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Stochastic gradient MCMC methods, such as stochastic gradient Langevin dynamics (SGLD), employ fast but noisy gradient estimates to enable large-scale posterior sampling. Although we can easily extend SGLD to distributed settings, it suffers from two issues when applied to federated non-IID data. First, the variance of these estimates increases significantly. Second, delaying communication causes the Markov chains to diverge from the true posterior even for very simple models. To alleviate both these problems, we propose conducive gradients, a simple mechanism that combines local likelihood approximations to correct gradient updates. Notably, conducive gradients are easy to compute, and since we only calculate the approximations once, they incur negligible overhead. We apply conducive gradients to distributed stochastic gradient Langevin dynamics (DSGLD) and call the resulting method federated stochastic gradient Langevin dynamics (FSGLD). We demonstrate that our approach can handle delayed communication rounds, converging to the target posterior in cases where DSGLD fails. We also show that FSGLD outperforms DSGLD for non-IID federated data with experiments on metric learning and neural networks.

UAI 2021

Federated Stochastic Gradient Langevin Dynamics

distributed sgld

federated learning

mcmc

The Conference on Uncertainty in Artificial Intelligence (UAI) is one of the premier international conferences on research related to knowledge representation, learning, and reasoning in the presence of uncertainty. It is supported by the [Association for Uncertainty in Artificial Intelligence (AUAI).](https://www.auai.org/)

The 37th Conference on Uncertainty in Artificial Intelligence (UAI 2021) is held fully online. We have an exciting program consisting of keynote talks by [Susan Murphy](https://www.auai.org/uai2021/program?block=A), [Eric Horvitz](https://www.auai.org/uai2021/program?block=B), [Lenka Zdeborová](https://www.auai.org/uai2021/program?block=C), [Judea Pearl](https://www.auai.org/uai2021/program?block=D) and [Ankur Moitra](https://www.auai.org/uai2021/program?block=E), a town hall meeting, peer-reviewed papers, and three workshops. The main conference is single-track and each paper is show-cased with a live component (either a live discussion and Q&A, or a live lightning talk). All papers are also featured in video presentations and in poster sessions in gather.town. The three parallel workshops on Friday allow for smaller meetings on current topics.

The walkthrough video below shows how you can navigate this site and use the different possibilities for interaction: UAIsland2021 on gather.town for posters and social interactions, the mementor platform for virtual mentoring sessions, and the chat and Q&A systems for discussions about talks and posters.

Have a great UAI 2021! 
<br>
<br>Cassio de Campos and Marloes Maathuis
<br>UAI 2021 Program Chairs
<br>uai2021programchairs@gmail.com

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A ticket is required to access this conference. Please use the provided link to register for the event.

https://auai.org/uai2021/registration

The Conference on Uncertainty in Artificial Intelligence (UAI) is one of the premier international conferences on research related to knowledge representation, learning, and reasoning in the presence of uncertainty. It is supported by the [Association for Uncertainty in Artificial Intelligence (AUAI).](https://www.auai.org/)

lightning talk

Hypothesis testing can help decision-making by quantifying distributional differences between two populations from observational data. However, these tests may inherit biases embedded in the data collection mechanism (some instances often being systematically more likely included in our sample) and consistently reproduce biased decisions. We propose a two-sample test that adjusts for selection bias by accounting for differences in marginal distributions of confounding variables. Our test statistic is a weighted distance between samples embedded in a reproducing kernel Hilbert space, whose balancing weights provably correct for bias. We establish the asymptotic distributions under null and alternative hypotheses, and prove the consistency of empirical approximations to the underlying population quantity. We conclude with performance evaluations on artificial data and experiments on treatment effect studies from economics.

A Kernel Two-Sample Test with Selection Bias

The variational auto-encoder (VAE) is a deep latent variable model that has two neural networks in an autoencoder-like architecture; one of them parameterizes the model's likelihood. Fitting its parameters via maximum likelihood (ML) is challenging since the computation of the marginal likelihood involves an intractable integral over the latent space; thus the VAE is trained instead by maximizing a variational lower bound. Here, we develop a ML training scheme for VAEs by introducing unbiased estimators of the log-likelihood gradient. We obtain the estimators by augmenting the latent space with a set of importance samples, similarly to the importance weighted auto-encoder (IWAE), and then constructing a Markov chain Monte Carlo coupling procedure on this augmented space. We provide the conditions under which the estimators can be computed in finite time and with finite variance. We show experimentally that VAEs fitted with unbiased estimators exhibit better predictive performance.

Unbiased Gradient Estimation for Variational Auto-Encoders using Coupled Markov Chains

Identifying the preferences of a given user through elicitation is a central part of multi-criteria decision aid (MCDA) or preference learning tasks. Two classical ways to perform this elicitation is to use either a robust or a Bayesian approach. However, both have their shortcoming: the robust approach has strong guarantees through very strong hypotheses, but cannot integrate uncertain information. while the Bayesian approach can integrate uncertainties, but sacrifices the previous guarantees and asks for stronger model assumptions. In this paper, we propose and test a method based on possibility theory, which keeps the guarantees of the robust approach without needing its strong hypotheses. Among other things, we show that it can detect user errors as well as model misspecification.

Possibilistic Preference Elicitation by Minimax Regret

Trustworthy deployment of ML models requires a proper measure of uncertainty, especially in safety-critical applications. We focus on uncertainty quantification (UQ) for classification problems via two avenues --- prediction sets using conformal prediction and calibration of probabilistic predictors by post-hoc binning --- since these possess distribution-free guarantees for i.i.d. data. Two common ways of generalizing beyond the i.i.d. setting include handling covariate and label shift. Within the context of distribution-free UQ, the former has already received attention, but not the latter. It is known that label shift hurts prediction, and we first argue that it also hurts UQ, by showing degradation in coverage and calibration. Piggybacking on recent progress in addressing label shift (for better prediction), we examine the right way to achieve UQ by reweighting the aforementioned conformal and calibration procedures whenever some unlabeled data from the target distribution is available. We examine these techniques theoretically in a distribution-free framework and demonstrate their excellent practical performance.

Distribution-free uncertainty quantification for classification under label shift

We propose two sum-product laws for imprecise Markov chains, and use these laws to derive two algorithms to efficiently compute lower and upper expectations for imprecise Markov chains under complete independence and epistemic irrelevance. These algorithms work for inferences that have a corresponding sum-product decomposition, and we argue that many well-known inferences fit their scope. We illustrate our results on a simple epidemiological example.

Sum-Product Laws and Efficient Algorithms for Imprecise Markov Chains

Deep Gaussian Processes (DGPs) are multi-layer, flexible extensions of Gaussian Processes but their training remains challenging. Most existing methods for inference in DGPs use sparse approximation which require optimization over a large number of inducing inputs and their locations across layers. In this paper, we simplify the training by setting the locations to a fixed subset of data and sampling the inducing inputs from a variational distribution. This reduces the trainable parameters and computation cost without any performance degradation, as demonstrated by our empirical results on regression data sets. Our modifications simplify and stabilize DGP training methods while making them amenable to sampling schemes such as leverage score and determinantal point processes.

Subset-of-Data Variational Inference for Deep Gaussian-Processes Regression

High sample complexity remains a barrier to the application of reinforcement learning (RL), particularly in multi-agent systems. A large body of work has demonstrated that exploration mechanisms based on the principle of optimism under uncertainty can significantly improve the sample efficiency of RL in single agent tasks. This work seeks to understand the role of optimistic exploration in non-cooperative multi-agent settings. We will show that, in zero-sum games, optimistic exploration can cause the learner to waste time sampling parts of the state space that are irrelevant to strategic play, as they can only be reached through cooperation between both players. To address this issue, we introduce a formal notion of strategically efficient} exploration in Markov games, and use this to develop two strategically efficient learning algorithms for finite Markov games. We demonstrate that these methods can be significantly more sample efficient than their optimistic counterparts.

Strategically Efficient Exploration in Competitive Multi-agent Reinforcement Learning

Max-Pooling operations are a core component of deep learning architectures. In particular, they are part of most convolutional architectures used in machine vision, since pooling is a natural approach to pattern detection problems. However, these architectures are not well understood from a theoretical perspective. For example, we do not understand when they can be globally optimized, and what is the effect of over-parameterization on generalization. Here we perform a theoretical analysis of a convolutional max-pooling architecture, proving that it can be globally optimized, and can generalize well even for highly over-parameterized models. Our analysis focuses on a data generating distribution inspired by pattern detection problem, where a ``discriminative'' pattern needs to be detected among ``spurious'' patterns. We empirically validate that CNNs significantly outperform fully connected networks in our setting, as predicted by our theoretical results.

An Optimization and Generalization Analysis for Max-Pooling Networks

Reinforcement learning policies based on deep neural networks are vulnerable to imperceptible adversarial perturbations to their inputs, in much the same way as neural network image classifiers. Recent work has proposed several methods to improve the robustness of deep reinforcement learning agents to adversarial perturbations based on training in the presence of these imperceptible perturbations (i.e. adversarial training). In this paper, we study the effects of adversarial training on the neural policy learned by the agent. In particular, we follow two distinct parallel approaches to investigate the outcomes of adversarial training on deep neural policies based on worst-case distributional shift and feature sensitivity. For the first approach, we compare the Fourier spectrum of minimal perturbations computed for both adversarially trained and vanilla trained neural policies. Via experiments in the OpenAI Atari environments we show that minimal perturbations computed for adversarially trained policies are more focused on lower frequencies in the Fourier domain, indicating a higher sensitivity of these policies to low frequency perturbations. For the second approach, we propose a novel method to measure the feature sensitivities of deep neural policies and we compare these feature sensitivity differences in state-of-the-art adversarially trained deep neural policies and vanilla trained deep neural policies. We believe our results can be an initial step towards understanding the relationship between adversarial training and different notions of robustness for neural policies.

Investigating Vulnerabilities of Deep Neural Policies

Inspired by recent developments on meta-learning with linear contextual bandit tasks, we study the benefit of feature learning in both the multi-task and meta-learning settings.

Federated Stochastic Gradient Langevin Dynamics

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