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In a variety of problems, a decision-maker is unaware of the loss function associated with a task, yet it has to minimize this unknown loss in order to accomplish the task. Furthermore, the decision-maker&#39;s task may evolve, resulting in a varying loss function. In this setting, we explore sequential decision-making problems modeled by adversarial Markov decision processes, where the loss function may arbitrarily change at every time step. We consider the bandit feedback scenario, where the agent observes only the loss corresponding to its actions. We propose an algorithm, called online relative-entropy policy search with implicit exploration, that achieves a sublinear regret not only in expectation but, more importantly, with high probability. In particular, we prove that by employing an optimistically biased loss estimator, the proposed algorithm achieves a regret of $\tilde{\mathcal{O}}(T^{2/3} \sqrt{\tau|A||S|})$, where $|S|$ is the number of states, $|A|$ is the number of actions, $\tau$ is the mixing time, and $T$ is the time horizon. To our knowledge, the proposed algorithm is the first scheme that enjoys such high-probability regret bounds for general adversarial Markov decision processes under the presence of bandit feedback.

UAI 2021

No-Regret Learning with High-Probability in Adversarial Markov Decision Processes

regret bounds

online mirror descent

bandit algorithms

markov decision process

online learning

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/)

In a variety of problems, a decision-maker is unaware of the loss function associated with a task, yet it has to minimize this unknown loss in order to accomplish the task. Furthermore, the decision-maker's task may evolve, resulting in a varying loss function. In this setting, we explore sequential decision-making problems modeled by adversarial Markov decision processes, where the loss function may arbitrarily change at every time step. We consider the bandit feedback scenario, where the agent observes only the loss corresponding to its actions. We propose an algorithm, called online relative-entropy policy search with implicit exploration, that achieves a sublinear regret not only in expectation but, more importantly, with high probability. In particular, we prove that by employing an optimistically biased loss estimator, the proposed algorithm achieves a regret of $\tilde{\mathcal{O}}(T^{2/3} \sqrt{\tau|A||S|})$, where $|S|$ is the number of states, $|A|$ is the number of actions, $\tau$ is the mixing time, and $T$ is the time horizon. To our knowledge, the proposed algorithm is the first scheme that enjoys such high-probability regret bounds for general adversarial Markov decision processes under the presence of bandit feedback.

lightning talk

Estimation of probability density function from samples is one of the central problems in statistics and machine learning. Modern neural network-based models can learn high dimensional distributions but have problems with hyperparameter selection and are often prone to instabilities during training and inference. We propose a new efficient tensor train-based model for density estimation (TTDE). Such density parametrization allows exact sampling, calculation of cumulative and marginal density functions, and partition function. It also has very intuitive hyperparameters. We develop an efficient non-adversarial training procedure for TTDE based on the Riemannian optimization. Experimental results demonstrate the competitive performance of the proposed method in density estimation and sampling tasks, while TTDE significantly outperforms competitors in training speed.

Tensor-Train Density Estimation

We propose a similarity measure for sparsely sampled time course data in the form of a log-likelihood ratio of Gaussian processes (GP). The proposed GP similarity is similar to a Bayes factor and provides enhanced robustness to noise in sparse time series, such as those found in various biological settings, e.g., gene transcriptomics. We show that the GP measure is equivalent to the Euclidean distance when the noise variance in the GP is negligible compared to the noise variance of the signal. Our numerical experiments on both synthetic and real data show improved performance of the GP similarity when used in conjunction with two distance-based clustering methods.

Similarity Measure for Sparse Time Course Data Based on Gaussian Processes

To capture the slowly time-varying spectral content of real-world time-series, a common paradigm is to partition the data into approximately stationary intervals and perform inference in the time-frequency domain. However, this approach lacks a corresponding nonstationary time-domain generative model for the entire data and thus, time-domain inference occurs in each interval separately. This results in distortion/discontinuity around interval boundaries and can consequently lead to erroneous inferences based on any quantities derived from the posterior, such as the phase. To address these shortcomings, we propose the Piecewise Locally Stationary Oscillation (PLSO) model for decomposing time-series data with slowly time-varying spectra into several oscillatory, piecewise-stationary processes. PLSO, as a nonstationary time-domain generative model, enables inference on the entire time-series without boundary effects and simultaneously provides a characterization of its time-varying spectral properties. We also propose a novel two-stage inference algorithm that combines Kalman theory and an accelerated proximal gradient algorithm. We demonstrate these points through experiments on simulated data and real neural data from the rat and the human brain.

A generative framework for decomposing nonstationary time-series into piecewise stationary oscillatory components

Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are approximated with, potentially crude, surrogates. This difficulty has engendered loss-calibrated techniques that aim to learn posterior approximations that favor high-utility decisions. In this paper, focusing on Bayesian neural networks, we develop methods for correcting approximate posterior predictive distributions encouraging them to prefer high-utility decisions. In contrast to previous work, our approach is agnostic to the choice of the approximate inference algorithm, allows for efficient test time decision making through amortization, and empirically produces higher quality decisions. We demonstrate the effectiveness of our approach through controlled experiments spanning a diversity of tasks and datasets.

Post-hoc loss-calibration for Bayesian neural networks

The principle of optimism in the face of uncertainty is prevalent throughout sequential decision making problems such as multi-armed bandits and reinforcement learning (RL). To be successful, an optimistic RL algorithm must over-estimate the true value function (optimism) but not by so much that it is inaccurate (estimation error). In the tabular setting, many state-of-the-art methods produce the required optimism through approaches which are intractable when scaling to deep RL. We re-interpret these scalable optimistic model-based algorithms as solving a tractable noise augmented MDP. This formulation achieves a competitive regret bound: $\tilde{\mathcal{O}}( |\mathcal{S}|H\sqrt{|\mathcal{A}| T } )$ when augmenting using Gaussian noise, where $T$ is the total number of environment steps. We also explore how this trade-off changes in the deep RL setting, where we show empirically that estimation error is significantly more troublesome. However, we also show that if this error is reduced, optimistic model-based RL algorithms can match state-of-the-art performance in continuous control problems.

Towards Tractable Optimism in Model-Based Reinforcement Learning

To address the communication bottleneck problem in distributed optimization within a master-worker framework, we propose LocalNewton, a distributed second-order algorithm with \emph{local averaging}. In LocalNewton, the worker machines update their model in every iteration by finding a suitable second-order descent direction using only the data and model stored in their own local memory. We let the workers run multiple such iterations locally and communicate the models to the master node only once every few (say $L$) iterations. LocalNewton is highly practical since it requires only one hyperparameter, the number $L$ of local iterations. We use novel matrix concentration based techniques to obtain theoretical guarantees for LocalNewton, and we validate them with detailed empirical evaluation. To enhance practicability, we devise an adaptive scheme to choose $L$, and we show that this reduces the number of local iterations in worker machines between two model synchronizations as the training proceeds, successively refining the model quality at the master. Via extensive experiments using several real-world datasets on AWS Lambda (a high-latency serverless computing platform), we show that LocalNewton requires fewer than $60\%$ of the communication rounds (between master and workers) and less than $40\%$ of the end-to-end running time, compared to state-of-the-art algorithms, to reach the same training~loss.

LocalNewton: Reducing Communication Bottleneck for Distributed Learning

We propose probabilistic task modelling -- a generative probabilistic model for collections of tasks used in meta-learning. The proposed model combines variational auto-encoding and latent Dirichlet allocation to model each task as a mixture of Gaussian distribution in an embedding space. Such modelling provides an explicit representation of a task through its task-theme mixture. We present an efficient approximation inference technique based on variational inference method for empirical Bayes parameter estimation. We perform empirical evaluations to validate the task uncertainty and task distance produced by the proposed method through correlation diagrams of the prediction accuracy on testing tasks. We also carry out experiments of task selection in meta-learning to demonstrate how the task relatedness inferred from the proposed model help to facilitate meta-learning algorithms.

Probabilistic task modelling for meta-learning

This paper studies the relationship between generalization and privacy preservation of machine learning in two steps. We first establish an alignment between the two facets for any learning algorithm. We prove that $(\varepsilon, \delta)$-differential privacy implies an on-average generalization bound for a multi-sample-set learning algorithm, which further leads to a high-probability bound for any learning algorithm. We then investigate how the iterative nature shared by most learning algorithms influences privacy preservation and further generalization. Three composition theorems are proved to approximate the differential privacy of an iterative algorithm through the differential privacy of its every iteration. Integrating the above two steps, we eventually deliver generalization bounds for iterative learning algorithms. Our results are strictly tighter than the existing works. Particularly, our generalization bounds do not rely on the model size which is prohibitively large in deep learning. Experiments of MLP, VGG, and ResNet on MNIST, CIFAR-10, and CIFAR-100 are in full agreement with our theory. The theory applies to a wide spectrum of learning algorithms. In this paper, it is applied to the Gaussian mechanism as an example.

Tighter Generalization Bounds for Iterative Privacy-Preserving Algorithms

In the area of natural language processing, deep learning models are recently known to be vulnerable to various types of adversarial perturbations, but relatively few works are done on the defense side. Especially, there exists few effective defense method against the successful synonym substitution based attacks that preserve the syntactic structure and semantic information of the original text while fooling the deep learning models. We contribute in this direction and propose a novel adversarial defense method called Synonym Encoding Method (SEM). Specifically, SEM inserts an encoder before the input layer of the target model to map each cluster of synonyms to a unique encoding and trains the model to eliminate possible adversarial perturbations without modifying the network architecture or adding extra data. Extensive experiments demonstrate that SEM can effectively defend the current synonym substitution based attacks and block the transferability of adversarial examples. SEM is also easy and efficient to scale to large models and big datasets.

Natural Language Adversarial Defense through Synonym Encoding

In this paper, we investigate the non-stationary combinatorial semi-bandit problem, both in the switching case and in the dynamic case. In the general case where (a) the reward function is non-linear, (b) arms may be probabilistically triggered, and (c) only approximate offline oracle exists \cite{wang2017improving}, our algorithm achieves $\tilde{O}(\sqrt{N T})$ distribution-dependent regret in the switching case, and $\tilde{O}({V}^{1/3}T^{2/3})$ in the dynamic case, where ${N}$ is the number of switchings and ${V}$ is the sum of the total ``distribution changes''. The regret bounds in both scenarios are nearly optimal, but our algorithm needs to know the parameter ${N}$ or ${V}$ in advance.

No-Regret Learning with High-Probability in Adversarial Markov Decision Processes

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