Ensemble Estimation of Information Divergence †.

Recent work has focused on the problem of nonparametric estimation of information divergence functionals between two continuous random variables. Many existing approaches require either restrictive assumptions about the density support set or difficult calculations at the support set boundary which must be known a priori. The mean squared error (MSE) convergence rate of a leave-one-out kernel density plug-in divergence functional estimator for general bounded density support sets is derived where knowledge of the support boundary, and therefore, the boundary correction is not required. The theory of optimally weighted ensemble estimation is generalized to derive a divergence estimator that achieves the parametric rate when the densities are sufficiently smooth. Guidelines for the tuning parameter selection and the asymptotic distribution of this estimator are provided. Based on the theory, an empirical estimator of Rényi-α divergence is proposed that greatly outperforms the standard kernel density plug-in estimator in terms of mean squared error, especially in high dimensions. The estimator is shown to be robust to the choice of tuning parameters. We show extensive simulation results that verify the theoretical results of our paper. Finally, we apply the proposed estimator to estimate the bounds on the Bayes error rate of a cell classification problem.

Personalized HeartSteps: A Reinforcement Learning Algorithm for Optimizing Physical Activity.

With the recent proliferation of mobile health technologies, health scientists are increasingly interested in developing just-in-time adaptive interventions (JITAIs), typically delivered via notifications on mobile devices and designed to help users prevent negative health outcomes and to promote the adoption and maintenance of healthy behaviors. A JITAI involves a sequence of decision rules (i.e., treatment policies) that take the user's current context as input and specify whether and what type of intervention should be provided at the moment. In this work, we describe a reinforcement learning (RL) algorithm that continuously learns and improves the treatment policy embedded in the JITAI as data is being collected from the user. This work is motivated by our collaboration on designing an RL algorithm for HeartSteps V2 based on data collected HeartSteps V1. HeartSteps is a physical activity mobile health application. The RL algorithm developed in this work is being used in HeartSteps V2 to decide, five times per day, whether to deliver a context-tailored activity suggestion.

Action Centered Contextual Bandits.

Contextual bandits have become popular as they offer a middle ground between very simple approaches based on multi-armed bandits and very complex approaches using the full power of reinforcement learning. They have demonstrated success in web applications and have a rich body of associated theoretical guarantees. Linear models are well understood theoretically and preferred by practitioners because they are not only easily interpretable but also simple to implement and debug. Furthermore, if the linear model is true, we get very strong performance guarantees. Unfortunately, in emerging applications in mobile health, the time-invariant linear model assumption is untenable. We provide an extension of the linear model for contextual bandits that has two parts: baseline reward and treatment effect. We allow the former to be complex but keep the latter simple. We argue that this model is plausible for mobile health applications. At the same time, it leads to algorithms with strong performance guarantees as in the linear model setting, while still allowing for complex nonlinear baseline modeling. Our theory is supported by experiments on data gathered in a recently concluded mobile health study.