NeurIPS 2024 论文列表

The Fisher information matrix can be used to characterize the local geometry of the parameter space of neural networks. It elucidates insightful theories and useful tools to understand and optimize neural networks. Given its high computational cost, practitioners often use random estimators and evaluate only the diagonal entries. We examine two popular estimators whose accuracy and sample complexity depend on their associated variances. We derive bounds of the variances and instantiate them in neural networks for regression and classification. We navigate trade-offs for both estimators based on analytical and numerical studies. We find that the variance quantities depend on the non-linearity w.r.t. different parameter groups and should not be neglected when estimating the Fisher information.

Bayesian optimization (BO) is a popular method for computationally expensive black-box optimization. However, traditional BO methods need to solve new problems from scratch, leading to slow convergence. Recent studies try to extend BO to a transfer learning setup to speed up the optimization, where search space transfer is one of the most promising approaches and has shown impressive performance on many tasks. However, existing search space transfer methods either lack an adaptive mechanism or are not flexible enough, making it difficult to efficiently identify promising search space during the optimization process. In this paper, we propose a search space transfer learning method based on Monte Carlo tree search (MCTS), called MCTS-transfer, to iteratively divide, select, and optimize in a learned subspace. MCTS-transfer can not only provide a well-performing search space for warm-start but also adaptively identify and leverage the information of similar source tasks to reconstruct the search space during the optimization process. Experiments on synthetic functions, real-world problems, Design-Bench and hyper-parameter optimization show that MCTS-transfer can demonstrate superior performance compared to other search space transfer methods under different settings. Our code is available at \url{https://github.com/lamda-bbo/mcts-transfer}.

Collaborative learning is an important tool to train multiple clients more effectively by enabling communication among clients. Identifying helpful clients, however, presents challenging and often introduces significant overhead. In this paper, we model **client-selection** and **model-training** as two interconnected optimization problems, proposing a novel bilevel optimization problem for collaborative learning. We introduce **CoBo**, a *scalable* and *elastic*, SGD-type alternating optimization algorithm that efficiently addresses these problem with theoretical convergence guarantees. Empirically, **CoBo** achieves superior performance, surpassing popular personalization algorithms by 9.3% in accuracy on a task with high heterogeneity, involving datasets distributed among 80 clients.

Augmented Lagrangian Methods (ALMs) are widely employed in solving constrained optimizations, and some efficient solvers are developed based on this framework. Under the quadratic growth assumption, it is known that the dual iterates and the Karush–Kuhn–Tucker (KKT) residuals of ALMs applied to conic programs converge linearly. In contrast, the convergence rate of the primal iterates has remained elusive. In this paper, we resolve this challenge by establishing new $\textit{quadratic growth}$ and $\textit{error bound}$ properties for primal and dual conic programs under the standard strict complementarity condition. Our main results reveal that both primal and dual iterates of the ALMs converge linearly contingent solely upon the assumption of strict complementarity and a bounded solution set. This finding provides a positive answer to an open question regarding the asymptotically linear convergence of the primal iterates of ALMs applied to conic optimization.

The necessity to align two graphs, minimizing a structural distance metric, is prevalent in biology, chemistry, recommender systems, and social network analysis. Due to the problem’s NP-hardness, prevailing graph alignment methods follow a modular and mediated approach, solving the problem by restricting to the domain of intermediary graph representations or products like embeddings, spectra, and graph signals. Restricting the problem to this intermediate space may distort the original problem and are hence predisposed to miss high-quality solutions. In this paper, we propose an unrestricted method, FUGAL, which finds a permutation matrix that maps one graph to another by directly operating on their adjacency matrices with judicious constraint relaxation. Extensive experimentation demonstrates that FUGAL consistently surpasses state-of-the-art graph alignment methods in accuracy across all benchmark datasets without encumbering efficiency.

In strategic classification, agents modify their features, at a cost, to obtain a positive classification outcome from the learner’s classifier, typically assuming agents have full knowledge of the deployed classifier. In contrast, we consider a Bayesian setting where agents have a common distributional prior on the classifier being used and agents manipulate their features to maximize their expected utility according to this prior. The learner can reveal truthful, yet not necessarily complete, information about the classifier to the agents, aiming to release just enough information to shape the agents' behavior and thus maximize accuracy. We show that partial information release can counter-intuitively benefit the learner’s accuracy, allowing qualified agents to pass the classifier while preventing unqualified agents from doing so. Despite the intractability of computing the best response of an agent in the general case, we provide oracle-efficient algorithms for scenarios where the learner’s hypothesis class consists of low-dimensional linear classifiers or when the agents’ cost function satisfies a sub-modularity condition. Additionally, we address the learner’s optimization problem, offering both positive and negative results on determining the optimal information release to maximize expected accuracy, particularly in settings where an agent’s qualification can be represented by a real-valued number.

Gradient descent and its variants are de facto standard algorithms for training machine learning models. As gradient descent is sensitive to its hyperparameters, we need to tune the hyperparameters carefully using a grid search. However, the method is time-consuming, particularly when multiple hyperparameters exist. Therefore, recent studies have analyzed parameter-free methods that adjust the hyperparameters on the fly. However, the existing work is limited to investigations of parameter-free methods for the stepsize, and parameter-free methods for other hyperparameters have not been explored. For instance, although the gradient clipping threshold is a crucial hyperparameter in addition to the stepsize for preventing gradient explosion issues, none of the existing studies have investigated parameter-free methods for clipped gradient descent. Therefore, in this study, we investigate the parameter-free methods for clipped gradient descent. Specifically, we propose Inexact Polyak Stepsize, which converges to the optimal solution without any hyperparameters tuning, and its convergence rate is asymptotically independent of $L$ under $L$-smooth and $(L_0, L_1)$-smooth assumptions of the loss function, similar to that of clipped gradient descent with well-tuned hyperparameters. We numerically validated our convergence results using a synthetic function and demonstrated the effectiveness of our proposed methods using LSTM, Nano-GPT, and T5.

To improve performance in contemporary deep learning, one is interested in scaling up the neural network in terms of both the number and the size of the layers. When ramping up the width of a single layer, graceful scaling of training has been linked to the need to normalize the weights and their updates in the "natural norm" particular to that layer. In this paper, we significantly generalize this idea by defining the modular norm, which is the natural norm on the full weight space of any neural network architecture. The modular norm is defined recursively in tandem with the network architecture itself. We show that the modular norm has several promising applications. On the practical side, the modular norm can be used to normalize the updates of any base optimizer so that the learning rate becomes transferable across width and depth. This means that the user does not need to compute optimizer-specific scale factors in order to scale training. On the theoretical side, we show that for any neural network built from "well-behaved" atomic modules, the gradient of the network is Lipschitz-continuous in the modular norm, with the Lipschitz constant admitting a simple recursive formula. This characterization opens the door to porting standard ideas in optimization theory over to deep learning. We have created a Python package called Modula that automatically normalizes weight updates in the modular norm of the architecture. Both the Modula package and code for our experiments are provided in the supplementary material.

Per-example gradient norms are a vital ingredient for estimating gradient noise scale (GNS) with minimal variance. Observing the tensor contractions required to compute them, we propose a method with minimal FLOPs in 3D or greater tensor regimes by simultaneously computing the norms while computing the parameter gradients. Using this method we are able to observe the GNS of different layers at higher accuracy than previously possible. We find that the total GNS of contemporary transformer models is predicted well by the GNS of only the normalization layers. As a result, focusing only on the normalization layer, we develop a custom kernel to compute the per-example gradient norms while performing the LayerNorm backward pass with zero throughput overhead. Tracking GNS on only those layers, we are able to guide a practical batch size schedule that reduces training time by 18% on a Chinchilla-optimal language model.

We study stochastic approximation algorithms with Markovian noise and constant step-size $\alpha$. We develop a method based on infinitesimal generator comparisons to study the bias of the algorithm, which is the expected difference between $\theta_n$ ---the value at iteration $n$--- and $\theta^*$ ---the unique equilibrium of the corresponding ODE. We show that, under some smoothness conditions, this bias is of order $O(\alpha)$. Furthermore, we show that the time-averaged bias is equal to $\alpha V + O(\alpha^2)$, where $V$ is a constant characterized by a Lyapunov equation, showing that $E[\bar{\theta}_n] \approx \theta^*+V\alpha + O(\alpha^2)$, where $\bar{\theta}_n$ is the Polyak-Ruppert average. We also show that $\bar{\theta}_n$ converges with high probability around $\theta^*+\alpha V$. We illustrate how to combine this with Richardson-Romberg extrapolation to derive an iterative scheme with a bias of order $O(\alpha^2)$.

Integer linear programs (ILPs) are commonly employed to model diverse practical problems such as scheduling and planning. Recently, machine learning techniques have been utilized to solve ILPs. A straightforward idea is to train a model via supervised learning, with an ILP as the input and an optimal solution as the label. An ILP is symmetric if its variables can be permuted without changing the problem structure, resulting in numerous equivalent and optimal solutions. Randomly selecting an optimal solution as the label can introduce variability in the training data, which may hinder the model from learning stable patterns. In this work, we incorporate the intrinsic symmetry of ILPs and propose a novel training framework called SymILO. Specifically, we modify the learning task by introducing solution permutation along with neural network weights as learnable parameters and then design an alternating algorithm to jointly optimize the loss function. We conduct extensive experiments on ILPs involving different symmetries and the computational results demonstrate that our symmetry-aware approach significantly outperforms three existing methods----achieving $50.3\\%$, $66.5\\%$, and $45.4\\%$ average improvements, respectively.

Machine learning systems often acquire biases by leveraging undesired features in the data, impacting accuracy variably across different sub-populations of the data. However, our current understanding of bias formation mostly focuses on the initial and final stages of learning, leaving a gap in knowledge regarding the transient dynamics. To address this gap, this paper explores the evolution of bias in a teacher-student setup that models different data sub-populations with a Gaussian-mixture model. We provide an analytical description of the stochastic gradient descent dynamics of a linear classifier in this setup, which we prove to be exact in high dimension. Notably, our analysis identifies different properties of the sub-populations that drive bias at different timescales and hence shows a shifting preference of our classifier during training. By applying our general solution to fairness and robustness, we delineate how and when heterogeneous data and spurious features can generate and amplify bias. We empirically validate our results in more complex scenarios by training deeper networks on synthetic and real data, i.e. using CIFAR10, MNIST, and CelebA datasets.

As a marriage between offline RL and meta-RL, the advent of offline meta-reinforcement learning (OMRL) has shown great promise in enabling RL agents to multi-task and quickly adapt while acquiring knowledge safely. Among which, context-based OMRL (COMRL) as a popular paradigm, aims to learn a universal policy conditioned on effective task representations. In this work, by examining several key milestones in the field of COMRL, we propose to integrate these seemingly independent methodologies into a unified framework. Most importantly, we show that the pre-existing COMRL algorithms are essentially optimizing the same mutual information objective between the task variable $M$ and its latent representation $Z$ by implementing various approximate bounds. Such theoretical insight offers ample design freedom for novel algorithms. As demonstrations, we propose a supervised and a self-supervised implementation of $I(Z; M)$, and empirically show that the corresponding optimization algorithms exhibit remarkable generalization across a broad spectrum of RL benchmarks, context shift scenarios, data qualities and deep learning architectures. This work lays the information theoretic foundation for COMRL methods, leading to a better understanding of task representation learning in the context of reinforcement learning. Given its generality, we envision our framework as a promising offline pre-training paradigm of foundation models for decision making.

A key challenge in lifelong reinforcement learning (RL) is the loss of plasticity, where previous learning progress hinders an agent's adaptation to new tasks. While regularization and resetting can help, they require precise hyperparameter selection at the outset and environment-dependent adjustments. Building on the principled theory of online convex optimization, we present a parameter-free optimizer for lifelong RL, called TRAC, which requires no tuning or prior knowledge about the distribution shifts. Extensive experiments on Procgen, Atari, and Gym Control environments show that TRAC works surprisingly well—mitigating loss of plasticity and rapidly adapting to challenging distribution shifts—despite the underlying optimization problem being nonconvex and nonstationary.

We provide a non-asymptotic analysis of the contrastive divergence (CD) algorithm, a training method for unnormalized models. While prior work has established that (for exponential family distributions) the CD iterates asymptotically converge at an $O(n^{-1 / 3})$ rate to the true parameter of the data distribution, we show that CD can achieve the parametric rate $O(n^{-1 / 2})$. Our analysis provides results for various data batching schemes, including fully online and minibatch. We additionally show that CD is near-optimal, in the sense that its asymptotic variance is close to the Cramér-Rao lower bound.

Transformers have achieved significant success in natural language modeling because of their exceptional capabilities to combine contextual information and global knowledge, yet their theoretical basis remains unclear. In this paper, we first propose Sparse Contextual Bigram (SCB), a natural extension to the classical bigram model, where the generation of the next token depends on a sparse set of earlier positions determined by the last token. We investigate the training dynamics and sample complexity of learning SCB using a one-layer linear transformer with a gradient-based algorithm. We show that when trained from scratch, the training process can be split into an initial sample-intensive stage where the correlation is boosted from zero to a nontrivial value, followed by a more sample-efficient stage of further improvement. Additionally, we prove that, provided a nontrivial correlation between the downstream and pretraining tasks, finetuning from a pretrained model allows us to bypass the initial sample-intensive stage. We also empirically demonstrate that our algorithm can outperform SGD in our setting.

The paper investigates the fundamental convergence properties of Sharpness-Aware Minimization (SAM), a recently proposed gradient-based optimization method (Foret et al., 2021) that significantly improves the generalization of deep neural networks. The convergence properties including the stationarity of accumulation points, the convergence of the sequence of gradients to the origin, the sequence of function values to the optimal value, and the sequence of iterates to the optimal solution are established for the method. The universality of the provided convergence analysis based on inexact gradient descent frameworks (Khanh et al., 2023b) allows its extensions to the normalized versions of SAM such as F-SAM (Li et al. 2024), VaSSO (Li & Giannakis, 2023), RSAM (Liu et al., 2022), and to the unnormalized versions of SAM such as USAM (Andriushchenko & Flammarion, 2022). Numerical experiments are conducted on classification tasks using deep learning models to confirm the practical aspects of our analysis.

We introduce a novel positional encoding strategy for Transformer-style models, addressing the shortcomings of existing, often ad hoc, approaches. Our framework implements a flexible mapping from the algebraic specification of a domain to a positional encoding scheme where positions are interpreted as orthogonal operators. This design preserves the structural properties of the source domain, thereby ensuring that the end-model upholds them. The framework can accommodate various structures, including sequences, grids and trees, but also their compositions. We conduct a series of experiments demonstrating the practical applicability of our method. Our results suggest performance on par with or surpassing the current state of the art, without hyper-parameter optimizations or ``task search'' of any kind. Code is available through https://aalto-quml.github.io/ape/.

This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the approximate optimal value of such problems is not obtainable by first-order zero-respecting algorithms. Then we follow recent works to pursue the weak approximate solutions. For this goal, we propose a novel method by reformulating them into functionally constrained problems. Our method achieves near-optimal rates for both smooth and nonsmooth problems. To the best of our knowledge, this is the first near-optimal algorithm that works under standard assumptions of smoothness or Lipschitz continuity for the objective functions.