We derive an alternative proof for the regret of Thompson sampling (\ts) in the stochastic linear bandit setting. While we obtain a regret bound of order $\widetilde{O}(d^{3/2}\sqrt{T})$ as in previous results, the proof sheds new light on the functioning of the \ts. We leverage on the structure of the problem to show how the regret is related to the sensitivity (i.e., the gradient) of the objective function and how selecting optimal arms associated to \textit{optimistic} parameters does control it. Thus we show that \ts can be seen as a generic randomized algorithm where the sampling distribution is designed to have a fixed probability of being optimistic, at the cost of an additional $\sqrt{d}$ regret factor compared to a UCB-like approach. Furthermore, we show that our proof can be readily applied to regularized linear optimization and generalized linear model problems.

In real-time monitoring of hospital patients, high-quality inference of patients' health status using all information available from clinical covariates and lab tests are essential to enable successful medical interventions and improve patient outcomes. In this work, we develop and explore a Bayesian nonparametric model based on Gaussian process (GP) regression for hospital patient monitoring. Our method, MedGP, incorporates 24 clinical and lab covariates and supports a rich reference data set from which the relationships between these observed covariates may be inferred and exploited for high-quality inference of patient state over time. To do this, we develop a highly structured sparse GP kernel to enable tractable computation over tens of thousands of time points while estimating correlations among clinical covariates, patients, and periodicity in high-dimensional time series measurements of physiological signals. We apply MedGP to data from hundreds of thousands of patients treated at the Hospital of the University of Pennsylvania. MedGP has a number of benefits over current methods, including (i) not requiring an alignment of the time series data, (ii) quantifying confidence intervals in the predictions, (iii) exploiting a vast and rich database of patients, and (iv) providing interpretable relationships among clinical covariates. We evaluate and compare results from MedGP on the task of online state prediction for three different patient subgroups.

Managers of US National Forests must decide what policy to apply for dealing with lightning-caused wildfires. Conflicts among stakeholders (e.g., timber companies, home owners, and wildlife biologists) have often led to spirited political debates and even violent eco-terrorism. One way to transform these conflicts into multi-stakeholder negotiations is to provide a high-fidelity simulation environment in which stakeholders can explore the space of alternative policies and understand the tradeoffs therein. Such an environment needs to support fast optimization of MDP policies so that users can adjust reward functions and analyze the resulting optimal policies. This paper assesses the suitability of SMAC---a black-box empirical function optimization algorithm---for rapid optimization of MDP policies. The paper describes five reward function components and four stakeholder constituencies. It then introduces a parameterized class of policies that can be easily understood by the stakeholders. SMAC is applied to find the optimal policy in this class for the reward functions of each of the stakeholder constituencies. The results confirm that SMAC is able to rapidly find good policies that make sense from the domain perspective. Because the full-fidelity forest fire simulator is far too expensive to support interactive optimization, SMAC is applied to a surrogate model constructed from a modest number of runs of the full-fidelity simulator. To check the quality of the SMAC-optimized policies, the policies are evaluated on the full-fidelity simulator. The results confirm that the surrogate values estimates are valid. This is the first successful optimization of wildfire management policies using a full-fidelity simulation. The same methodology should be applicable to other contentious natural resource management problems where high-fidelity simulation is extremely expensive.

We consider the exploration-exploitation tradeoff in linear quadratic (LQ) control problems, where the state dynamics is linear and the cost function is quadratic in states and controls. We analyze the regret of Thompson sampling (TS) (a.k.a. posterior-sampling for reinforcement learning) in the frequentist setting, i.e., when the parameters characterizing the LQ dynamics are fixed. Despite the empirical and theoretical success in a wide range of problems from multi-armed bandit to linear bandit, we show that when studying the frequentist regret TS in control problems, we need to trade-off the frequency of sampling optimistic parameters and the frequency of switches in the control policy. This results in an overall regret of $O(T^{2/3})$, which is significantly worse than the regret $O(\sqrt{T})$ achieved by the optimism-in-face-of-uncertainty algorithm in LQ control problems.

Markov networks are extensively used to model complex sequential, spatial, and relational interactions in a wide range of fields. By learning the structure of independences of a domain, more accurate joint probability distributions can be obtained for inference tasks or, more directly, for interpreting the most significant relations among the variables. Recently, several researchers have investigated techniques for automatically learning the structure from data by obtaining the probabilistic maximum-a-posteriori structure given the available data. However, all the approximations proposed decompose the posterior of the whole structure into local sub-problems, by assuming that the posteriors of the Markov blankets of all the variables are mutually independent. In this work, we propose a scoring function for relaxing such assumption. The Blankets Joint Posterior score computes the joint posterior of structures as a joint distribution of the collection of its Markov blankets. Essentially, the whole posterior is obtained by computing the posterior of the blanket of each variable as a conditional distribution that takes into account information from other blankets in the network. We show in our experimental results that the proposed approximation can improve the sample complexity of state-of-the-art scores when learning complex networks, where the independence assumption between blanket variables is clearly incorrect.

Datasets with hundreds of variables and many missing values are commonplace. In this setting, it is both statistically and computationally challenging to detect true predictive relationships between variables and also to suppress false positives. This paper proposes an approach that combines probabilistic programming, information theory, and non-parametric Bayes. It shows how to use Bayesian non-parametric modeling to (i) build an ensemble of joint probability models for all the variables; (ii) efficiently detect marginal independencies; and (iii) estimate the conditional mutual information between arbitrary subsets of variables, subject to a broad class of constraints. Users can access these capabilities using BayesDB, a probabilistic programming platform for probabilistic data analysis, by writing queries in a simple, SQL-like language. This paper demonstrates empirically that the method can (i) detect context-specific (in)dependencies on challenging synthetic problems and (ii) yield improved sensitivity and specificity over baselines from statistics and machine learning, on a real-world database of over 300 sparsely observed indicators of macroeconomic development and public health.

This paper introduces a method for efficiently inferring a high-dimensional distributed quantity from a few observations. The quantity of interest (QoI) is approximated in a basis (dictionary) learned from a training set. The coefficients associated with the approximation of the QoI in the basis are determined by minimizing the misfit with the observations. To obtain a probabilistic estimate of the quantity of interest, a Bayesian approach is employed. The QoI is treated as a random field endowed with a hierarchical prior distribution so that closed-form expressions can be obtained for the posterior distribution. The main contribution of the present work lies in the derivation of \emph{a representation basis consistent with the observation chain} used to infer the associated coefficients. The resulting dictionary is then tailored to be both observable by the sensors and accurate in approximating the posterior mean. An algorithm for deriving such an observable dictionary is presented. The method is illustrated with the estimation of the velocity field of an open cavity flow from a handful of wall-mounted point sensors. Comparison with standard estimation approaches relying on Principal Component Analysis and K-SVD dictionaries is provided and illustrates the superior performance of the present approach.

Bayesian inference for complex models is challenging due to the need to explore high-dimensional spaces and multimodality and standard Monte Carlo samplers can have difficulties effectively exploring the posterior. We introduce a general purpose rejection-free ensemble Markov Chain Monte Carlo (MCMC) technique to improve on existing poorly mixing samplers. This is achieved by combining parallel tempering and an auxiliary variable move to exchange information between the chains. We demonstrate this ensemble MCMC scheme on Bayesian inference in Factorial Hidden Markov Models. This high-dimensional inference problem is difficult due to the exponentially sized latent variable space. Existing sampling approaches mix slowly and can get trapped in local modes. We show that the performance of these samplers is improved by our rejection-free ensemble technique and that the method is attractive and "easy-to-use" since no parameter tuning is required.

Inverse reinforcement learning (IRL) has become a useful tool for learning behavioral models from demonstration data. However, IRL remains mostly unexplored for multi-agent systems. In this paper, we show how the principle of IRL can be extended to homogeneous large-scale problems, inspired by the collective swarming behavior of natural systems. In particular, we make the following contributions to the field: 1) We introduce the swarMDP framework, a sub-class of decentralized partially observable Markov decision processes endowed with a swarm characterization. 2) Exploiting the inherent homogeneity of this framework, we reduce the resulting multi-agent IRL problem to a single-agent one by proving that the agent-specific value functions in this model coincide. 3) To solve the corresponding control problem, we propose a novel heterogeneous learning scheme that is particularly tailored to the swarm setting. Results on two example systems demonstrate that our framework is able to produce meaningful local reward models from which we can replicate the observed global system dynamics.

Machine learning is the art of using computer algorithms to learn from experiences and use those experiences for future predictions. Tom Mitchell gave a really simple definition of machine learning. A computer program is said to learn from experience (E) with respect to some task (T) and some performance measure (P), if its performance on (T), as measured by (P), improves with experience (E). This definition dazzled me a bit, too. In human language, if you want your program to predict, for example, buy patterns at a busy grocery store (task T), you can run it through a Machine Learning algorithm with data about past buying patterns (experience E) and, if it has successfully learned, it will then do better at predicting future buy patterns (performance measure P).