The growing prospect of deep reinforcement learning (DRL) being used in cyber-physical systems has raised concerns around safety and robustness of autonomous agents. Recent work on generating adversarial attacks have shown that it is computationally feasible for a bad actor to fool a DRL policy into behaving sub optimally. Although certain adversarial attacks with specific attack models have been addressed, most studies are only interested in off-line optimization in the data space (e.g., example fitting, distillation). This paper introduces a Meta-Learned Advantage Hierarchy (MLAH) framework that is attack model-agnostic and more suited to reinforcement learning, via handling the attacks in the decision space (as opposed to data space) and directly mitigating learned bias introduced by the adversary. In MLAH, we learn separate sub-policies (nominal and adversarial) in an online manner, as guided by a supervisory master agent that detects the presence of the adversary by leveraging the advantage function for the sub-policies. We demonstrate that the proposed algorithm enables policy learning with significantly lower bias as compared to the state-of-the-art policy learning approaches even in the presence of heavy state information attacks. We present algorithm analysis and simulation results using popular OpenAI Gym environments.

Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a variant of stochastic gradient descent where the random samples are taken on the trajectory of a Markov chain. Existing results of this method assume convex objectives and a reversible Markov chain and thus have their limitations. We establish new non-ergodic convergence under wider step sizes, for nonconvex problems, and for non-reversible finite-state Markov chains. Nonconvexity makes our method applicable to broader problem classes. Non-reversible finite-state Markov chains, on the other hand, can mix substatially faster. To obtain these results, we introduce a new technique that varies the mixing levels of the Markov chains. The reported numerical results validate our contributions.

We introduce a method which enables a recurrent dynamics model to be temporally abstract. Our approach, which we call Adaptive Skip Intervals (ASI), is based on the observation that in many sequential prediction tasks, the exact time at which events occur is irrelevant to the underlying objective. Moreover, in many situations, there exist prediction intervals which result in particularly easy-to-predict transitions. We show that there are prediction tasks for which we gain both computational efficiency and prediction accuracy by allowing the model to make predictions at a sampling rate which it can choose itself.

Entropy estimation is one of the prototypical problems in distribution property testing. To consistently estimate the Shannon entropy of a distribution on $S$ elements with independent samples, the optimal sample complexity scales sublinearly with $S$ as $\Theta(\frac{S}{\log S})$ as shown by Valiant and Valiant \cite{Valiant--Valiant2011}. Extending the theory and algorithms for entropy estimation to dependent data, this paper considers the problem of estimating the entropy rate of a stationary reversible Markov chain with $S$ states from a sample path of $n$ observations. We show that \begin{itemize} \item Provided the Markov chain mixes not too slowly, \textit{i.e.}, the relaxation time is at most $O(\frac{S}{\ln^3 S})$, consistent estimation is achievable when $n \gg \frac{S^2}{\log S}$. \item Provided the Markov chain has some slight dependency, \textit{i.e.}, the relaxation time is at least $1+\Omega(\frac{\ln^2 S}{\sqrt{S}})$, consistent estimation is impossible when $n \lesssim \frac{S^2}{\log S}$. \end{itemize} Under both assumptions, the optimal estimation accuracy is shown to be $\Theta(\frac{S^2}{n \log S})$. In comparison, the empirical entropy rate requires at least $\Omega(S^2)$ samples to be consistent, even when the Markov chain is memoryless. In addition to synthetic experiments, we also apply the estimators that achieve the optimal sample complexity to estimate the entropy rate of the English language in the Penn Treebank and the Google One Billion Words corpora, which provides a natural benchmark for language modeling and relates it directly to the widely used perplexity measure.

What policy should be employed in a Markov decision process with uncertain parameters? Robust optimization answer to this question is to use rectangular uncertainty sets, which independently reflect available knowledge about each state, and then obtains a decision policy that maximizes expected reward for the worst-case decision process parameters from these uncertainty sets. While this rectangularity is convenient computationally and leads to tractable solutions, it often produces policies that are too conservative in practice, and does not facilitate knowledge transfer between portions of the state space or across related decision processes. In this work, we propose non-rectangular uncertainty sets that bound marginal moments of state-action features defined over entire trajectories through a decision process. This enables generalization to different portions of the state space while retaining appropriate uncertainty of the decision process. We develop algorithms for solving the resulting robust decision problems, which reduce to finding an optimal policy for a mixture of decision processes, and demonstrate the benefits of our approach experimentally.

In many real-world reinforcement learning (RL) problems, besides optimizing the main objective function, an agent must concurrently avoid violating a number of constraints. In particular, besides optimizing performance, it is crucial to guarantee the safety of an agent during training as well as deployment (e.g., a robot should avoid taking actions - exploratory or not - which irrevocably harm its hard- ware). To incorporate safety in RL, we derive algorithms under the framework of constrained Markov decision processes (CMDPs), an extension of the standard Markov decision processes (MDPs) augmented with constraints on expected cumulative costs. Our approach hinges on a novel Lyapunov method. We define and present a method for constructing Lyapunov functions, which provide an effective way to guarantee the global safety of a behavior policy during training via a set of local linear constraints. Leveraging these theoretical underpinnings, we show how to use the Lyapunov approach to systematically transform dynamic programming (DP) and RL algorithms into their safe counterparts. To illustrate their effectiveness, we evaluate these algorithms in several CMDP planning and decision-making tasks on a safety benchmark domain. Our results show that our proposed method significantly outperforms existing baselines in balancing constraint satisfaction and performance.

Expectation-Maximization (EM) is a popular tool for learning latent variable models, but the vanilla batch EM does not scale to large data sets because the whole data set is needed at every E-step. Stochastic Expectation Maximization (sEM) reduces the cost of E-step by stochastic approximation. However, sEM has a slower asymptotic convergence rate than batch EM, and requires a decreasing sequence of step sizes, which is difficult to tune. In this paper, we propose a variance reduced stochastic EM (sEM-vr) algorithm inspired by variance reduced stochastic gradient descent algorithms. We show that sEM-vr has the same exponential asymptotic convergence rate as batch EM. Moreover, sEM-vr only requires a constant step size to achieve this rate, which alleviates the burden of parameter tuning. We compare sEM-vr with batch EM, sEM and other algorithms on Gaussian mixture models and probabilistic latent semantic analysis, and sEM-vr converges significantly faster than these baselines.

At their core, many unsupervised learning models provide a compact representation of homogeneous density mixtures, but their similarities and differences are not always clearly understood. In this work, we formally establish the relationships among latent tree graphical models (including special cases such as hidden Markov models and tensorial mixture models), hierarchical tensor formats and sum-product networks. Based on this connection, we then give a unified treatment of exponential separation in \emph{exact} representation size between deep mixture architectures and shallow ones. In contrast, for \emph{approximate} representation, we show that the conditional gradient algorithm can approximate any homogeneous mixture within $\epsilon$ accuracy by combining $O(1/\epsilon^2)$ ``shallow'' architectures, where the hidden constant may decrease (exponentially) with respect to the depth. Our experiments on both synthetic and real datasets confirm the benefits of depth in density estimation.

Implicit feedback is widely used in collaborative filtering methods for recommendation. It is well known that implicit feedback contains a large number of values that are \emph{missing not at random} (MNAR); and the missing data is a mixture of negative and unknown feedback, making it difficult to learn user's negative preferences. Recent studies modeled \emph{exposure}, a latent missingness variable which indicates whether an item is missing to a user, to give each missing entry a confidence of being negative feedback. However, these studies use static models and ignore the information in temporal dependencies among items, which seems to be a essential underlying factor to subsequent missingness. To model and exploit the dynamics of missingness, we propose a latent variable named ``\emph{user intent}'' to govern the temporal changes of item missingness, and a hidden Markov model to represent such a process. The resulting framework captures the dynamic item missingness and incorporate it into matrix factorization (MF) for recommendation. We also explore two types of constraints to achieve a more compact and interpretable representation of \emph{user intents}. Experiments on real-world datasets demonstrate the superiority of our method against state-of-the-art recommender systems.

A conjugate Gamma-Poisson model for Dynamic Matrix Factorization incorporated with metadata influence (mGDMF for short) is proposed to effectively and efficiently model massive, sparse and dynamic data in recommendations. Modeling recommendation problems with a massive number of ratings and very sparse or even no ratings on some users/items in a dynamic setting is very demanding and poses critical challenges to well-studied matrix factorization models due to the large-scale, sparse and dynamic nature of the data. Our proposed mGDMF tackles these challenges by introducing three strategies: (1) constructing a stable Gamma-Markov chain model that smoothly drifts over time by combining both static and dynamic latent features of data; (2) incorporating the user/item metadata into the model to tackle sparse ratings; and (3) undertaking stochastic variational inference to efficiently handle massive data. mGDMF is conjugate, dynamic and scalable. Experiments show that mGDMF significantly (both effectively and efficiently) outperforms the state-of-the-art static and dynamic models on large, sparse and dynamic data.