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Kaiwen Wu

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9 papers

2 author rows

NeurIPS Conference 2024 Conference Paper

Computation-Aware Gaussian Processes: Model Selection And Linear-Time Inference

Jonathan Wenger
Kaiwen Wu
Philipp Hennig
Jacob R. Gardner
Geoff Pleiss
John P. Cunningham

Model selection in Gaussian processes scales prohibitively with the size of the training dataset, both in time and memory. While many approximations exist, all incur inevitable approximation error. Recent work accounts for this error in the form of computational uncertainty, which enables---at the cost of quadratic complexity---an explicit tradeoff between computational efficiency and precision. Here we extend this development to model selection, which requires significant enhancements to the existing approach, including linear-time scaling in the size of the dataset. We propose a novel training loss for hyperparameter optimization and demonstrate empirically that the resulting method can outperform SGPR, CGGP and SVGP, state-of-the-art methods for GP model selection, on medium to large-scale datasets. Our experiments show that model selection for computation-aware GPs trained on 1. 8 million data points can be done within a few hours on a single GPU. As a result of this work, Gaussian processes can be trained on large-scale datasets without significantly compromising their ability to quantify uncertainty---a fundamental prerequisite for optimal decision-making.

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ICML Conference 2024 Conference Paper

Understanding Stochastic Natural Gradient Variational Inference

Kaiwen Wu
Jacob R. Gardner

Stochastic natural gradient variational inference (NGVI) is a popular posterior inference method with applications in various probabilistic models. Despite its wide usage, little is known about the non-asymptotic convergence rate in the stochastic setting. We aim to lessen this gap and provide a better understanding. For conjugate likelihoods, we prove the first $\mathcal{O}(\frac{1}{T})$ non-asymptotic convergence rate of stochastic NGVI. The complexity is no worse than stochastic gradient descent (a. k. a. black-box variational inference) and the rate likely has better constant dependency that leads to faster convergence in practice. For non-conjugate likelihoods, we show that stochastic NGVI with the canonical parameterization implicitly optimizes a non-convex objective. Thus, a global convergence rate of $\mathcal{O}(\frac{1}{T})$ is unlikely without some significant new understanding of optimizing the ELBO using natural gradients.

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NeurIPS Conference 2023 Conference Paper

On the Convergence of Black-Box Variational Inference

Kyurae Kim
Jisu Oh
Kaiwen Wu
Yian Ma
Jacob Gardner

We provide the first convergence guarantee for black-box variational inference (BBVI) with the reparameterization gradient. While preliminary investigations worked on simplified versions of BBVI (e. g. , bounded domain, bounded support, only optimizing for the scale, and such), our setup does not need any such algorithmic modifications. Our results hold for log-smooth posterior densities with and without strong log-concavity and the location-scale variational family. Notably, our analysis reveals that certain algorithm design choices commonly employed in practice, such as nonlinear parameterizations of the scale matrix, can result in suboptimal convergence rates. Fortunately, running BBVI with proximal stochastic gradient descent fixes these limitations and thus achieves the strongest known convergence guarantees. We evaluate this theoretical insight by comparing proximal SGD against other standard implementations of BBVI on large-scale Bayesian inference problems.

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ICML Conference 2023 Conference Paper

Practical and Matching Gradient Variance Bounds for Black-Box Variational Bayesian Inference

Kyurae Kim
Kaiwen Wu
Jisu Oh
Jacob R. Gardner

Understanding the gradient variance of black-box variational inference (BBVI) is a crucial step for establishing its convergence and developing algorithmic improvements. However, existing studies have yet to show that the gradient variance of BBVI satisfies the conditions used to study the convergence of stochastic gradient descent (SGD), the workhorse of BBVI. In this work, we show that BBVI satisfies a matching bound corresponding to the ABC condition used in the SGD literature when applied to smooth and quadratically-growing log-likelihoods. Our results generalize to nonlinear covariance parameterizations widely used in the practice of BBVI. Furthermore, we show that the variance of the mean-field parameterization has provably superior dimensional dependence.

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NeurIPS Conference 2023 Conference Paper

The Behavior and Convergence of Local Bayesian Optimization

Kaiwen Wu
Kyurae Kim
Roman Garnett
Jacob Gardner

A recent development in Bayesian optimization is the use of local optimization strategies, which can deliver strong empirical performance on high-dimensional problems compared to traditional global strategies. The "folk wisdom" in the literature is that the focus on local optimization sidesteps the curse of dimensionality; however, little is known concretely about the expected behavior or convergence of Bayesian local optimization routines. We first study the behavior of the local approach, and find that the statistics of individual local solutions of Gaussian process sample paths are surprisingly good compared to what we would expect to recover from global methods. We then present the first rigorous analysis of such a Bayesian local optimization algorithm recently proposed by Müller et al. (2021), and derive convergence rates in both the noisy and noiseless settings.

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NeurIPS Conference 2023 Conference Paper

Variational Gaussian Processes with Decoupled Conditionals

Xinran Zhu
Kaiwen Wu
Natalie Maus
Jacob Gardner
David Bindel

Variational Gaussian processes (GPs) approximate exact GP inference by using a small set of inducing points to form a sparse approximation of the true posterior, with the fidelity of the model increasing with additional inducing points. Although the approximation error in principle can be reduced through the use of more inducing points, this leads to scaling optimization challenges and computational complexity. To achieve scalability, inducing point methods typically introduce conditional independencies and then approximations to the training and test conditional distributions. In this paper, we consider an alternative approach to modifying the training and test conditionals, in which we make them more flexible. In particular, we investigate decoupling the parametric form of the predictive mean and covariance in the conditionals, and learn independent parameters for predictive mean and covariance. We derive new evidence lower bounds (ELBO) under these more flexible conditionals, and provide two concrete examples of applying the decoupled conditionals. Empirically, we find this additional flexibility leads to improved model performance on a variety of regression tasks and Bayesian optimization (BO) applications.

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NeurIPS Conference 2022 Conference Paper

Local Bayesian optimization via maximizing probability of descent

Quan Nguyen
Kaiwen Wu
Jacob Gardner
Roman Garnett

Local optimization presents a promising approach to expensive, high-dimensional black-box optimization by sidestepping the need to globally explore the search space. For objective functions whose gradient cannot be evaluated directly, Bayesian optimization offers one solution -- we construct a probabilistic model of the objective, design a policy to learn about the gradient at the current location, and use the resulting information to navigate the objective landscape. Previous work has realized this scheme by minimizing the variance in the estimate of the gradient, then moving in the direction of the expected gradient. In this paper, we re-examine and refine this approach. We demonstrate that, surprisingly, the expected value of the gradient is not always the direction maximizing the probability of descent, and in fact, these directions may be nearly orthogonal. This observation then inspires an elegant optimization scheme seeking to maximize the probability of descent while moving in the direction of most-probable descent. Experiments on both synthetic and real-world objectives show that our method outperforms previous realizations of this optimization scheme and is competitive against other, significantly more complicated baselines.

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ICML Conference 2020 Conference Paper

Stronger and Faster Wasserstein Adversarial Attacks

Kaiwen Wu
Allen Houze Wang
Yaoliang Yu

Deep models, while being extremely flexible and accurate, are surprisingly vulnerable to “small, imperceptible” perturbations known as adversarial attacks. While the majority of existing attacks focus on measuring perturbations under the $\ell_p$ metric, Wasserstein distance, which takes geometry in pixel space into account, has long been known to be a suitable metric for measuring image quality and has recently risen as a compelling alternative to the $\ell_p$ metric in adversarial attacks. However, constructing an effective attack under the Wasserstein metric is computationally much more challenging and calls for better optimization algorithms. We address this gap in two ways: (a) we develop an exact yet efficient projection operator to enable a stronger projected gradient attack; (b) we show that the Frank-Wolfe method equipped with a suitable linear minimization oracle works extremely fast under Wasserstein constraints. Our algorithms not only converge faster but also generate much stronger attacks. For instance, we decrease the accuracy of a residual network on CIFAR-10 to $3. 4%$ within a Wasserstein perturbation ball of radius $0. 005$, in contrast to $65. 6%$ using the previous Wasserstein attack based on an \emph{approximate} projection operator. Furthermore, employing our stronger attacks in adversarial training significantly improves the robustness of adversarially trained models.

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ICML Conference 2019 Conference Paper

Distributional Reinforcement Learning for Efficient Exploration

Borislav Mavrin
Hengshuai Yao
Linglong Kong
Kaiwen Wu
Yaoliang Yu

In distributional reinforcement learning (RL), the estimated distribution of value functions model both the parametric and intrinsic uncertainties. We propose a novel and efficient exploration method for deep RL that has two components. The first is a decaying schedule to suppress the intrinsic uncertainty. The second is an exploration bonus calculated from the upper quantiles of the learned distribution. In Atari 2600 games, our method achieves 483 % average gain across 49 games in cumulative rewards over QR-DQN. We also compared our algorithm with QR-DQN in a challenging 3D driving simulator (CARLA). Results show that our algorithm achieves nearoptimal safety rewards twice faster than QRDQN.

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