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We study reinforcement learning for two-player zero-sum Markov games with simultaneous moves in the finite-horizon setting, where the transition kernel of the underlying Markov games can be parameterized by a linear function over the current state, both players' actions and the next state. In particular, we assume that we can control both players and aim to find the Nash Equilibrium by minimizing the duality gap. We propose an algorithm Nash-UCRL based on the principle "Optimism-in-Face-of-Uncertainty". Our algorithm only needs to find a Coarse Correlated Equilibrium (CCE), which is computationally efficient. Specifically, we show that Nash-UCRL can provably achieve an $\tilde{O}(dH\sqrt{T})$ regret, where $d$ is the linear function dimension, $H$ is the length of the game and $T$ is the total number of steps in the game. To assess the optimality of our algorithm, we also prove an $\tilde{\Omega}( dH\sqrt{T})$ lower bound on the regret. Our upper bound matches the lower bound up to logarithmic factors, which suggests the optimality of our algorithm.

We consider the problem of extracting joint and individual signals from multi-view data, that is data collected from different sources on matched samples. While existing methods for multi-view data decomposition explore single matching of data by samples, we focus on double-matched multi-view data (matched by both samples and source features). Our motivating example is the miRNA data collected from both primary tumor and normal tissues of the same subjects; the measurements from two tissues are thus matched both by subjects and by miRNAs. Our proposed double-matched matrix decomposition allows to simultaneously extract joint and individual signals across subjects, as well as joint and individual signals across miRNAs. Our estimation approach takes advantage of double-matching by formulating a new type of optimization problem with explicit row space and column space constraints, for which we develop an efficient iterative algorithm. Numerical studies indicate that taking advantage of double-matching leads to superior signal estimation performance compared to existing multi-view data decomposition based on single-matching. We apply our method to miRNA data as well as data from the English Premier League soccer matches, and find joint and individual multi-view signals that align with domain specific knowledge.

Common tasks encountered in epidemiology, including disease incidence estimation and causal inference, rely on predictive modeling. Constructing a predictive model can be thought of as learning a prediction function, i.e., a function that takes as input covariate data and outputs a predicted value. Many strategies for learning these functions from data are available, from parametric regressions to machine learning algorithms. It can be challenging to choose an approach, as it is impossible to know in advance which one is the most suitable for a particular dataset and prediction task at hand. The super learner (SL) is an algorithm that alleviates concerns over selecting the one "right" strategy while providing the freedom to consider many of them, such as those recommended by collaborators, used in related research, or specified by subject-matter experts. It is an entirely pre-specified and data-adaptive strategy for predictive modeling. To ensure the SL is well-specified for learning the prediction function, the analyst does need to make a few important choices. In this Education Corner article, we provide step-by-step guidelines for making these choices, walking the reader through each of them and providing intuition along the way. In doing so, we aim to empower the analyst to tailor the SL specification to their prediction task, thereby ensuring their SL performs as well as possible. A flowchart provides a concise, easy-to-follow summary of key suggestions and heuristics, based on our accumulated experience, and guided by theory.

Data collection and research methodology represents a critical part of the research pipeline. On the one hand, it is important that we collect data in a way that maximises the validity of what we are measuring, which may involve the use of long scales with many items. On the other hand, collecting a large number of items across multiple scales results in participant fatigue, and expensive and time consuming data collection. It is therefore important that we use the available resources optimally. In this work, we consider how a consideration for theory and the associated causal/structural model can help us to streamline data collection procedures by not wasting time collecting data for variables which are not causally critical for subsequent analysis. This not only saves time and enables us to redirect resources to attend to other variables which are more important, but also increases research transparency and the reliability of theory testing. In order to achieve this streamlined data collection, we leverage structural models, and Markov conditional independency structures implicit in these models to identify the substructures which are critical for answering a particular research question. In this work, we review the relevant concepts and present a number of didactic examples with the hope that psychologists can use these techniques to streamline their data collection process without invalidating the subsequent analysis. We provide a number of simulation results to demonstrate the limited analytical impact of this streamlining.

The problem of Byzantine consensus has been key to designing secure distributed systems. However, it is particularly difficult, mainly due to the presence of Byzantine processes that act arbitrarily and the unknown message delays in general networks. Although it is well known that both safety and liveness are at risk as soon as $n/3$ Byzantine processes fail, very few works attempted to characterize precisely the faults that produce safety violations from the faults that produce termination violations. In this paper, we present a new lower bound on the solvability of the consensus problem by distinguishing deceitful faults violating safety and benign faults violating termination from the more general Byzantine faults, in what we call the Byzantine-deceitful-benign fault model. We show that one cannot solve consensus if $n\leq 3t+d+2q$ with $t$ Byzantine processes, $d$ deceitful processes, and $q$ benign processes. In addition, we show that this bound is tight by presenting the Basilic class of consensus protocols that solve consensus when $n > 3t+d+2q$. These protocols differ in the number of processes from which they wait to receive messages before progressing. Each of these protocols is thus better suited for some applications depending on the predominance of benign or deceitful faults. Finally, we study the fault tolerance of the Basilic class of consensus protocols in the context of blockchains that need to solve the weaker problem of eventual consensus. We demonstrate that Basilic solves this problem with only $n > 2t+d+q$, hence demonstrating how it can strengthen blockchain security.

We present a new approach for efficient exploration which leverages a low-dimensional encoding of the environment learned with a combination of model-based and model-free objectives. Our approach uses intrinsic rewards that are based on the distance of nearest neighbors in the low dimensional representational space to gauge novelty. We then leverage these intrinsic rewards for sample-efficient exploration with planning routines in representational space for hard exploration tasks with sparse rewards. One key element of our approach is the use of information theoretic principles to shape our representations in a way so that our novelty reward goes beyond pixel similarity. We test our approach on a number of maze tasks, as well as a control problem and show that our exploration approach is more sample-efficient compared to strong baselines.

Present-day atomistic simulations generate long trajectories of ever more complex systems. Analyzing these data, discovering metastable states, and uncovering their nature is becoming increasingly challenging. In this paper, we first use the variational approach to conformation dynamics to discover the slowest dynamical modes of the simulations. This allows the different metastable states of the system to be located and organized hierarchically. The physical descriptors that characterize metastable states are discovered by means of a machine learning method. We show in the cases of two proteins, Chignolin and Bovine Pancreatic Trypsin Inhibitor, how such analysis can be effortlessly performed in a matter of seconds. Another strength of our approach is that it can be applied to the analysis of both unbiased and biased simulations.

We propose a new fast streaming algorithm for the tensor completion problem of imputing missing entries of a low-tubal-rank tensor using the tensor singular value decomposition (t-SVD) algebraic framework. We show the t-SVD is a specialization of the well-studied block-term decomposition for third-order tensors, and we present an algorithm under this model that can track changing free submodules from incomplete streaming 2-D data. The proposed algorithm uses principles from incremental gradient descent on the Grassmann manifold of subspaces to solve the tensor completion problem with linear complexity and constant memory in the number of time samples. We provide a local expected linear convergence result for our algorithm. Our empirical results are competitive in accuracy but much faster in compute time than state-of-the-art tensor completion algorithms on real applications to recover temporal chemo-sensing and MRI data under limited sampling.

This paper proposes an active learning algorithm for solving regression and classification problems based on inverse-distance weighting functions for selecting the feature vectors to query. The algorithm has the following features: (i) supports both pool-based and population-based sampling; (ii) is independent of the type of predictor used; (iii) can handle known and unknown constraints on the queryable feature vectors; and (iv) can run either sequentially, or in batch mode, depending on how often the predictor is retrained. The method's potential is shown in numerical tests on illustrative synthetic problems and real-world regression and classification datasets from the UCI repository. A Python implementation of the algorithm that we call IDEAL (Inverse-Distance based Exploration for Active Learning), is available at \url{//cse.lab.imtlucca.it/~bemporad/ideal}.