Eric B. Laber

Tao Ma, Jin Zhu, Hengrui Cai et al.

In real-world applications of reinforcement learning, it is often challenging to obtain a state representation that is parsimonious and satisfies the Markov property without prior knowledge. Consequently, it is common practice to construct a state larger than necessary, e.g., by concatenating measurements over contiguous time points. However, needlessly increasing the dimension of the state may slow learning and obfuscate the learned policy. We introduce the notion of a minimal sufficient state in a Markov decision process (MDP) as the subvector of the original state under which the process remains an MDP and shares the same reward function as the original process. We propose a novel SEquEntial Knockoffs (SEEK) algorithm that estimates the minimal sufficient state in a system with high-dimensional complex nonlinear dynamics. In large samples, the proposed method achieves selection consistency. As the method is agnostic to the reinforcement learning algorithm being applied, it benefits downstream tasks such as policy learning. Empirical experiments verify theoretical results and show the proposed approach outperforms several competing methods regarding variable selection accuracy and regret.

Hwanwoo Kim, Dongkyu Derek Cho, Eric Laber

Temporal difference (TD) learning is a cornerstone of reinforcement learning. In the average-reward setting, standard TD($λ$) is highly sensitive to the choice of step-size and thus requires careful tuning to maintain numerical stability. We introduce average-reward implicit TD($λ$), which employs an implicit fixed point update to provide data-adaptive stabilization while preserving the per iteration computational complexity of standard average-reward TD($λ$). In contrast to prior finite-time analyses of average-reward TD($λ$), which impose restrictive step-size conditions, we establish finite-time error bounds for the implicit variant under substantially weaker step-size requirements. Empirically, average-reward implicit TD($λ$) operates reliably over a much broader range of step-sizes and exhibits markedly improved numerical stability. This enables more efficient policy evaluation and policy learning, highlighting its effectiveness as a robust alternative to average-reward TD($λ$).

Kevin Li, Eric Laber

The contextual bandit framework is widely used to solve sequential optimization problems where the reward of each decision depends on auxiliary context variables. In settings such as medicine, business, and engineering, the decision maker often possesses additional structural information on the generative model that can potentially be used to improve the efficiency of bandit algorithms. We consider settings in which the mean reward is known to be a concave function of the action for each fixed context. Examples include patient-specific dose-response curves in medicine and expected profit in online advertising auctions. We propose a contextual bandit algorithm that accelerates optimization by conditioning the posterior of a Bayesian Gaussian Process model on this concavity information. We design a novel shape-constrained reward function estimator using a specially chosen regression spline basis and constrained Gaussian Process posterior. Using this model, we propose a UCB algorithm and derive corresponding regret bounds. We evaluate our algorithm on numerical examples and test functions used to study optimal dosing of Anti-Clotting medication.

Naim U. Rashid, Daniel J. Luckett, Jingxiang Chen et al.

The complexity of human cancer often results in significant heterogeneity in response to treatment. Precision medicine offers potential to improve patient outcomes by leveraging this heterogeneity. Individualized treatment rules (ITRs) formalize precision medicine as maps from the patient covariate space into the space of allowable treatments. The optimal ITR is that which maximizes the mean of a clinical outcome in a population of interest. Patient-derived xenograft (PDX) studies permit the evaluation of multiple treatments within a single tumor and thus are ideally suited for estimating optimal ITRs. PDX data are characterized by correlated outcomes, a high-dimensional feature space, and a large number of treatments. Existing methods for estimating optimal ITRs do not take advantage of the unique structure of PDX data or handle the associated challenges well. In this paper, we explore machine learning methods for estimating optimal ITRs from PDX data. We analyze data from a large PDX study to identify biomarkers that are informative for developing personalized treatment recommendations in multiple cancers. We estimate optimal ITRs using regression-based approaches such as Q-learning and direct search methods such as outcome weighted learning. Finally, we implement a superlearner approach to combine a set of estimated ITRs and show that the resulting ITR performs better than any of the input ITRs, mitigating uncertainty regarding user choice of any particular ITR estimation methodology. Our results indicate that PDX data are a valuable resource for developing individualized treatment strategies in oncology.

Longshaokan Wang, Eric Laber, Yeng Saanchi et al.

Sex trafficking is a global epidemic. Escort websites are a primary vehicle for selling the services of such trafficking victims and thus a major driver of trafficker revenue. Many law enforcement agencies do not have the resources to manually identify leads from the millions of escort ads posted across dozens of public websites. We propose an ordinal regression neural network to identify escort ads that are likely linked to sex trafficking. Our model uses a modified cost function to mitigate inconsistencies in predictions often associated with nonparametric ordinal regression and leverages recent advancements in deep learning to improve prediction accuracy. The proposed method significantly improves on the previous state-of-the-art on Trafficking-10K, an expert-annotated dataset of escort ads. Additionally, because traffickers use acronyms, deliberate typographical errors, and emojis to replace explicit keywords, we demonstrate how to expand the lexicon of trafficking flags through word embeddings and t-SNE.

Zhen Li, Eric Laber

In this paper, we show the convergence rates of posterior distributions of the model dynamics in a MDP for both episodic and continuous tasks. The theoretical results hold for general state and action space and the parameter space of the dynamics can be infinite dimensional. Moreover, we show the convergence rates of posterior distributions of the mean accumulative reward under a fixed or the optimal policy and of the regret bound. A variant of Thompson sampling algorithm is proposed which provides both posterior convergence rates for the dynamics and the regret-type bound. Then the previous results are extended to Markov games. Finally, we show numerical results with three simulation scenarios and conclude with discussions.

Jesse Clifton, Lili Wu, Eric Laber

We introduce Parameterized Exploration (PE), a simple family of methods for model-based tuning of the exploration schedule in sequential decision problems. Unlike common heuristics for exploration, our method accounts for the time horizon of the decision problem as well as the agent's current state of knowledge of the dynamics of the decision problem. We show our method as applied to several common exploration techniques has superior performance relative to un-tuned counterparts in Bernoulli and Gaussian multi-armed bandits, contextual bandits, and a Markov decision process based on a mobile health (mHealth) study. We also examine the effects of the accuracy of the estimated dynamics model on the performance of PE.

Neal S. Grantham, Brian J. Reich, Eric B. Laber et al.

An important problem in forensic analyses is identifying the provenance of materials at a crime scene, such as biological material on a piece of clothing. This procedure, known as geolocation, is conventionally guided by expert knowledge of the biological evidence and therefore tends to be application-specific, labor-intensive, and subjective. Purely data-driven methods have yet to be fully realized due in part to the lack of a sufficiently rich data source. However, high-throughput sequencing technologies are able to identify tens of thousands of microbial taxa using DNA recovered from a single swab collected from nearly any object or surface. We present a new algorithm for geolocation that aggregates over an ensemble of deep neural network classifiers trained on randomly-generated Voronoi partitions of a spatial domain. We apply the algorithm to fungi present in each of 1300 dust samples collected across the continental United States and then to a global dataset of dust samples from 28 countries. Our algorithm makes remarkably good point predictions with more than half of the geolocation errors under 100 kilometers for the continental analysis and nearly 90% classification accuracy of a sample's country of origin for the global analysis. We suggest that the effectiveness of this model sets the stage for a new, quantitative approach to forensic geolocation.

Zhen Li, Nicholas J. Meyer, Eric B. Laber et al.

Pursuit-evasion is a multi-agent sequential decision problem wherein a group of agents known as pursuers coordinate their traversal of a spatial domain to locate an agent trying to evade them. Pursuit evasion problems arise in a number of import application domains including defense and route planning. Learning to optimally coordinate pursuer behaviors so as to minimize time to capture of the evader is challenging because of a large action space and sparse noisy state information; consequently, previous approaches have relied primarily on heuristics. We propose a variant of Thompson Sampling for pursuit-evasion that allows for the application of existing model-based planning algorithms. This approach is general in that it allows for an arbitrary number of pursuers, a general spatial domain, and the integration of auxiliary information provided by informants. In a suite of simulation experiments, Thompson Sampling for pursuit evasion significantly reduces time-to-capture relative to competing algorithms.

Daniel J. Luckett, Eric B. Laber, Samer S. El-Kamary et al.

Many problems that appear in biomedical decision making, such as diagnosing disease and predicting response to treatment, can be expressed as binary classification problems. The costs of false positives and false negatives vary across application domains and receiver operating characteristic (ROC) curves provide a visual representation of this trade-off. Nonparametric estimators for the ROC curve, such as a weighted support vector machine (SVM), are desirable because they are robust to model misspecification. While weighted SVMs have great potential for estimating ROC curves, their theoretical properties were heretofore underdeveloped. We propose a method for constructing confidence bands for the SVM ROC curve and provide the theoretical justification for the SVM ROC curve by showing that the risk function of the estimated decision rule is uniformly consistent across the weight parameter. We demonstrate the proposed confidence band method and the superior sensitivity and specificity of the weighted SVM compared to commonly used methods in diagnostic medicine using simulation studies. We present two illustrative examples: diagnosis of hepatitis C and a predictive model for treatment response in breast cancer.

Daniel J. Luckett, Eric B. Laber, Michael R. Kosorok

There is tremendous interest in precision medicine as a means to improve patient outcomes by tailoring treatment to individual characteristics. An individualized treatment rule formalizes precision medicine as a map from patient information to a recommended treatment. A treatment rule is defined to be optimal if it maximizes the mean of a scalar outcome in a population of interest, e.g., symptom reduction. However, clinical and intervention scientists often must balance multiple and possibly competing outcomes, e.g., symptom reduction and the risk of an adverse event. One approach to precision medicine in this setting is to elicit a composite outcome which balances all competing outcomes; unfortunately, eliciting a composite outcome directly from patients is difficult without a high-quality instrument, and an expert-derived composite outcome may not account for heterogeneity in patient preferences. We propose a new paradigm for the study of precision medicine using observational data that relies solely on the assumption that clinicians are approximately (i.e., imperfectly) making decisions to maximize individual patient utility. Estimated composite outcomes are subsequently used to construct an estimator of an individualized treatment rule which maximizes the mean of patient-specific composite outcomes. The estimated composite outcomes and estimated optimal individualized treatment rule provide new insights into patient preference heterogeneity, clinician behavior, and the value of precision medicine in a given domain. We derive inference procedures for the proposed estimators under mild conditions and demonstrate their finite sample performance through a suite of simulation experiments and an illustrative application to data from a study of bipolar depression.

Longshaokan Wang, Eric B. Laber, Katie Witkiewitz

Advances in mobile computing technologies have made it possible to monitor and apply data-driven interventions across complex systems in real time. Markov decision processes (MDPs) are the primary model for sequential decision problems with a large or indefinite time horizon. Choosing a representation of the underlying decision process that is both Markov and low-dimensional is non-trivial. We propose a method for constructing a low-dimensional representation of the original decision process for which: 1. the MDP model holds; 2. a decision strategy that maximizes mean utility when applied to the low-dimensional representation also maximizes mean utility when applied to the original process. We use a deep neural network to define a class of potential process representations and estimate the process of lowest dimension within this class. The method is illustrated using data from a mobile study on heavy drinking and smoking among college students.

Daniel J. Luckett, Eric B. Laber, Anna R. Kahkoska et al.

The vision for precision medicine is to use individual patient characteristics to inform a personalized treatment plan that leads to the best healthcare possible for each patient. Mobile technologies have an important role to play in this vision as they offer a means to monitor a patient's health status in real-time and subsequently to deliver interventions if, when, and in the dose that they are needed. Dynamic treatment regimes formalize individualized treatment plans as sequences of decision rules, one per stage of clinical intervention, that map current patient information to a recommended treatment. However, existing methods for estimating optimal dynamic treatment regimes are designed for a small number of fixed decision points occurring on a coarse time-scale. We propose a new reinforcement learning method for estimating an optimal treatment regime that is applicable to data collected using mobile technologies in an outpatient setting. The proposed method accommodates an indefinite time horizon and minute-by-minute decision making that are common in mobile health applications. We show the proposed estimators are consistent and asymptotically normal under mild conditions. The proposed methods are applied to estimate an optimal dynamic treatment regime for controlling blood glucose levels in patients with type 1 diabetes.

S. A. Murphy, Y. Deng, E. B. Laber et al.

We develop an off-policy actor-critic algorithm for learning an optimal policy from a training set composed of data from multiple individuals. This algorithm is developed with a view towards its use in mobile health.

Eric B. Laber, Daniel J. Lizotte, Bradley Ferguson

Dynamic treatment regimes operationalize the clinical decision process as a sequence of functions, one for each clinical decision, where each function takes as input up-to-date patient information and gives as output a single recommended treatment. Current methods for estimating optimal dynamic treatment regimes, for example Q-learning, require the specification of a single outcome by which the `goodness' of competing dynamic treatment regimes are measured. However, this is an over-simplification of the goal of clinical decision making, which aims to balance several potentially competing outcomes. For example, often a balance must be struck between treatment effectiveness and side-effect burden. We propose a method for constructing dynamic treatment regimes that accommodates competing outcomes by recommending sets of treatments at each decision point. Formally, we construct a sequence of set-valued functions that take as input up-to-date patient information and give as output a recommended subset of the possible treatments. For a given patient history, the recommended set of treatments contains all treatments that are not inferior according to any of the competing outcomes. When there is more than one decision point, constructing these set-valued functions requires solving a non-trivial enumeration problem. We offer an exact enumeration algorithm by recasting the problem as a linear mixed integer program. The proposed methods are illustrated using data from a depression study and the CATIE schizophrenia study.

Eric B. Laber, Susan A. Murphy

Confidence measures for the generalization error are crucial when small training samples are used to construct classifiers. A common approach is to estimate the generalization error by resampling and then assume the resampled estimator follows a known distribution to form a confidence set [Kohavi 1995, Martin 1996,Yang 2006]. Alternatively, one might bootstrap the resampled estimator of the generalization error to form a confidence set. Unfortunately, these methods do not reliably provide sets of the desired confidence. The poor performance appears to be due to the lack of smoothness of the generalization error as a function of the learned classifier. This results in a non-normal distribution of the estimated generalization error. We construct a confidence set for the generalization error by use of a smooth upper bound on the deviation between the resampled estimate and generalization error. The confidence set is formed by bootstrapping this upper bound. In cases in which the approximation class for the classifier can be represented as a parametric additive model, we provide a computationally efficient algorithm. This method exhibits superior performance across a series of test and simulated data sets.