Contextual Thompson Sampling via Generation of Missing Data

We introduce a framework for Thompson sampling contextual bandit algorithms, in which the algorithm's ability to quantify uncertainty and make decisions depends on the quality of a generative model that is learned offline. Instead of viewing uncertainty in the environment as arising from unobservable latent parameters, our algorithm treats uncertainty as stemming from missing, but potentially observable, future outcomes. If these future outcomes were all observed, one could simply make decisions using an "oracle" policy fit on the complete dataset. Inspired by this conceptualization, at each decision-time, our algorithm uses a generative model to probabilistically impute missing future outcomes, fits a policy using the imputed complete dataset, and uses that policy to select the next action. We formally show that this algorithm is a generative formulation of Thompson Sampling and prove a state-of-the-art regret bound for it. Notably, our regret bound i) depends on the probabilistic generative model only through the quality of its offline prediction loss, and ii) applies to any method of fitting the "oracle" policy, which easily allows one to adapt Thompson sampling to decision-making settings with fairness and/or resource constraints.

Impatient Bandits: Optimizing for the Long-Term Without Delay

Increasingly, recommender systems are tasked with improving users' long-term satisfaction. In this context, we study a content exploration task, which we formalize as a bandit problem with delayed rewards. There is an apparent trade-off in choosing the learning signal: waiting for the full reward to become available might take several weeks, slowing the rate of learning, whereas using short-term proxy rewards reflects the actual long-term goal only imperfectly. First, we develop a predictive model of delayed rewards that incorporates all information obtained to date. Rewards as well as shorter-term surrogate outcomes are combined through a Bayesian filter to obtain a probabilistic belief. Second, we devise a bandit algorithm that quickly learns to identify content aligned with long-term success using this new predictive model. We prove a regret bound for our algorithm that depends on the \textit{Value of Progressive Feedback}, an information theoretic metric that captures the quality of short-term leading indicators that are observed prior to the long-term reward. We apply our approach to a podcast recommendation problem, where we seek to recommend shows that users engage with repeatedly over two months. We empirically validate that our approach significantly outperforms methods that optimize for short-term proxies or rely solely on delayed rewards, as demonstrated by an A/B test in a recommendation system that serves hundreds of millions of users.

A Deployed Online Reinforcement Learning Algorithm In An Oral Health Clinical Trial

Dental disease is a prevalent chronic condition associated with substantial financial burden, personal suffering, and increased risk of systemic diseases. Despite widespread recommendations for twice-daily tooth brushing, adherence to recommended oral self-care behaviors remains sub-optimal due to factors such as forgetfulness and disengagement. To address this, we developed Oralytics, a mHealth intervention system designed to complement clinician-delivered preventative care for marginalized individuals at risk for dental disease. Oralytics incorporates an online reinforcement learning algorithm to determine optimal times to deliver intervention prompts that encourage oral self-care behaviors. We have deployed Oralytics in a registered clinical trial. The deployment required careful design to manage challenges specific to the clinical trials setting in the U.S. In this paper, we (1) highlight key design decisions of the RL algorithm that address these challenges and (2) conduct a re-sampling analysis to evaluate algorithm design decisions. A second phase (randomized control trial) of Oralytics is planned to start in spring 2025.

Oralytics Reinforcement Learning Algorithm

Dental disease is still one of the most common chronic diseases in the United States. While dental disease is preventable through healthy oral self-care behaviors (OSCB), this basic behavior is not consistently practiced. We have developed Oralytics, an online, reinforcement learning (RL) algorithm that optimizes the delivery of personalized intervention prompts to improve OSCB. In this paper, we offer a full overview of algorithm design decisions made using prior data, domain expertise, and experiments in a simulation test bed. The finalized RL algorithm was deployed in the Oralytics clinical trial, conducted from fall 2023 to summer 2024.

The Fallacy of Minimizing Local Regret in the Sequential Task Setting

In the realm of Reinforcement Learning (RL), online RL is often conceptualized as an optimization problem, where an algorithm interacts with an unknown environment to minimize cumulative regret. In a stationary setting, strong theoretical guarantees, like a sublinear ($\sqrt{T}$) regret bound, can be obtained, which typically implies the convergence to an optimal policy and the cessation of exploration. However, these theoretical setups often oversimplify the complexities encountered in real-world RL implementations, where tasks arrive sequentially with substantial changes between tasks and the algorithm may not be allowed to adaptively learn within certain tasks. We study the changes beyond the outcome distributions, encompassing changes in the reward designs (mappings from outcomes to rewards) and the permissible policy spaces. Our results reveal the fallacy of myopically minimizing regret within each task: obtaining optimal regret rates in the early tasks may lead to worse rates in the subsequent ones, even when the outcome distributions stay the same. To realize the optimal cumulative regret bound across all the tasks, the algorithm has to overly explore in the earlier tasks. This theoretical insight is practically significant, suggesting that due to unanticipated changes (e.g., rapid technological development or human-in-the-loop involvement) between tasks, the algorithm needs to explore more than it would in the usual stationary setting within each task. Such implication resonates with the common practice of using clipped policies in mobile health clinical trials and maintaining a fixed rate of $\epsilon$-greedy exploration in robotic learning.

Monitoring Fidelity of Online Reinforcement Learning Algorithms in Clinical Trials

Online reinforcement learning (RL) algorithms offer great potential for personalizing treatment for participants in clinical trials. However, deploying an online, autonomous algorithm in the high-stakes healthcare setting makes quality control and data quality especially difficult to achieve. This paper proposes algorithm fidelity as a critical requirement for deploying online RL algorithms in clinical trials. It emphasizes the responsibility of the algorithm to (1) safeguard participants and (2) preserve the scientific utility of the data for post-trial analyses. We also present a framework for pre-deployment planning and real-time monitoring to help algorithm developers and clinical researchers ensure algorithm fidelity. To illustrate our framework's practical application, we present real-world examples from the Oralytics clinical trial. Since Spring 2023, this trial successfully deployed an autonomous, online RL algorithm to personalize behavioral interventions for participants at risk for dental disease.

Reward Design For An Online Reinforcement Learning Algorithm Supporting Oral Self-Care

Dental disease is one of the most common chronic diseases despite being largely preventable. However, professional advice on optimal oral hygiene practices is often forgotten or abandoned by patients. Therefore patients may benefit from timely and personalized encouragement to engage in oral self-care behaviors. In this paper, we develop an online reinforcement learning (RL) algorithm for use in optimizing the delivery of mobile-based prompts to encourage oral hygiene behaviors. One of the main challenges in developing such an algorithm is ensuring that the algorithm considers the impact of the current action on the effectiveness of future actions (i.e., delayed effects), especially when the algorithm has been made simple in order to run stably and autonomously in a constrained, real-world setting (i.e., highly noisy, sparse data). We address this challenge by designing a quality reward which maximizes the desired health outcome (i.e., high-quality brushing) while minimizing user burden. We also highlight a procedure for optimizing the hyperparameters of the reward by building a simulation environment test bed and evaluating candidates using the test bed. The RL algorithm discussed in this paper will be deployed in Oralytics, an oral self-care app that provides behavioral strategies to boost patient engagement in oral hygiene practices.

A Bayesian Approach to Learning Bandit Structure in Markov Decision Processes

In the reinforcement learning literature, there are many algorithms developed for either Contextual Bandit (CB) or Markov Decision Processes (MDP) environments. However, when deploying reinforcement learning algorithms in the real world, even with domain expertise, it is often difficult to know whether it is appropriate to treat a sequential decision making problem as a CB or an MDP. In other words, do actions affect future states, or only the immediate rewards? Making the wrong assumption regarding the nature of the environment can lead to inefficient learning, or even prevent the algorithm from ever learning an optimal policy, even with infinite data. In this work we develop an online algorithm that uses a Bayesian hypothesis testing approach to learn the nature of the environment. Our algorithm allows practitioners to incorporate prior knowledge about whether the environment is that of a CB or an MDP, and effectively interpolate between classical CB and MDP-based algorithms to mitigate against the effects of misspecifying the environment. We perform simulations and demonstrate that in CB settings our algorithm achieves lower regret than MDP-based algorithms, while in non-bandit MDP settings our algorithm is able to learn the optimal policy, often achieving comparable regret to MDP-based algorithms.

Designing Reinforcement Learning Algorithms for Digital Interventions: Pre-implementation Guidelines

Online reinforcement learning (RL) algorithms are increasingly used to personalize digital interventions in the fields of mobile health and online education. Common challenges in designing and testing an RL algorithm in these settings include ensuring the RL algorithm can learn and run stably under real-time constraints, and accounting for the complexity of the environment, e.g., a lack of accurate mechanistic models for the user dynamics. To guide how one can tackle these challenges, we extend the PCS (Predictability, Computability, Stability) framework, a data science framework that incorporates best practices from machine learning and statistics in supervised learning (Yu and Kumbier, 2020), to the design of RL algorithms for the digital interventions setting. Further, we provide guidelines on how to design simulation environments, a crucial tool for evaluating RL candidate algorithms using the PCS framework. We illustrate the use of the PCS framework for designing an RL algorithm for Oralytics, a mobile health study aiming to improve users' tooth-brushing behaviors through the personalized delivery of intervention messages. Oralytics will go into the field in late 2022.

Statistical Inference with M-Estimators on Adaptively Collected Data

Bandit algorithms are increasingly used in real-world sequential decision-making problems. Associated with this is an increased desire to be able to use the resulting datasets to answer scientific questions like: Did one type of ad lead to more purchases? In which contexts is a mobile health intervention effective? However, classical statistical approaches fail to provide valid confidence intervals when used with data collected with bandit algorithms. Alternative methods have recently been developed for simple models (e.g., comparison of means). Yet there is a lack of general methods for conducting statistical inference using more complex models on data collected with (contextual) bandit algorithms; for example, current methods cannot be used for valid inference on parameters in a logistic regression model for a binary reward. In this work, we develop theory justifying the use of M-estimators -- which includes estimators based on empirical risk minimization as well as maximum likelihood -- on data collected with adaptive algorithms, including (contextual) bandit algorithms. Specifically, we show that M-estimators, modified with particular adaptive weights, can be used to construct asymptotically valid confidence regions for a variety of inferential targets.