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In this paper, we consider constrained optimization problems subject to a convex set C. Stochastic gradient descent (SGD) is a simple and popular stochastic optimization algorithm that has been the workhorse of machine learning for many years. We show a new and surprising fact about SGD, in that depending on the constraint set C, one can operate SGD with much lower-dimensional stochastic gradients without affecting its performance. In particular, we design an optimization algorithm that operates with the lower-dimensional (compressed) stochastic gradients, and establish that with the right set of parameters it has the exact same dimension-free convergence guarantees as that of regular SGD for popular convex and nonconvex optimization settings. We also present two applications of these bounds, one for improving the empirical risk minimization bounds in differentially private nonconvex optimization, and other for reducing communication costs with distributed SGD. Additionally, we also show that this connection between constraint set structure and gradient compression also extends beyond SGD to the conditional gradient (Frank-Wolfe) method. The geometry of the constraint set, captured by its Gaussian width, plays an important role in all our results.

UAI 2021

E5 SGD with Low-Dimensional Gradients with Applications to Private and Distributed Learning

distributed learning

private learning

dimensionality reduction

convex and nonconvex optimization

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

AAAI 2021

lightning talk

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/)

Information-based Bayesian optimization (BO) algorithms have achieved state-of-the-art performance in optimizing a black-box objective function. However, they usually require several approximations or simplifying assumptions (without clearly understanding their effects on the BO performance) and/or their generalization to batch BO is computationally unwieldy, especially with an increasing batch size. To alleviate these issues, this paper presents a novel trusted-maximizers entropy search (TES) acquisition function: It measures how much an input query contributes to the information gain on the maximizer over a ﬁnite set of trusted maximizers, i.e., inputs optimizing functions that are sampled from the Gaussian process posterior belief of the objective function. Evaluating TES requires either only a stochastic approximation with sampling or a deterministic approximation with expectation propagation, both of which are investigated and empirically evaluated using synthetic benchmark objective functions and real-world optimization problems, e.g., hyperparameter tuning of a convolutional neural network and synthesizing ‘physically realizable’ faces to fool a black-box face recognition system. Though TES can naturally be generalized to a batch variant with either approximation, the latter is amenable to be scaled to a much larger batch size in our experiments.

Trusted-Maximizers Entropy Search for Efficient Bayesian Optimization

The empirical success of multi-agent reinforcement learning is encouraging, while few theoretical guarantees have been revealed. In this work, we prove that the plug-in solver approach, probably the most natural reinforcement learning algorithm, achieves minimax sample complexity for turn-based stochastic game (TBSG). Specifically, we perform planning in an empirical TBSG by utilizing a `simulator' that allows sampling from arbitrary state-action pair. We show that the empirical Nash equilibrium strategy is an approximate Nash equilibrium strategy in the true TBSG and give both problem-dependent and problem-independent bound. We develop reward perturbation techniques to tackle the non-stationarity in the game and Taylor-expansion-type analysis to improve the dependence on approximation error. With these novel techniques, we prove the minimax sample complexity of turn-based stochastic game.

Minimax Sample Complexity for Turn-based Stochastic Game

Graph-based semi-supervised learning (G-SSL) algorithms have witnessed rapid development and widespread usage across a variety of applications in recent years. However, the theoretical characterisation of the efficacy of such algorithms has remained an under-explored area. We introduce a novel algorithm for G-SSL, CSX, whose objective function extends those of Label Propagation and Expander, two popular G-SSL algorithms. We provide data-dependent generalisation error bounds for all three aforementioned algorithms when they are applied to graphs drawn from a partially labelled extension of a versatile latent space graph generative model. The bounds we obtain enable us to characterise the predictive performance as measured by accuracy in terms of homophily and label quantity. Building on this we develop a key notion of GLM-safety which enables us to compare G-SSL algorithms on the basis of the range of graphs on which they obtain a guaranteed accuracy. We show that the proposed algorithm CSX has a better GLM-safety profile than Label Propagation and Expander while achieving comparable or better accuracy on synthetic as well as real-world benchmark networks.

Graph-Based Semi-Supervised Learning through the Lens of Safety

Generative Adversarial Networks (GANs) have swiftly evolved to imitate increasingly complex image distributions. However, the majority of the developments focus on performance of GANs on balanced datasets. We find that the existing GANs and their training regimes which work well on balanced datasets fail to be effective in case of imbalanced (i.e. long-tailed) datasets. In this work we introduce a novel and theoretically motivated Class Balancing regularizer for training GANs. Our regularizer makes use of the knowledge from a pre-trained classifier to ensure balanced learning of all the classes in the dataset. This is achieved via modelling the effective class frequency based on the exponential forgetting observed in neural networks and encouraging the GAN to focus on underrepresented classes. We demonstrate the utility of our regularizer in learning representations for long-tailed distributions via achieving better performance than existing approaches over multiple datasets. Specifically, when applied to an unconditional GAN, it improves the FID from $13.03$ to $9.01$ on the long-tailed iNaturalist-$2019$ dataset.

Class Balancing GAN with a Classifier in the Loop

Hierarchical learning of generative models is useful for representing and interpreting complex data. For instance, one application is to learn an HMM to represent an individual's eye fixations on a stimuli, and then cluster individuals' HMMs to discover common eye gaze strategies. However, learning the individual representation models from observations and clustering individual models to group models are often considered as two separate tasks.In this paper, we propose a novel tree structure variational Bayesian method to learn the individual model and group model simultaneously by treating the group models as the parents of individual models, so that the individual model is learned from observations and regularized by its parents, and conversely, the parent model will be optimized to best represent its children. Due to the regularization process, our method has advantages when the number of training samples decreases. Experimental results on the synthetic datasets demonstrate the effectiveness of the proposed method.

Hierarchical Learning of Hidden Markov Models with Clustering Regularization

In the financial realm, profit generation greatly relies on the complicated task of stock prediction. Lately, neural methods have shown success in exploiting stock affecting signals from textual data across news and tweets to forecast stock performance. However, the dynamic, stochastic, and variably influential nature of text and prices makes it difficult to train neural stock trading models, limiting predictive performance and profits. To transcend this limitation, we propose a novel multi-modal curriculum learning approach: FinCLASS, which evaluates stock affecting signals via entropy-based heuristics and measures their linguistic and price-based complexities in a time-aware, hierarchical fashion. We show that training financial models can benefit by exposing neural networks to easier examples of stock affecting signals early during the training phase, before introducing samples having more complex linguistic and price-based temporal variations. Through experiments on benchmark English tweets and Chinese financial news spanning two major indexes and four global markets, we show how FinCLASS outperforms state-of-the-art across financial tasks of stock movement prediction, volatility regression, and profit generation. Through ablative and qualitative experiments, we set the case for FinCLASS as a generalizable framework for developing natural language-centric neural models for financial tasks.

Modeling Financial Uncertainty with Multivariate Temporal Entropy-based Curriculums

Variational Inference (VI) is a popular alternative to asymptotically exact sampling in Bayesian inference. Its main workhorse is optimization over a reverse Kullback-Leibler divergence (RKL), which typically underestimates the tail of the posterior leading to miscalibration and potential degeneracy. Importance sampling (IS), on the other hand, is often used to fine-tune and de-bias the estimates of approximate Bayesian inference procedures. The quality of IS crucially depends on the choice of the proposal distribution. Ideally, the proposal distribution has heavier tails than the target, which is rarely achievable by minimizing the RKL. We thus propose a novel combination of optimization and sampling techniques for approximate Bayesian inference by constructing an IS proposal distribution through the minimization of a forward KL (FKL) divergence. This approach guarantees asymptotic consistency and a fast convergence towards both the optimal IS estimator and the optimal variational approximation. We empirically demonstrate on real data that our method is competitive with variational boosting and MCMC.

Variational Refinement for Importance Sampling Using the Forward Kullback-Leibler Divergence

Creating representations of shapes that are invariant to isometric or almost-isometric transformations has long been an area of interest in shape analysis, since enforcing invariance allows the learning of more effective and robust shape representations. Most existing invariant shape representations are handcrafted, and previous work on learning shape representations do not focus on producing invariant representations. To solve the problem of learning unsupervised invariant shape representations, we use contrastive learning, which produces discriminative representations through learning invariance to user-specified data augmentations. To produce representations that are specifically isometry and almost-isometry invariant, we propose new data augmentations that randomly sample these transformations. We show experimentally that our method outperforms previous unsupervised learning approaches in both effectiveness and robustness.

Staying in Shape: Learning Invariant Shape Representations using ContrastiveLearning

Online imitation learning (IL) is an algorithmic framework that leverages interactions with expert policies for efficient policy optimization. Here policies are optimized by performing online learning on a sequence of loss functions that encourage the learner to mimic expert actions, and if the online learning has no regret, the agent can provably learn an expert-like policy. Online IL has demonstrated empirical successes in many applications and interestingly, its policy improvement speed observed in practice is usually much faster than existing theory suggests. In this work, we provide an explanation of this phenomenon. Let $\xi$ denote the policy class bias and assume the online IL loss functions are convex, smooth, and non-negative. We prove that, after $N$ rounds of online IL with stochastic feedback, the policy improves in $\tilde{O}(1/N + \sqrt{\xi/N})$ in both expectation and high probability. In other words, we show that adopting a sufficiently expressive policy class in online IL has two benefits: both the policy improvement speed increases and the performance bias decreases.

Explaining Fast Improvement in Online Imitation Learning

Resource allocation for coverage of geographical spaces is a challenging problem in robotics, sensor networks and security domains. Conventional solution approaches either: (a) rely on exploiting spatio-temporal structure of specific coverage problems, or (b) use genetic algorithms when targeting general coverage problems where no special exploitable structure exists. In this work, we propose the coverage gradient theorem, which provides a gradient estimator for a broad class of spatial coverage objectives using a combination of Newton-Leibniz theorem and implicit boundary differentiation. We also propose a tractable framework to approximate the coverage objectives and their gradients using spatial discretization and empirically demonstrate the efficacy of our framework on multi-resource spatial coverage problems.

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Trusted-Maximizers Entropy Search for Efficient Bayesian Optimization

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