the first to achieve a *double-logarithmic* dependence on $d$ in the query complexity under weaker assumptions. Our proposed GraCe generalizes the Indyk–Price–Woodruff (IPW) algorithm in compressed sensing from linear measurements to nonlinear functions. Furthermore, since the IPW algorithm is purely theoretical due to its impractically large constant, we improve the IPW algorithm via our *dependent random partition* technique together with our corresponding novel analysis and successfully reduce the constant by a factor of nearly $4300$. Our GraCe is not only theoretically query-efficient but also achieves strong empirical performance. We benchmark our GraCe against $12$ existing ZOO methods with $10000$-dimensional functions and demonstrate that GraCe significantly outperforms existing methods. Our code is publicly available at https://github.com/q-rz/ICML24-GraCe.

Despite large neural networks demonstrating remarkable abilities to complete different tasks, they require excessive memory usage to store the optimization states for training. To alleviate this, the low-rank adaptation (LoRA) is proposed to reduce the optimization states by training fewer parameters. However, LoRA restricts overall weight update matrices to be low-rank, limiting the model performance. In this work, we investigate the dynamics of LoRA and identify that it can be approximated by a random projection. Based on this observation, we propose Flora, which is able to achieve high-rank updates by resampling the projection matrices while enjoying the sublinear space complexity of optimization states. We conduct experiments across different tasks and model architectures to verify the effectiveness of our approach.

The maximal coding rate reduction (MCR$^2$) objective for learning structured and compact deep representations is drawing increasing attention, especially after its recent usage in the derivation of fully explainable and highly effective deep network architectures. However, it lacks a complete theoretical justification: only the properties of its global optima are known, and its global landscape has not been studied. In this work, we give a complete characterization of the properties of all its local and global optima as well as other types of critical points. Specifically, we show that each (local or global) maximizer of the MCR$^2$ problem corresponds to a low-dimensional, discriminative, and diverse representation, and furthermore, each critical point of the objective is either a local maximizer or a strict saddle point. Such a favorable landscape makes MCR$^2$ a natural choice of objective for learning diverse and discriminative representations via first-order optimization. To further verify our theoretical findings, we illustrate these properties with extensive experiments on both synthetic and real data sets.

In this paper we theoretically show that interior-point methods based on self-concordant barriers possess favorable global complexity beyond their standard application area of convex optimization. To do that we propose first- and second-order methods for non-convex optimization problems with general convex set constraints and linear constraints. Our methods attain a suitably defined class of approximate first- or second-order KKT points with the worst-case iteration complexity similar to unconstrained problems, namely $O(\varepsilon^{-2})$ (first-order) and $O(\varepsilon^{-3/2})$ (second-order), respectively.

We consider Bayesian optimization using Gaussian Process models, also referred to as kernel-based bandit optimization. We study the methodology of exploring the domain using random samples drawn from a distribution. We show that this random exploration approach achieves the optimal error rates. Our analysis is based on novel concentration bounds in an infinite dimensional Hilbert space established in this work, which may be of independent interest. We further develop an algorithm based on random exploration with domain shrinking and establish its order-optimal regret guarantees under both noise-free and noisy settings. In the noise-free setting, our analysis closes the existing gap in regret performance under a mild assumption on the underlying function and thereby *partially resolves a COLT open problem*. The proposed algorithm also enjoys a computational advantage over prevailing methods due to the random exploration that obviates the expensive optimization of a non-convex acquisition function for choosing the query points at each iteration.

Dynamic Sparse Training (DST) is an effective approach for addressing the substantial training resource requirements posed by the ever-increasing size of the Deep Neural Networks (DNNs). Characterized by its dynamic "train-prune-grow'' schedule during training, DST implicitly develops a bi-level structure for training the weights while discovering a subnetwork topology. However, such a structure is consistently overlooked by the current DST algorithms for further optimization opportunities, and these algorithms, on the other hand, solely optimize the weights while determining masks heuristically. In this paper, we extensively study DST algorithms and argue that the training scheme of DST naturally forms a bi-level problem in which the updating of weight and mask is interdependent. Based on this observation, we introduce a novel efficient training framework called BiDST, which for the first time, introduces bi-level optimization methodology into dynamic sparse training domain. Unlike traditional partial-heuristic DST schemes, which suffer from sub-optimal search efficiency for masks and miss the opportunity to fully explore the topological space of neural networks, BiDST excels at discovering excellent sparse patterns by optimizing mask and weight simultaneously, resulting in maximum 2.62% higher accuracy, 2.1$\times$ faster execution speed, and 25$\times$ reduced overhead. Code available at https://github.com/jjsrf/BiDST-ICML2024.

Bayesian optimization is a powerful framework for optimizing functions that are expensive or time-consuming to evaluate. Recent work has considered Bayesian optimization of function networks (BOFN), where the objective function is given by a network of functions, each taking as input the output of previous nodes in the network as well as additional parameters. Leveraging this network structure has been shown to yield significant performance improvements. Existing BOFN algorithms for general-purpose networks evaluate the full network at each iteration. However, many real-world applications allow for evaluating nodes individually. To exploit this, we propose a novel knowledge gradient acquisition function that chooses which node and corresponding inputs to evaluate in a cost-aware manner, thereby reducing query costs by evaluating only on a part of the network at each step. We provide an efficient approach to optimizing our acquisition function and show that it outperforms existing BOFN methods and other benchmarks across several synthetic and real-world problems. Our acquisition function is the first to enable cost-aware optimization of a broad class of function networks.

This paper addresses the challenge of preserving privacy in Federated Learning (FL) within centralized systems, focusing on both trusted and untrusted server scenarios. We analyze this setting within the Stochastic Convex Optimization (SCO) framework, and devise methods that ensure Differential Privacy (DP) while maintaining optimal convergence rates for homogeneous and heterogeneous data distributions. Our approach, based on a recent stochastic optimization technique, offers linear computational complexity, comparable to non-private FL methods, and reduced gradient obfuscation. This work enhances the practicality of DP in FL, balancing privacy, efficiency, and robustness in a variety of server trust environments.

Data-parallel SGD is the de facto algorithm for distributed optimization, especially for large scale machine learning. Despite its merits, communication bottleneck is one of its persistent issues. Most compression schemes to alleviate this either assume noiseless communication links, or fail to achieve good performance on practical tasks. In this paper, we close this gap and introduce **LASER**: **L**ine**A**r Compre**S**sion in Wir**E**less Dist**R**ibuted Optimization. LASER capitalizes on the inherent low-rank structure of gradients and transmits them efficiently over the noisy channels. Whilst enjoying theoretical guarantees similar to those of the classical SGD, LASER shows consistent gains over baselines on a variety of practical benchmarks. In particular, it outperforms the state-of-the-art compression schemes on challenging computer vision and GPT language modeling tasks. On the latter, we obtain 50-64% improvement in perplexity over our baselines for noisy channels.

The Gradient Descent-Ascent (GDA) algorithm, designed to solve minimax optimization problems, takes the descent and ascent steps either simultaneously (Sim-GDA) or alternately (Alt-GDA). While Alt-GDA is commonly observed to converge faster, the performance gap between the two is not yet well understood theoretically, especially in terms of global convergence rates. To address this theory-practice gap, we present fine-grained convergence analyses of both algorithms for strongly-convex-strongly-concave and Lipschitz-gradient objectives. Our new iteration complexity upper bound of Alt-GDA is strictly smaller than the lower bound of Sim-GDA; i.e., Alt-GDA is provably faster. Moreover, we propose Alternating-Extrapolation GDA (Alex-GDA), a general algorithmic framework that subsumes Sim-GDA and Alt-GDA, for which the main idea is to alternately take gradients from extrapolations of the iterates. We show that Alex-GDA satisfies a smaller iteration complexity bound, identical to that of the Extra-gradient method, while requiring less gradient computations. We also prove that Alex-GDA enjoys linear convergence for bilinear problems, for which both Sim-GDA and Alt-GDA fail to converge at all.

In federated learning (FL), data heterogeneity is the main reason that existing theoretical analyses are pessimistic about the convergence rate. In particular, for many FL algorithms, the convergence rate grows dramatically when the number of local updates becomes large, especially when the product of the gradient divergence and local Lipschitz constant is large. However, empirical studies can show that more local updates can improve the convergence rate even when these two parameters are large, which is inconsistent with the theoretical findings. This paper aims to bridge this gap between theoretical understanding and practical performance by providing a theoretical analysis from a new perspective on data heterogeneity. In particular, we propose a new and weaker assumption compared to the local Lipschitz gradient assumption, named the heterogeneity-driven pseudo-Lipschitz assumption. We show that this and the gradient divergence assumptions can jointly characterize the effect of data heterogeneity. By deriving a convergence upper bound for FedAvg and its extensions, we show that, compared to the existing works, local Lipschitz constant is replaced by the much smaller heterogeneity-driven pseudo-Lipschitz constant and the corresponding convergence upper bound can be significantly reduced for the same number of local updates, although its order stays the same. In addition, when the local objective function is quadratic, more insights on the impact of data heterogeneity can be obtained using the heterogeneity-driven pseudo-Lipschitz constant. For example, we can identify a region where FedAvg can outperform mini-batch SGD even when the gradient divergence can be arbitrarily large. Our findings are validated using experiments.

This work focuses on addressing two major challenges in the context of large-scale nonconvex Bi-Level Optimization (BLO) problems, which are increasingly applied in machine learning due to their ability to model nested structures. These challenges involve ensuring computational efficiency and providing theoretical guarantees. While recent advances in scalable BLO algorithms have primarily relied on lower-level convexity simplification, our work specifically tackles large-scale BLO problems involving nonconvexity in both the upper and lower levels. We simultaneously address computational and theoretical challenges by introducing an innovative single-loop gradient-based algorithm, utilizing the Moreau envelope-based reformulation, and providing non-asymptotic convergence analysis for general nonconvex BLO problems. Notably, our algorithm relies solely on first-order gradient information, enhancing its practicality and efficiency, especially for large-scale BLO learning tasks. We validate our approach's effectiveness through experiments on various synthetic problems, two typical hyper-parameter learning tasks, and a real-world neural architecture search application, collectively demonstrating its superior performance.

The current state-of-the-art theoretical analysis of Actor-Critic (AC) algorithms significantly lags in addressing the practical aspects of AC implementations. This crucial gap needs bridging to bring the analysis in line with practical implementations of AC. To address this, we advocate for considering the MMCLG criteria: **M**ulti-layer neural network parametrization for actor/critic, **M**arkovian sampling, **C**ontinuous state-action spaces, the performance of the **L**ast iterate, and **G**lobal optimality. These aspects are practically significant and have been largely overlooked in existing theoretical analyses of AC algorithms. In this work, we address these gaps by providing the first comprehensive theoretical analysis of AC algorithms that encompasses all five crucial practical aspects (covers MMCLG criteria). We establish global convergence sample complexity bounds of $\tilde{\mathcal{O}}\left( \epsilon^{-3} \right)$. We achieve this result through our novel use of the weak gradient domination property of MDP's and our unique analysis of the error in critic estimation.