NeurIPS 2024 论文列表

Bi-level optimizaiton (BO) has become a fundamental mathematical framework for addressing hierarchical machine learning problems. As deep learning models continue to grow in size, the demand for scalable bi-level optimization has become increasingly critical. Traditional gradient-based bi-level optimizaiton algorithms, due to their inherent characteristics, are ill-suited to meet the demands of large-scale applications. In this paper, we introduce **F**orward **G**radient **U**nrolling with **F**orward **G**radient, abbreviated as **$($FG$)^2$U**, which achieves an unbiased stochastic approximation of the meta gradient for bi-level optimizaiton. $($FG$)^2$U circumvents the memory and approximation issues associated with classical bi-level optimizaiton approaches, and delivers significantly more accurate gradient estimates than existing large-scale bi-level optimizaiton approaches. Additionally, $($FG$)^2$U is inherently designed to support parallel computing, enabling it to effectively leverage large-scale distributed computing systems to achieve significant computational efficiency. In practice, $($FG$)^2$U and other methods can be strategically placed at different stages of the training process to achieve a more cost-effective two-phase paradigm. Further, $($FG$)^2$U is easy to implement within popular deep learning frameworks, and can be conveniently adapted to address more challenging zeroth-order bi-level optimizaiton scenarios. We provide a thorough convergence analysis and a comprehensive practical discussion for $($FG$)^2$U, complemented by extensive empirical evaluations, showcasing its superior performance in diverse large-scale bi-level optimizaiton tasks.

Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian manifolds. We present several hypergradient estimation strategies on manifolds and analyze their estimation errors. Furthermore, we provide comprehensive convergence and complexity analyses for the proposed hypergradient descent algorithm on manifolds. We also extend our framework to encompass stochastic bilevel optimization and incorporate the use of general retraction. The efficacy of the proposed framework is demonstrated through several applications.

Approximate Natural Gradient Descent (NGD) methods are an important family of optimisers for deep learning models, which use approximate Fisher information matrices to pre-condition gradients during training. The empirical Fisher (EF) method approximates the Fisher information matrix empirically by reusing the per-sample gradients collected during back-propagation. Despite its ease of implementation, the EF approximation has its theoretical and practical limitations. This paper investigates the *inversely-scaled projection* issue of EF, which is shown to be a major cause of its poor empirical approximation quality. An improved empirical Fisher (iEF) method is proposed to address this issue, which is motivated as a generalised NGD method from a loss reduction perspective, meanwhile retaining the practical convenience of EF. The exact iEF and EF methods are experimentally evaluated using practical deep learning setups, including widely-used setups for parameter-efficient fine-tuning of pre-trained models (T5-base with LoRA and Prompt-Tuning on GLUE tasks, and ViT with LoRA for CIFAR100). Optimisation experiments show that applying exact iEF directly as an optimiser provides strong convergence and generalisation. It achieves the best test performance and the lowest training loss for the majority of the tasks, even when compared to well-tuned AdamW/Adafactor baselines. Additionally, under a novel empirical evaluation framework, the proposed iEF method shows consistently better approximation quality to exact Natural Gradient updates than both the EF and the more expensive sampled Fisher methods, meanwhile demonstrating the superior property of being robust to the choice of damping across tasks and training stages. Improving existing approximate NGD optimisers with iEF is expected to lead to better convergence and robustness. Furthermore, the iEF method also serves as a better approximation method to the Fisher information matrix itself, which enables the improvement of a variety of Fisher-based methods, not limited to the scope of optimisation.

We study a class of optimization problems in the Wasserstein space (the space of probability measures) where the objective function is nonconvex along generalized geodesics. Specifically, the objective exhibits some difference-of-convex structure along these geodesics. The setting also encompasses sampling problems where the logarithm of the target distribution is difference-of-convex. We derive multiple convergence insights for a novel semi Forward-Backward Euler scheme under several nonconvex (and possibly nonsmooth) regimes. Notably, the semi Forward-Backward Euler is just a slight modification of the Forward-Backward Euler whose convergence is---to our knowledge---still unknown in our very general non-geodesically-convex setting.

Transformers excel at *in-context learning* (ICL)---learning from demonstrations without parameter updates---but how they do so remains a mystery. Recent work suggests that Transformers may internally run Gradient Descent (GD), a first-order optimization method, to perform ICL. In this paper, we instead demonstrate that Transformers learn to approximate second-order optimization methods for ICL. For in-context linear regression, Transformers share a similar convergence rate as *Iterative Newton's Method*, both *exponentially* faster than GD. Empirically, predictions from successive Transformer layers closely match different iterations of Newton’s Method linearly, with each middle layer roughly computing 3 iterations; thus, Transformers and Newton’s method converge at roughly the same rate. In contrast, Gradient Descent converges exponentially more slowly. We also show that Transformers can learn in-context on ill-conditioned data, a setting where Gradient Descent struggles but Iterative Newton succeeds. Finally, to corroborate our empirical findings, we prove that Transformers can implement $k$ iterations of Newton's method with $k + \mathcal O(1)$ layers.

We address the problem of optimizing over functions defined on node subsets in a graph. The optimization of such functions is often a non-trivial task given their combinatorial, black-box and expensive-to-evaluate nature. Although various algorithms have been introduced in the literature, most are either task-specific or computationally inefficient and only utilize information about the graph structure without considering the characteristics of the function. To address these limitations, we utilize Bayesian Optimization (BO), a sample-efficient black-box solver, and propose a novel framework for combinatorial optimization on graphs. More specifically, we map each $k$-node subset in the original graph to a node in a new combinatorial graph and adopt a local modeling approach to efficiently traverse the latter graph by progressively sampling its subgraphs using a recursive algorithm. Extensive experiments under both synthetic and real-world setups demonstrate the effectiveness of the proposed BO framework on various types of graphs and optimization tasks, where its behavior is analyzed in detail with ablation studies.

Large language models (LLMs) have shown remarkable progress in code generation, but their generated code often suffers from inefficiency, resulting in longer execution times and higher memory consumption. To address this issue, we propose EffiLearner, a self-optimization framework that utilizes execution overhead profiles to improve the efficiency of LLM-generated code. EffiLearner first generates code using an LLM, then executes it locally to capture execution time and memory usage profiles. These profiles are fed back to the LLM, which then revises the code to reduce overhead. To evaluate the effectiveness of EffiLearner, we conduct extensive experiments on EffiBench and two commonly used code generation benchmarks with 16 open-source and 6 closed-source models. Our evaluation results demonstrate that through iterative self-optimization, EffiLearner significantly enhances the efficiency of LLM-generated code. For example, the execution time (ET) of StarCoder2-15B for the EffiBench decreases from 0.93 (s) to 0.12 (s) which reduces 87.1\% execution time requirement compared with the initial code. The total memory usage (TMU) of StarCoder2-15B also decreases from 22.02 (Mb*s) to 2.03 (Mb*s), which decreases 90.8\% total memory consumption during the execution process.

Conformal prediction converts nearly any point estimator into a prediction interval under standard assumptions while ensuring valid coverage. However, the extensive computational demands of full conformal prediction are daunting in practice, as it necessitates a comprehensive number of trainings across the entire latent label space. Unfortunately, existing efforts to expedite conformalization often carry strong assumptions and are developed specifically for certain models, or they only offer approximate solution sets. To address this gap, we develop a method for fast exact conformalization of generalized statistical estimation. Our analysis reveals that the structure of the solution path is inherently piecewise smooth, and indicates that utilizing second-order information of difference equations suffices to approximate the entire solution spectrum arbitrarily. We provide a unified view that not only encompasses existing work but also attempts to offer geometric insights. Practically, our framework integrates seamlessly with well-studied numerical solvers. The significant speedups of our algorithm as compared to the existing standard methods are demonstrated across numerous benchmarks.

Classification with rejection emerges as a learning paradigm which allows models to abstain from making predictions. The predominant approach is to alter the supervised learning pipeline by augmenting typical loss functions, letting model rejection incur a lower loss than an incorrect prediction. Instead, we propose a different distributional perspective, where we seek to find an idealized data distribution which maximizes a pretrained model's performance. This can be formalized via the optimization of a loss's risk with a $ \phi$-divergence regularization term. Through this idealized distribution, a rejection decision can be made by utilizing the density ratio between this distribution and the data distribution. We focus on the setting where our $ \phi $-divergences are specified by the family of $ \alpha $-divergence. Our framework is tested empirically over clean and noisy datasets.

Algorithms with (machine-learned) predictions is a powerful framework for combining traditional worst-case algorithms with modern machine learning. However, the vast majority of work in this space assumes that the prediction itself is non-probabilistic, even if it is generated by some stochastic process (such as a machine learning system). This is a poor fit for modern ML, particularly modern neural networks, which naturally generate a *distribution*. We initiate the study of algorithms with *distributional* predictions, where the prediction itself is a distribution. We focus on one of the simplest yet fundamental settings: binary search (or searching a sorted array). This setting has one of the simplest algorithms with a point prediction, but what happens if the prediction is a distribution? We show that this is a richer setting: there are simple distributions where using the classical prediction-based algorithm with any single prediction does poorly. Motivated by this, as our main result, we give an algorithm with query complexity $O(H(p) + \log \eta)$, where $H(p)$ is the entropy of the true distribution $p$ and $\eta$ is the earth mover's distance between $p$ and the predicted distribution $\hat p$. This also yields the first *distributionally-robust* algorithm for the classical problem of computing an optimal binary search tree given a distribution over target keys. We complement this with a lower bound showing that this query complexity is essentially optimal (up to constants), and experiments validating the practical usefulness of our algorithm.

Radiation therapy, treating over half of all cancer patients, involves using specialized machines to direct high-energy beams at tumors, aiming to damage cancer cells while minimizing harm to nearby healthy tissues. Customizing the shape and intensity of radiation beams for each patient leads to solving large-scale constrained optimization problems that need to be solved within tight clinical time-frame. At the core of these challenges is a large matrix that is commonly sparsified for computational efficiency by neglecting small elements. Such a crude approximation can degrade the quality of treatment, potentially causing unnecessary radiation exposure to healthy tissues—this may lead to significant radiation-induced side effects—or delivering inadequate radiation to the tumor, which is crucial for effective tumor treatment. In this work, we demonstrate, for the first time, that randomized sketch tools can effectively sparsify this matrix without sacrificing treatment quality. We also develop a novel randomized sketch method with desirable theoretical guarantees that outperforms existing techniques in practical application. Beyond developing a novel randomized sketch method, this work emphasizes the potential of harnessing scientific computing tools, crucial in today's big data analysis, to tackle computationally intensive challenges in healthcare. The application of these tools could have a profound impact on the lives of numerous cancer patients. Code and sample data available at https://github.com/PortPy-Project/CompressRTP

Large language models have demonstrated remarkable capabilities but their performance is heavily reliant on effective prompt engineering. Automatic prompt optimization (APO) methods are designed to automate this and can be broadly categorized into those targeting instructions (instruction optimization, IO) vs. those targeting exemplars (exemplar optimization, EO). Despite their shared objective, these have evolved rather independently, with IO receiving more research attention recently. This paper seeks to bridge this gap by comprehensively comparing the performance of representative IO and EO techniques both isolation and combination on a diverse set of challenging tasks. Our findings reveal that intelligently reusing model-generated input-output pairs obtained from evaluating prompts on the validation set as exemplars, consistently improves performance on top of IO methods but is currently under-investigated. We also find that despite the recent focus on IO, how we select exemplars can outweigh how we optimize instructions, with EO strategies as simple as random search outperforming state-of-the-art IO methods with seed instructions without any optimization. Moreover, we observe a synergy between EO and IO, with optimal combinations surpassing the individual contributions. We conclude that studying exemplar optimization both as a standalone method and its optimal combination with instruction optimization remain a crucial aspect of APO and deserve greater consideration in future research, even in the era of highly capable instruction-following models.

We consider the decentralized stochastic asynchronous optimization setup, where many workers asynchronously calculate stochastic gradients and asynchronously communicate with each other using edges in a multigraph. For both homogeneous and heterogeneous setups, we prove new time complexity lower bounds under the assumption that computation and communication speeds are bounded by constants. After that, we developed a new nearly optimal method, Fragile SGD, and a new optimal method, Amelie SGD, that converge with arbitrary heterogeneous computation and communication speeds and match our lower bounds (up to a logarithmic factor in the homogeneous setting). Our time complexities are new, nearly optimal, and provably improve all previous asynchronous/synchronous stochastic methods in the decentralized setup.

We consider the task of minimizing the sum of convex functions stored in a decentralized manner across the nodes of a communication network. This problem is relatively well-studied in the scenario when the objective functions are smooth, or the links of the network are fixed in time, or both. In particular, lower bounds on the number of decentralized communications and (sub)gradient computations required to solve the problem have been established, along with matching optimal algorithms. However, the remaining and most challenging setting of non-smooth decentralized optimization over time-varying networks is largely underexplored, as neither lower bounds nor optimal algorithms are known in the literature. We resolve this fundamental gap with the following contributions: (i) we establish the first lower bounds on the communication and subgradient computation complexities of solving non-smooth convex decentralized optimization problems over time-varying networks; (ii) we develop the first optimal algorithm that matches these lower bounds and offers substantially improved theoretical performance compared to the existing state of the art.

This paper addresses the minimization of the sum of strongly convex, smooth functions over a network of agents without a centralized server. Existing decentralized algorithms require knowledge of functions and network parameters, such as the Lipschitz constant of the global gradient and/or network connectivity, for hyperparameter tuning. Agents usually cannot access this information, leading to conservative selections and slow convergence or divergence. This paper introduces a decentralized algorithm that eliminates the need for specific parameter tuning. Our approach employs an operator splitting technique with a novel variable metric, enabling a local backtracking line-search to adaptively select the stepsize without global information or extensive communications. This results in favorable convergence guarantees and dependence on optimization and network parameters compared to existing nonadaptive methods. Notably, our method is the first adaptive decentralized algorithm that achieves linear convergence for strongly convex, smooth objectives. Preliminary numerical experiments support our theoretical findings, demonstrating superior performance in convergence speed and scalability.

In this paper, we formalize the active set ordering problem, which involves actively discovering a set of inputs based on their orderings determined by expensive evaluations of a blackbox function. We then propose the mean prediction (MP) algorithm and theoretically analyze it in terms of the regret of predicted pairwise orderings between inputs. Notably, as a special case of this framework, we can cast Bayesian optimization as an active set ordering problem by recognizing that maximizers can be identified solely by comparison rather than by precisely estimating the function evaluations. As a result, we are able to construct the popular Gaussian process upper confidence bound (GP-UCB) algorithm through the lens of ordering with several nuanced insights. We empirically validate the performance of our proposed solution using various synthetic functions and real-world datasets.

Brain stimulation has the potential to create desired neural population activity states. However, it is challenging to search the large space of stimulation parameters, for example, selecting which subset of electrodes to be used for stimulation. In this scenario, creating a model that maps the configuration of stimulation parameters to the brain’s response can be beneficial. Training such an expansive model usually requires more stimulation-response samples than can be collected in a given experimental session. Furthermore, changes in the properties of the recorded activity over time can make it challenging to merge stimulation-response samples across sessions. To address these challenges, we propose MiSO (MicroStimulation Optimization), a closed-loop stimulation framework to drive neural population activity toward specified states by optimizing over a large stimulation parameter space. MiSO consists of three key components: 1) a neural activity alignment method to merge stimulation-response samples across sessions, 2) a statistical model trained on the merged samples to predict the brain's response to untested stimulation parameter configurations, and 3) an online optimization algorithm to adaptively update the stimulation parameter configuration based on the model's predictions. In this study, we implemented MiSO with a factor analysis (FA) based alignment method, a convolutional neural network (CNN), and an epsilon greedy optimization algorithm. We tested MiSO in closed-loop experiments using electrical microstimulation in the prefrontal cortex of a non-human primate. Guided by the CNN predictions, MiSO successfully searched amongst thousands of stimulation parameter configurations to drive the neural population activity toward specified states. More broadly, MiSO increases the clinical viability of neuromodulation technologies by enabling the use of many-fold larger stimulation parameter spaces.

Multi-block minimax bilevel optimization has been studied recently due to its great potential in multi-task learning, robust machine learning, and few-shot learning. However, due to the complex three-level optimization structure, existing algorithms often suffer from issues such as high computing costs due to the second-order model derivatives or high memory consumption in storing all blocks' parameters. In this paper, we tackle these challenges by proposing two novel fully first-order algorithms named FOSL and MemCS. FOSL features a fully single-loop structure by updating all three variables simultaneously, and MemCS is a memory-efficient double-loop algorithm with cold-start initialization. We provide a comprehensive convergence analysis for both algorithms under full and partial block participation, and show that their sample complexities match or outperform those of the same type of methods in standard bilevel optimization. We evaluate our methods in two applications: the recently proposed multi-task deep AUC maximization and a novel rank-based robust meta-learning. Our methods consistently improve over existing methods with better performance over various datasets.

Distributed learning has emerged as a leading paradigm for training large machine learning models. However, in real-world scenarios, participants may be unreliable or malicious, posing a significant challenge to the integrity and accuracy of the trained models. Byzantine fault tolerance mechanisms have been proposed to address these issues, but they often assume full participation from all clients, which is not always practical due to the unavailability of some clients or communication constraints. In our work, we propose the first distributed method with client sampling and provable tolerance to Byzantine workers. The key idea behind the developed method is the use of gradient clipping to control stochastic gradient differences in recursive variance reduction. This allows us to bound the potential harm caused by Byzantine workers, even during iterations when all sampled clients are Byzantine. Furthermore, we incorporate communication compression into the method to enhance communication efficiency. Under general assumptions, we prove convergence rates for the proposed method that match the existing state-of-the-art (SOTA) theoretical results. We also propose a heuristic on how to adjust any Byzantine-robust method to a partial participation scenario via clipping.