We study the problem of episodic reinforcement learning in continuous state-action spaces with unknown rewards and transitions. Specifically, we consider the setting where the rewards and transitions are modeled using parametric bilinear exponential families. We propose an algorithm, BEF-RLSVI, that a) uses penalized maximum likelihood estimators to learn the unknown parameters, b) injects a calibrated Gaussian noise in the parameter of rewards to ensure exploration, and c) leverages linearity of the exponential family with respect to an underlying RKHS to perform tractable planning. We further provide a frequentist regret analysis of BEF-RLSVI that yields an upper bound of $\tilde{\mathcal{O}}(\sqrt{d^3H^3K})$, where $d$ is the dimension of the parameters, $H$ is the episode length, and $K$ is the number of episodes. Our analysis improves the existing bounds for the bilinear exponential family of MDPs by $\sqrt{H}$ and removes the handcrafted clipping deployed in existing \RLSVI-type algorithms. Our regret bound is order-optimal with respect to $H$ and $K$.

We consider a multi-armed bandit problem with $M$ latent contexts, where an agent interacts with the environment for an episode of $H$ time steps. Depending on the length of the episode, the learner may not be able to estimate accurately the latent context. The resulting partial observation of the environment makes the learning task significantly more challenging. Without any additional structural assumptions, existing techniques to tackle partially observed settings imply the decision maker can learn a near-optimal policy with $O(A)^H$ episodes, but do not promise more. In this work, we show that learning with {\em polynomial} samples in $A$ is possible. We achieve this by using techniques from experiment design. Then, through a method-of-moments approach, we design a procedure that provably learns a near-optimal policy with $O(\texttt{poly}(A) + \texttt{poly}(M,H)^{\min(M,H)})$ interactions. In practice, we show that we can formulate the moment-matching via maximum likelihood estimation. In our experiments, this significantly outperforms the worst-case guarantees, as well as existing practical methods.

Knowledge tracing (KT) is a fundamental task in educational data mining that mainly focuses on students' dynamic cognitive states of skills. The question-answering process of students can be regarded as a thinking process that considers the following two problems. One problem is which skills are needed to answer the question, and the other is how to use these skills in order. If a student wants to answer a question correctly, the student should not only master the set of skills involved in the question but also think and obtain the associative path on the skills graph. The nodes in the associative path refer to the skills needed and the path shows the order of using them. The associative path is referred to as the skill mode. Thus, obtaining the skill modes is the key to answering questions successfully. However, most existing KT models only focus on a set of skills, without considering the skill modes. We propose a KT model, called APGKT, that exploits skill modes. Specifically, we extract the subgraph topology of the skills involved in the question and combine the difficulty level of the skills to obtain the skill modes via encoding; then, through multi-layer recurrent neural networks, we obtain a student's higher-order cognitive states of skills, which is used to predict the student's future answering performance. Experiments on five benchmark datasets validate the effectiveness of the proposed model.

Abstract--In this paper, we propose a new technique to uniquely classify and identify multiple users accessing a single application using keystroke dynamics. This problem is usually encountered when multiple users have legitimate access to shared computers and accounts, where, at times, one user can inadvertently be logged in on another user's account. Since the login processes are usually bypassed at this stage, we rely on keystroke dynamics in order to tell users apart. Our algorithm uses the quantile transform and techniques from localization to classify and identify users. Specifically, we use an algorithm known as ordinal Unfolding based Localization (UNLOC), which uses only ordinal data obtained from comparing distance proxies, by "locating" users in a reduced PCA/Kernel-PCA/t-SNE space based on their typing patterns. Our results are validated with the help of benchmark keystroke datasets and show that our algorithm outperforms other methods. In this paper, we consider With increasing digital presence, securing sensitive and personal both sources of keystrokes. In general, systems authentication [9], [12], [14], where a profile is built for only or web applications utilize one-time authentication using one user. The algorithms used in single-user authentication single sign-on for providing security. Banking and financial determine whether the user at the keyboard is the user in the institutions generally use a knowledge-based mechanism to model.

Aggregating a dataset, then injecting some noise, is a simple and common way to release differentially private data.However, aggregated data -- even without noise -- is not an appropriate input for machine learning classifiers.In this work, we show how a new model, similar to a logistic regression, may be learned from aggregated data only by approximating the unobserved feature distribution with a maximum entropy hypothesis. The resulting model is a Markov Random Field (MRF), and we detail how to apply, modify and scale a MRF training algorithm to our setting. Finally we present empirical evidence on several public datasets that the model learned this way can achieve performances comparable to those of a logistic model trained with the full unaggregated data.

In this work, we apply information theory inspired methods to quantify changes in daily activity patterns. We use in-home movement monitoring data and show how they can help indicate the occurrence of healthcare-related events. Three different types of entropy measures namely Shannon's entropy, entropy rates for Markov chains, and entropy production rate have been utilised. The measures are evaluated on a large-scale in-home monitoring dataset that has been collected within our dementia care clinical study. The study uses Internet of Things (IoT) enabled solutions for continuous monitoring of in-home activity, sleep, and physiology to develop care and early intervention solutions to support people living with dementia (PLWD) in their own homes. Our main goal is to show the applicability of the entropy measures to time-series activity data analysis and to use the extracted measures as new engineered features that can be fed into inference and analysis models. The results of our experiments show that in most cases the combination of these measures can indicate the occurrence of healthcare-related events. We also find that different participants with the same events may have different measures based on one entropy measure. So using a combination of these measures in an inference model will be more effective than any of the single measures.

Driven by several successful applications such as in stochastic gradient descent or in Bayesian computation, control variates have become a major tool for Monte Carlo integration. However, standard methods do not allow the distribution of the particles to evolve during the algorithm, as is the case in sequential simulation methods. Within the standard adaptive importance sampling framework, a simple weighted least squares approach is proposed to improve the procedure with control variates. The procedure takes the form of a quadrature rule with adapted quadrature weights to reflect the information brought in by the control variates. The quadrature points and weights do not depend on the integrand, a computational advantage in case of multiple integrands. Moreover, the target density needs to be known only up to a multiplicative constant. Our main result is a non-asymptotic bound on the probabilistic error of the procedure. The bound proves that for improving the estimate's accuracy, the benefits from adaptive importance sampling and control variates can be combined. The good behavior of the method is illustrated empirically on synthetic examples and real-world data for Bayesian linear regression.

This paper tackles the problem of human motion prediction, consisting in forecasting future body poses from historically observed sequences. State-of-the-art approaches provide good results, however, they rely on deep learning architectures of arbitrary complexity, such as Recurrent Neural Networks(RNN), Transformers or Graph Convolutional Networks(GCN), typically requiring multiple training stages and more than 2 million parameters. In this paper, we show that, after combining with a series of standard practices, such as applying Discrete Cosine Transform(DCT), predicting residual displacement of joints and optimizing velocity as an auxiliary loss, a light-weight network based on multi-layer perceptrons(MLPs) with only 0.14 million parameters can surpass the state-of-the-art performance. An exhaustive evaluation on the Human3.6M, AMASS, and 3DPW datasets shows that our method, named siMLPe, consistently outperforms all other approaches. We hope that our simple method could serve as a strong baseline for the community and allow re-thinking of the human motion prediction problem. The code is publicly available at \url{https://github.com/dulucas/siMLPe}.

Robust Markov decision processes (MDPs) provide a general framework to model decision problems where the system dynamics are changing or only partially known. Efficient methods for some \texttt{sa}-rectangular robust MDPs exist, using its equivalence with reward regularized MDPs, generalizable to online settings. In comparison to \texttt{sa}-rectangular robust MDPs, \texttt{s}-rectangular robust MDPs are less restrictive but much more difficult to deal with. Interestingly, recent works have established the equivalence between \texttt{s}-rectangular robust MDPs and policy regularized MDPs. But we don't have a clear understanding to exploit this equivalence, to do policy improvement steps to get the optimal value function or policy. We don't have a clear understanding of greedy/optimal policy except it can be stochastic. There exist no methods that can naturally be generalized to model-free settings. We show a clear and explicit equivalence between \texttt{s}-rectangular $L_p$ robust MDPs and policy regularized MDPs that resemble very much policy entropy regularized MDPs widely used in practice. Further, we dig into the policy improvement step and concretely derive optimal robust Bellman operators for \texttt{s}-rectangular $L_p$ robust MDPs. We find that the greedy/optimal policies in \texttt{s}-rectangular $L_p$ robust MDPs are threshold policies that play top $k$ actions whose $Q$ value is greater than some threshold (value), proportional to the $(p-1)$th power of its advantage. In addition, we show time complexity of (\texttt{sa} and \texttt{s}-rectangular) $L_p$ robust MDPs is the same as non-robust MDPs up to some log factors. Our work greatly extends the existing understanding of \texttt{s}-rectangular robust MDPs and naturally generalizable to online settings.

Motivated by theoretical advancements in dimensionality reduction techniques we use a recent model, called Block Markov Chains, to conduct a practical study of clustering in real-world sequential data. Clustering algorithms for Block Markov Chains possess theoretical optimality guarantees and can be deployed in sparse data regimes. Despite these favorable theoretical properties, a thorough evaluation of these algorithms in realistic settings has been lacking. We address this issue and investigate the suitability of these clustering algorithms in exploratory data analysis of real-world sequential data. In particular, our sequential data is derived from human DNA, written text, animal movement data and financial markets. In order to evaluate the determined clusters, and the associated Block Markov Chain model, we further develop a set of evaluation tools. These tools include benchmarking, spectral noise analysis and statistical model selection tools. An efficient implementation of the clustering algorithm and the new evaluation tools is made available together with this paper. Practical challenges associated to real-world data are encountered and discussed. It is ultimately found that the Block Markov Chain model assumption, together with the tools developed here, can indeed produce meaningful insights in exploratory data analyses despite the complexity and sparsity of real-world data.