NeurIPS 2022 Papers

Random forests are some of the most widely used machine learning models today, especially in domains that necessitate interpretability. We present an algorithm that accelerates the training of random forests and other popular tree-based learning methods. At the core of our algorithm is a novel node-splitting subroutine, dubbed MABSplit, used to efficiently find split points when constructing decision trees. Our algorithm borrows techniques from the multi-armed bandit literature to judiciously determine how to allocate samples and computational power across candidate split points. We provide theoretical guarantees that MABSplit improves the sample complexity of each node split from linear to logarithmic in the number of data points. In some settings, MABSplit leads to 100x faster training (an 99% reduction in training time) without any decrease in generalization performance. We demonstrate similar speedups when MABSplit is used across a variety of forest-based variants, such as Extremely Random Forests and Random Patches. We also show our algorithm can be used in both classification and regression tasks. Finally, we show that MABSplit outperforms existing methods in generalization performance and feature importance calculations under a fixed computational budget. All of our experimental results are reproducible via a one-line script at https://github.com/ThrunGroup/FastForest.

Molecular optimization is a fundamental goal in the chemical sciences and is of central interest to drug and material design. In recent years, significant progress has been made in solving challenging problems across various aspects of computational molecular optimizations, emphasizing high validity, diversity, and, most recently, synthesizability. Despite this progress, many papers report results on trivial or self-designed tasks, bringing additional challenges to directly assessing the performance of new methods. Moreover, the sample efficiency of the optimization---the number of molecules evaluated by the oracle---is rarely discussed, despite being an essential consideration for realistic discovery applications. To fill this gap, we have created an open-source benchmark for practical molecular optimization, PMO, to facilitate the transparent and reproducible evaluation of algorithmic advances in molecular optimization. This paper thoroughly investigates the performance of 25 molecular design algorithms on 23 single-objective (scalar) optimization tasks with a particular focus on sample efficiency. Our results show that most ``state-of-the-art'' methods fail to outperform their predecessors under a limited oracle budget allowing 10K queries and that no existing algorithm can efficiently solve certain molecular optimization problems in this setting. We analyze the influence of the optimization algorithm choices, molecular assembly strategies, and oracle landscapes on the optimization performance to inform future algorithm development and benchmarking. PMO provides a standardized experimental setup to comprehensively evaluate and compare new molecule optimization methods with existing ones. All code can be found at https://github.com/wenhao-gao/mol_opt.

A cursory reading of the literature suggests that we have made a lot of progress in designing effective adversarial defenses for Graph Neural Networks (GNNs). Yet, the standard methodology has a serious flaw – virtually all of the defenses are evaluated against non-adaptive attacks leading to overly optimistic robustness estimates. We perform a thorough robustness analysis of 7 of the most popular defenses spanning the entire spectrum of strategies, i.e., aimed at improving the graph, the architecture, or the training. The results are sobering – most defenses show no or only marginal improvement compared to an undefended baseline. We advocate using custom adaptive attacks as a gold standard and we outline the lessons we learned from successfully designing such attacks. Moreover, our diverse collection of perturbed graphs forms a (black-box) unit test offering a first glance at a model's robustness.

We introduce a multi-modes tensor clustering method that implements a fused version of the alternating least squares algorithm (Fused-Orth-ALS) for simultaneous tensor factorization and clustering. The statistical convergence rates of recovery and clustering are established when the data are a noise contaminated tensor with a latent low rank CP decomposition structure. Furthermore, we show that a modified alternating least squares algorithm can provably recover the true latent low rank factorization structure when the data form an asymmetric tensor with perturbation. Clustering consistency is also established. Finally, we illustrate the accuracy and computational efficient implementation of the Fused-Orth-ALS algorithm by using both simulations and real datasets.

Neural networks have shown great predictive power when applied to unstructured data such as images and natural languages. The Bayesian neural network captures the uncertainty of prediction by computing the posterior distribution of the model parameters. In this paper, we show that the Bayesian neural network with spikeand-slab prior has posterior consistency with a near minimax optimal convergence rate when the true regression function belongs to the Besov space. The spikeand-slab prior is adaptive to the smoothness of the regression function and the posterior convergence rate does not change even when the smoothness of the regression function is unknown. We also consider the shrinkage prior, which is computationally more feasible than the spike-and-slab prior, and show that it has the same posterior convergence rate as the spike-and-slab prior.

Recent studies reveal that a well-trained deep reinforcement learning (RL) policy can be particularly vulnerable to adversarial perturbations on input observations. Therefore, it is crucial to train RL agents that are robust against any attacks with a bounded budget. Existing robust training methods in deep RL either treat correlated steps separately, ignoring the robustness of long-term rewards, or train the agents and RL-based attacker together, doubling the computational burden and sample complexity of the training process. In this work, we propose a strong and efficient robust training framework for RL, named Worst-case-aware Robust RL (WocaR-RL) that directly estimates and optimizes the worst-case reward of a policy under bounded l_p attacks without requiring extra samples for learning an attacker. Experiments on multiple environments show that WocaR-RL achieves state-of-the-art performance under various strong attacks, and obtains significantly higher training efficiency than prior state-of-the-art robust training methods. The code of this work is available at https://github.com/umd-huang-lab/WocaR-RL.

The distance matrix of a dataset $X$ of $n$ points with respect to a distance function $f$ represents all pairwise distances between points in $X$ induced by $f$. Due to their wide applicability, distance matrices and related families of matrices have been the focus of many recent algorithmic works. We continue this line of research and take a broad view of algorithm design for distance matrices with the goal of designing fast algorithms, which are specifically tailored for distance matrices, for fundamental linear algebraic primitives. Our results include efficient algorithms for computing matrix-vector products for a wide class of distance matrices, such as the $\ell_1$ metric for which we get a linear runtime, as well as an $\Omega(n^2)$ lower bound for any algorithm which computes a matrix-vector product for the $\ell_{\infty}$ case, showing a separation between the $\ell_1$ and the $\ell_{\infty}$ metrics. Our upper bound results in conjunction with recent works on the matrix-vector query model have many further downstream applications, including the fastest algorithm for computing a relative error low-rank approximation for the distance matrix induced by $\ell_1$ and $\ell_2^2$ functions and the fastest algorithm for computing an additive error low-rank approximation for the $\ell_2$ metric, in addition to applications for fast matrix multiplication among others. We also give algorithms for constructing distance matrices and show that one can construct an approximate $\ell_2$ distance matrix in time faster than the bound implied by the Johnson-Lindenstrauss lemma.

We consider a linear stochastic bandit problem involving $M$ agents that can collaborate via a central server to minimize regret. A fraction $\alpha$ of these agents are adversarial and can act arbitrarily, leading to the following tension: while collaboration can potentially reduce regret, it can also disrupt the process of learning due to adversaries. In this work, we provide a fundamental understanding of this tension by designing new algorithms that balance the exploration-exploitation trade-off via carefully constructed robust confidence intervals. We also complement our algorithms with tight analyses. First, we develop a robust collaborative phased elimination algorithm that achieves $\tilde{O}\left(\alpha+ 1/\sqrt{M}\right) \sqrt{dT}$ regret for each good agent; here, $d$ is the model-dimension and $T$ is the horizon. For small $\alpha$, our result thus reveals a clear benefit of collaboration despite adversaries. Using an information-theoretic argument, we then prove a matching lower bound, thereby providing the first set of tight, near-optimal regret bounds for collaborative linear bandits with adversaries. Furthermore, by leveraging recent advances in high-dimensional robust statistics, we significantly extend our algorithmic ideas and results to (i) the generalized linear bandit model that allows for non-linear observation maps; and (ii) the contextual bandit setting that allows for time-varying feature vectors.

Score-based diffusion models (SBDMs) have achieved the SOTA FID results in unpaired image-to-image translation (I2I). However, we notice that existing methods totally ignore the training data in the source domain, leading to sub-optimal solutions for unpaired I2I. To this end, we propose energy-guided stochastic differential equations (EGSDE) that employs an energy function pretrained on both the source and target domains to guide the inference process of a pretrained SDE for realistic and faithful unpaired I2I. Building upon two feature extractors, we carefully design the energy function such that it encourages the transferred image to preserve the domain-independent features and discard domain-specific ones. Further, we provide an alternative explanation of the EGSDE as a product of experts, where each of the three experts (corresponding to the SDE and two feature extractors) solely contributes to faithfulness or realism. Empirically, we compare EGSDE to a large family of baselines on three widely-adopted unpaired I2I tasks under four metrics. EGSDE not only consistently outperforms existing SBDMs-based methods in almost all settings but also achieves the SOTA realism results without harming the faithful performance. Furthermore, EGSDE allows for flexible trade-offs between realism and faithfulness and we improve the realism results further (e.g., FID of 51.04 in Cat $\to$ Dog and FID of 50.43 in Wild $\to$ Dog on AFHQ) by tuning hyper-parameters. The code is available at https://github.com/ML-GSAI/EGSDE.

Spiking neural networks (SNNs) are promising to be widely deployed in real-time and safety-critical applications with the advance of neuromorphic computing. Recent work has demonstrated the insensitivity of SNNs to small random perturbations due to the discrete internal information representation. The variety of training algorithms and the involvement of the temporal dimension pose more threats to the robustness of SNNs than that of typical neural networks. We account for the vulnerability of SNNs by constructing adversaries based on different differentiable approximation techniques. By deriving a Lipschitz constant specifically for the spike representation, we first theoretically answer the question of how much adversarial invulnerability is retained in SNNs. Hence, to defend against the broad attack methods, we propose a regularized adversarial training scheme with low computational overheads. SNNs can benefit from the constraint of the perturbed spike distance's amplification and the generalization on multiple adversarial $\epsilon$-neighbourhoods. Our experiments on the image recognition benchmarks have proven that our training scheme can defend against powerful adversarial attacks crafted from strong differentiable approximations. To be specific, our approach makes the black-box attacks of the Projected Gradient Descent attack nearly ineffective. We believe that our work will facilitate the spread of SNNs for safety-critical applications and help understand the robustness of the human brain.

An interactive mechanism is an algorithm that stores a data set and answers adaptively chosen queries to it. The mechanism is called differentially private, if any adversary cannot distinguish whether a specific individual is in the data set by interacting with the mechanism. We study composition properties of differential privacy in concurrent compositions. In this setting, an adversary interacts with $k$ interactive mechanisms in parallel and can interleave its queries to the mechanisms arbitrarily. Previously, Vadhan and Wang [2021] proved an optimal concurrent composition theorem for pure-differential privacy. We significantly generalize and extend their results. Namely, we prove optimal parallel composition properties for several major notions of differential privacy in the literature, including approximate DP, Renyi DP, and zero-concentrated DP. Our results demonstrate that the adversary gains no advantage by interleaving its queries to independently running mechanisms. Hence, interactivity is a feature that differential privacy grants us for free. Concurrently and independently of our work, Vadhan and Zhang [2022] proved an optimal concurrent composition theorem for f-DP [Dong et al., 2022], which implies our result for the approximate DP case.

Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems. However, both classical solvers and recent deep learning-based surrogate models are typically extremely computationally intensive, because of their local evolution: they need to update the state of each discretized cell at each time step during inference. Here we develop Latent Evolution of PDEs (LE-PDE), a simple, fast and scalable method to accelerate the simulation and inverse optimization of PDEs. LE-PDE learns a compact, global representation of the system and efficiently evolves it fully in the latent space with learned latent evolution models. LE-PDE achieves speedup by having a much smaller latent dimension to update during long rollout as compared to updating in the input space. We introduce new learning objectives to effectively learn such latent dynamics to ensure long-term stability. We further introduce techniques for speeding-up inverse optimization of boundary conditions for PDEs via backpropagation through time in latent space, and an annealing technique to address the non-differentiability and sparse interaction of boundary conditions. We test our method in a 1D benchmark of nonlinear PDEs, 2D Navier-Stokes flows into turbulent phase and an inverse optimization of boundary conditions in 2D Navier-Stokes flow. Compared to state-of-the-art deep learning-based surrogate models and other strong baselines, we demonstrate up to 128x reduction in the dimensions to update, and up to 15x improvement in speed, while achieving competitive accuracy.

We study the generalisation properties of majority voting on finite ensembles of classifiers, proving margin-based generalisation bounds via the PAC-Bayes theory. These provide state-of-the-art guarantees on a number of classification tasks. Our central results leverage the Dirichlet posteriors studied recently by Zantedeschi et al. (2021) for training voting classifiers; in contrast to that work our bounds apply to non-randomised votes via the use of margins. Our contributions add perspective to the debate on the ``margins theory'' proposed by Schapire et al. (1998) for the generalisation of ensemble classifiers.

Stochastic Gradient Descent (SGD) has been the method of choice for learning large-scale non-convex models. While a general analysis of when SGD works has been elusive, there has been a lot of recent progress in understanding the convergence of Gradient Flow (GF) on the population loss, partly due to the simplicity that a continuous-time analysis buys us. An overarching theme of our paper is providing general conditions under which SGD converges, assuming that GF on the population loss converges. Our main tool to establish this connection is a general \textit{converse Lyapunov} like theorem, which implies the existence of a Lyapunov potential under mild assumptions on the rates of convergence of GF. In fact, using these potentials, we show a one-to-one correspondence between rates of convergence of GF and geometrical properties of the underlying objective. When these potentials further satisfy certain self-bounding properties, we show that they can be used to provide a convergence guarantee for Gradient Descent (GD) and SGD (even when the GF path and GD/SGD paths are quite far apart). It turns out that these self-bounding assumptions are in a sense also necessary for GD/SGD to work. Using our framework, we provide a unified analysis for GD/SGD not only for classical settings like convex losses, or objectives that satisfy PL/ KL properties, but also for more complex problems including Phase Retrieval and Matrix sq-root, and extending the results in the recent work of Chatterjee 2022.

Collaborative Metric Learning (CML) has recently emerged as a popular method in recommendation systems (RS), closing the gap between metric learning and Collaborative Filtering. Following the convention of RS, existing methods exploit unique user representation in their model design. This paper focuses on a challenging scenario where a user has multiple categories of interests. Under this setting, we argue that the unique user representation might induce preference bias, especially when the item category distribution is imbalanced. To address this issue, we propose a novel method called Diversity-Promoting Collaborative Metric Learning (DPCML), with the hope of considering the commonly ignored minority interest of the user. The key idea behind DPCML is to include a multiple set of representations for each user in the system. Based on this embedding paradigm, user preference toward an item is aggregated from different embeddings by taking the minimum item-user distance among the user embedding set. Furthermore, we observe that the diversity of the embeddings for the same user also plays an essential role in the model. To this end, we propose a diversity control regularization term to accommodate the multi-vector representation strategy better. Theoretically, we show that DPCML could generalize well to unseen test data by tackling the challenge of the annoying operation that comes from the minimum value. Experiments over a range of benchmark datasets speak to the efficacy of DPCML.

In cooperative multi-agent reinforcement learning, centralized training and decentralized execution (CTDE) has achieved remarkable success. Individual Global Max (IGM) decomposition, which is an important element of CTDE, measures the consistency between local and joint policies. The majority of IGM-based research focuses on how to establish this consistent relationship, but little attention has been paid to examining IGM's potential flaws. In this work, we reveal that the IGM condition is a lossy decomposition, and the error of lossy decomposition will accumulated in hypernetwork-based methods. To address the above issue, we propose to adopt an imitation learning strategy to separate the lossy decomposition from Bellman iterations, thereby avoiding error accumulation. The proposed strategy is theoretically proved and empirically verified on the StarCraft Multi-Agent Challenge benchmark problem with zero sight view. The results also confirm that the proposed method outperforms state-of-the-art IGM-based approaches.

Training deep learning models can be computationally expensive. Prior works have shown that increasing the batch size can potentially lead to better overall throughput. However, the batch size is frequently limited by the accelerator memory capacity due to the activations/feature maps stored for the training backward pass, as larger batch sizes require larger feature maps to be stored. Transformer-based models, which have recently seen a surge in popularity due to their good performance and applicability to a variety of tasks, have a similar problem. To remedy this issue, we propose Tempo, a new approach to efficiently use accelerator (e.g., GPU) memory resources for training Transformer-based models. Our approach provides drop-in replacements for the GELU, LayerNorm, and Attention layers, reducing the memory usage and ultimately leading to more efficient training. We implement Tempo and evaluate the throughput, memory usage, and accuracy/loss on the BERT Large pre-training task. We demonstrate that Tempo enables up to 2× higher batch sizes and 16% higher training throughput over the state-of-the-art baseline. We also evaluate Tempo on GPT2 and RoBERTa models, showing 19% and 26% speedup over the baseline.

We study stochastic optimization algorithms for constrained nonconvex stochastic optimization problems with Markovian data. In particular, we focus on the case when the transition kernel of the Markov chain is state-dependent. Such stochastic optimization problems arise in various machine learning problems including strategic classification and reinforcement learning. For this problem, we study both projection-based and projection-free algorithms. In both cases, we establish that the number of calls to the stochastic first-order oracle to obtain an appropriately defined $\epsilon$-stationary point is of the order $\mathcal{O}(1/\epsilon^{2.5})$. In the projection-free setting we additionally establish that the number of calls to the linear minimization oracle is of order $\mathcal{O}(1/\epsilon^{5.5})$. We also empirically demonstrate the performance of our algorithm on the problem of strategic classification with neural networks.

Motivated by applications to process massive datasets, we study streaming algorithms for pure exploration in Stochastic Multi-Armed Bandits (MABs). This problem was first formulated by Assadi and Wang [STOC 2020] as follows: A collection of $n$ arms with unknown rewards are arriving one by one in a stream, and the algorithm is only allowed to store a limited number of arms at any point. The goal is to find the arm with the largest reward while minimizing the number of arm pulls (sample complexity) and the maximum number of stored arms (space complexity). Assuming $\Delta_{[2]}$ is known, Assadi and Wang designed an algorithm that uses a memory of just one arm and still achieves the sample complexity of $O(n/\Delta_{[2]}^2)$ which is worst-case optimal even for non-streaming algorithms; here $\Delta_{[i]}$ is the gap between the rewards of the best and the $i$-th best arms. In this paper, we extended this line of work to stochastic MABs in the streaming model with the instance-sensitive sample complexity, i.e. the sample complexity of $O(\sum_{i=2}^{n} \frac{1}{\Delta_{[i]}^2}\log\log{(\frac{1}{\Delta_{[i]}})})$, similar in spirit to Karnin et.al. [ICML 2013] and Jamieson et.al. [COLT 2014] in the classical setting. We devise strong negative results under this setting: our results show that any streaming algorithm under a single pass has to use either asymptotically higher sample complexity than the instance-sensitive bound, or a memory of $\Omega(n)$ arms, even if the parameter $\Delta_{[2]}$ is known. In fact, the lower bound holds under much stronger assumptions, including the random order streams or the knowledge of all gap parameters $\{\Delta_{[i]}\}_{i=2}^n$. We complement our lower bounds by proposing a new algorithm that uses a memory of a single arm and achieves the instance-optimal sample complexity when all the strong assumptions hold simultaneously. Our results are developed based on a novel arm-trapping lemma. This generic complexity result shows that any algorithm to trap the index of the best arm among $o(n)$ indices (but not necessarily to find it) has to use $\Theta(n/\Delta_{[2]}^2)$ sample complexity. This result is not restricted to the streaming setting, and to the best of our knowledge, this is the first result that captures the sample-space trade-off for `trapping' arms in multi-armed bandits, and it can be of independent interest.