Kelly W. Zhang

Anna L. Trella, Kelly W. Zhang, Inbal Nahum-Shani et al. · harvard

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.

Anna L. Trella, Kelly W. Zhang, Inbal Nahum-Shani et al. · harvard

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.

Anna L. Trella, Kelly W. Zhang, Hinal Jajal et al. · harvard

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.

Anna L. Trella, Susobhan Ghosh, Erin E. Bonar et al. · harvard

Online AI decision-making algorithms are increasingly used by digital interventions to dynamically personalize treatment to individuals. These algorithms determine, in real-time, the delivery of treatment based on accruing data. The objective of this paper is to provide guidelines for enabling effective monitoring of online decision-making algorithms with the goal of (1) safeguarding individuals and (2) ensuring data quality. We elucidate guidelines and discuss our experience in monitoring online decision-making algorithms in two digital intervention clinical trials (Oralytics and MiWaves). Our guidelines include (1) developing fallback methods, pre-specified procedures executed when an issue occurs, and (2) identifying potential issues categorizing them by severity (red, yellow, and green). Across both trials, the monitoring systems detected real-time issues such as out-of-memory issues, database timeout, and failed communication with an external source. Fallback methods prevented participants from not receiving any treatment during the trial and also prevented the use of incorrect data in statistical analyses. These trials provide case studies for how health scientists can build monitoring systems for their digital intervention. Without these algorithm monitoring systems, critical issues would have gone undetected and unresolved. Instead, these monitoring systems safeguarded participants and ensured the quality of the resulting data for updating the intervention and facilitating scientific discovery. These monitoring guidelines and findings give digital intervention teams the confidence to include online decision-making algorithms in digital interventions.

Samya Praharaj, Chih-Yu Chang, Koulik Khamaru et al.

Multi-arm bandit algorithms are increasingly used in online platforms, clinical trials, and social science experiments, but valid statistical inference on their performance remains an open challenge. After deploying bandits, a natural question is whether one can construct a confidence interval for its mean reward and assess whether it reliably outperforms a baseline policy. The total reward achieved in any single bandit deployment is random, and deploying a bandit twice on the same population typically yields different reward trajectories due to stochastic rewards. Standard statistical inference methods cannot be used because bandit algorithms introduce complex dependencies in the collected data, which violate the i.i.d. assumption underlying many classical approaches. Moreover, existing inference methods for adaptively collected data only apply to estimands that do not depend on the data-collection algorithm (such as the mean reward under a fixed action). We propose Bandit Simulation for Inference (BSI), a framework that fits a simulator of the bandit environment from observed data--either on-policy or off-policy--and uses it to estimate the mean reward under any evaluation policy, including adaptive blackbox algorithms. BSI formally propagates uncertainty in the estimated simulator parameters into the confidence interval construction. Furthermore, for BSI to be valid, it requires only weak exploration assumptions on the behavior policy and avoids importance weighting. We prove that BSI yields asymptotically valid confidence intervals, and demonstrate empirically that it maintains nominal coverage in settings where standard off-policy evaluation methods fail.

Kelly W. Zhang, Omer Gottesman, Finale Doshi-Velez

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.

Da In Kim, Wei Siang Lai, Kelly W. Zhang

While tabular foundation models have achieved remarkable success in classification and regression, adapting them to model time-to-event outcomes for survival analysis is non-trivial due to right-censoring, where data observations may end before the event occurs. We develop a classification-based framework that reformulates both static and dynamic survival analysis as a series of binary classification problems by discretizing event times. Censored observations are naturally handled as examples with missing labels at certain time points. This classification formulation enables existing tabular foundation models to perform survival analysis through in-context learning without explicit training. We prove that under standard censoring assumptions, minimizing our binary classification loss recovers the true survival probabilities as the training set size increases. We demonstrate through evaluation across $53$ real-world datasets that off-the-shelf tabular foundation models with this classification formulation outperform classical and deep learning baselines on average over multiple survival metrics.

Anna L. Trella, Kelly W. Zhang, Inbal Nahum-Shani et al. · harvard

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.

Kelly W. Zhang, Tiffany Tianhui Cai, Hongseok Namkoong et al.

We introduce a framework for Thompson sampling (TS) 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 outcomes (including both future and counterfactual outcomes). If these 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 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 TS and establish a state-of-the-art regret bound. Notably, our regret bound depends on the generative model only through the quality of its offline prediction loss, and applies to any method of fitting the "oracle" policy.

Asim H. Gazi, Yongyi Guo, Daiqi Gao et al.

Reinforcement learning (RL) has achieved remarkable success in real-world decision-making across diverse domains, including gaming, robotics, online advertising, public health, and natural language processing. Despite these advances, a substantial gap remains between RL research and its deployment in many practical settings. Two recurring challenges often underlie this gap. First, many settings offer limited opportunity for the agent to interact extensively with the target environment due to practical constraints. Second, many target environments often undergo substantial changes, requiring redesign and redeployment of RL systems (e.g., advancements in science and technology that change the landscape of healthcare delivery). Addressing these challenges and bridging the gap between basic research and application requires theory and methodology that directly inform the design, implementation, and continual improvement of RL systems in real-world settings. In this paper, we frame the application of RL in practice as a three-component process: (i) online learning and optimization during deployment, (ii) post- or between-deployment offline analyses, and (iii) repeated cycles of deployment and redeployment to continually improve the RL system. We provide a narrative review of recent advances in statistical RL that address these components, including methods for maximizing data utility for between-deployment inference, enhancing sample efficiency for online learning within-deployment, and designing sequences of deployments for continual improvement. We also outline future research directions in statistical RL that are use-inspired -- aiming for impactful application of RL in practice.

Kelly W. Zhang, Thomas Baldwin-McDonald, Kamil Ciosek et al.

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.

Anna L. Trella, Kelly W. Zhang, Stephanie M. Carpenter et al.

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.

Ziping Xu, Kelly W. Zhang, Susan A. Murphy

Online Reinforcement Learning (RL) is typically framed as the process of minimizing cumulative regret (CR) through interactions with an unknown environment. However, real-world RL applications usually involve a sequence of tasks, and the data collected in the first task is used to warm-start the second task. The performance of the warm-start policy is measured by simple regret (SR). While minimizing both CR and SR is generally a conflicting objective, previous research has shown that in stationary environments, both can be optimized in terms of the duration of the task, $T$. In practice, however, in real-world applications, human-in-the-loop decisions between tasks often results in non-stationarity. For instance, in clinical trials, scientists may adjust target health outcomes between implementations. Our results show that task non-stationarity leads to a more restrictive trade-off between CR and SR. To balance these competing goals, the algorithm must explore excessively, leading to a CR bound worse than the typical optimal rate of $T^{1/2}$. These findings are practically significant, indicating that increased exploration is necessary in non-stationary environments to accommodate task changes, impacting the design of RL algorithms in fields such as healthcare and beyond.

Kelly W. Zhang, Lucas Janson, Susan A. Murphy

Online reinforcement learning and other adaptive sampling algorithms are increasingly used in digital intervention experiments to optimize treatment delivery for users over time. In this work, we focus on longitudinal user data collected by a large class of adaptive sampling algorithms that are designed to optimize treatment decisions online using accruing data from multiple users. Combining or "pooling" data across users allows adaptive sampling algorithms to potentially learn faster. However, by pooling, these algorithms induce dependence between the sampled user data trajectories; we show that this can cause standard variance estimators for i.i.d. data to underestimate the true variance of common estimators on this data type. We develop novel methods to perform a variety of statistical analyses on such adaptively sampled data via Z-estimation. Specifically, we introduce the \textit{adaptive} sandwich variance estimator, a corrected sandwich estimator that leads to consistent variance estimates under adaptive sampling. Additionally, to prove our results we develop novel theoretical tools for empirical processes on non-i.i.d., adaptively sampled longitudinal data which may be of independent interest. This work is motivated by our efforts in designing experiments in which online reinforcement learning algorithms optimize treatment decisions, yet statistical inference is essential for conducting analyses after experiments conclude.

Kelly W. Zhang, Lucas Janson, Susan A. Murphy

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.

Kelly W. Zhang, Lucas Janson, Susan A. Murphy

As bandit algorithms are increasingly utilized in scientific studies and industrial applications, there is an associated increasing need for reliable inference methods based on the resulting adaptively-collected data. In this work, we develop methods for inference on data collected in batches using a bandit algorithm. We first prove that the ordinary least squares estimator (OLS), which is asymptotically normal on independently sampled data, is not asymptotically normal on data collected using standard bandit algorithms when there is no unique optimal arm. This asymptotic non-normality result implies that the naive assumption that the OLS estimator is approximately normal can lead to Type-1 error inflation and confidence intervals with below-nominal coverage probabilities. Second, we introduce the Batched OLS estimator (BOLS) that we prove is (1) asymptotically normal on data collected from both multi-arm and contextual bandits and (2) robust to non-stationarity in the baseline reward.

Kelly W. Zhang, Samuel R. Bowman

Recent work using auxiliary prediction task classifiers to investigate the properties of LSTM representations has begun to shed light on why pretrained representations, like ELMo (Peters et al., 2018) and CoVe (McCann et al., 2017), are so beneficial for neural language understanding models. We still, though, do not yet have a clear understanding of how the choice of pretraining objective affects the type of linguistic information that models learn. With this in mind, we compare four objectives---language modeling, translation, skip-thought, and autoencoding---on their ability to induce syntactic and part-of-speech information. We make a fair comparison between the tasks by holding constant the quantity and genre of the training data, as well as the LSTM architecture. We find that representations from language models consistently perform best on our syntactic auxiliary prediction tasks, even when trained on relatively small amounts of data. These results suggest that language modeling may be the best data-rich pretraining task for transfer learning applications requiring syntactic information. We also find that the representations from randomly-initialized, frozen LSTMs perform strikingly well on our syntactic auxiliary tasks, but this effect disappears when the amount of training data for the auxiliary tasks is reduced.