research

2023

1. Robust Fitted-Q-Evaluation and Iteration under Sequentially Exogenous Unobserved Confounders

   David Bruns-Smith, and Angela Zhou

   2023

   Abs arXiv

   Offline reinforcement learning is important in domains such as medicine, economics, and e-commerce where online experimentation is costly, dangerous or unethical, and where the true model is unknown. However, most methods assume all covariates used in the behavior policy’s action decisions are observed. This untestable assumption may be incorrect. We study robust policy evaluation and policy optimization in the presence of unobserved confounders. We assume the extent of possible unobserved confounding can be bounded by a sensitivity model, and that the unobserved confounders are sequentially exogenous. We propose and analyze an (orthogonalized) robust fitted-Q-iteration that uses closed-form solutions of the robust Bellman operator to derive a loss minimization problem for the robust Q function. Our algorithm enjoys the computational ease of fitted-Q-iteration and statistical improvements (reduced dependence on quantile estimation error) from orthogonalization. We provide sample complexity bounds, insights, and show effectiveness in simulations.

2. Optimizing and Learning Sequential Assortment Decisions with Platform Disengagement

   Mika Sumida, and Angela Zhou

   2023

   Abs PDF

   We consider a problem where customers repeatedly interact with a platform. During each interaction with the platform, the customer is shown an assortment of items and selects among these items according to a Multinomial Logit choice model. The probability that a customer interacts with the platform in the next period depends on the customer’s past purchase history. The goal of the platform is to maximize the total revenue obtained from each customer over a finite time horizon. First, we study a non-learning version of the problem where consumer preferences are completely known. We formulate the problem as a dynamic program and prove structural properties of the optimal policy. Next, we provide a formulation in a contextual episodic reinforcement learning setting, where the parameters governing contextual consumer preferences and return probabilities are unknown and learned over multiple episodes. We develop an algorithm based on the principle of optimism under uncertainty for this problem and provide a regret bound. We numerically illustrate model insights and evaluate effectiveness on simulations, parametrized by real data from Expedia, where the algorithm outperforms naively myopic learning algorithms.

3. Optimal and Fair Encouragement Policy Evaluation and Learning

   Angela Zhou

   Neurips 2023

   Abs PDF

   In consequential domains, it is often impossible to compel individuals to take treatment, so that optimal policy rules are merely suggestions in the presence of human non-adherence to treatment recommendations. In these same domains, there may be heterogeneity both in who responds in taking-up treatment, and heterogeneity in treatment efficacy. While optimal treatment rules can maximize causal outcomes across the population, access parity constraints or other fairness considerations can be relevant in the case of encouragement. For example, in social services, a persistent puzzle is the gap in take-up of beneficial services among those who may benefit from them the most. When in addition the decision-maker has distributional preferences over both access and average outcomes, the optimal decision rule changes. We study causal identification, statistical variance-reduced estimation, and robust estimation of optimal treatment rules, including under potential violations of positivity. We consider fairness constraints such as demographic parity in treatment take-up, and other constraints, via constrained optimization. Our framework can be extended to handle algorithmic recommendations under an often-reasonable covariate-conditional exclusion restriction, using our robustness checks for lack of positivity in the recommendation. We develop a two-stage algorithm for solving over parametrized policy classes under general constraints to obtain variance-sensitive regret bounds. We illustrate the methods in two case studies based on data from randomized encouragement to enroll in insurance and from pretrial supervised release with electronic monitoring.

2022

1. A Note on Task-Aware Loss via Reweighing Prediction Loss by Decision-Regret

   Connor Lawless, and Angela Zhou

   2022

   arXiv
2. Stateful Offline Contextual Policy Evaluation and Learning

   Angela Zhou, and Nathan Kallus

   Proceedings of The 25nd International Conference on Artificial Intelligence and Statistics 2022

   Abs arXiv

   We study off-policy evaluation and learning from sequential data in a structured class of Markov decision processes that arise from repeated interactions with an exogenous sequence of arrivals with contexts, which generate unknown individual-level responses to agent actions. This model can be thought of as an offline generalization of contextual bandits with resource constraints. We formalize the relevant causal structure of problems such as dynamic personalized pricing and other operations management problems in the presence of potentially high-dimensional user types. The key insight is that an individual-level response is often not causally affected by the state variable and can therefore easily be generalized across timesteps and states. When this is true, we study implications for (doubly robust) off-policy evaluation and learning by instead leveraging single time-step evaluation, estimating the expectation over a single arrival via data from a population, for fitted-value iteration in a marginal MDP. We study sample complexity and analyze error amplification that leads to the persistence, rather than attenuation, of confounding error over time. In simulations of dynamic and capacitated pricing, we show improved out-of-sample policy performance in this class of relevant problems.

3. Off-Policy Evaluation with Policy-Dependent Optimization Response

   Wenshuo Guo, Michael Jordan, and Angela Zhou

   Neurips 2022

   Abs arXiv

   The intersection of causal inference and machine learning for decision-making is rapidly expanding, but the default decision criterion remains an average of individual causal outcomes across a population. In practice, various operational restrictions ensure that a decision-maker’s utility is not realized as an average but rather as an output of a downstream decision-making problem (such as matching, assignment, network flow, minimizing predictive risk). In this work, we develop a new framework for off-policy evaluation with a policy-dependent linear optimization response: causal outcomes introduce stochasticity in objective function coefficients. In this framework, a decision-maker’s utility depends on the policy-dependent optimization, which introduces a fundamental challenge of optimization bias even for the case of policy evaluation. We construct unbiased estimators for the policy-dependent estimand by a perturbation method. We also discuss the asymptotic variance properties for a set of plug-in regression estimators adjusted to be compatible with that perturbation method. Lastly, attaining unbiased policy evaluation allows for policy optimization, and we provide a general algorithm for optimizing causal interventions. We corroborate our theoretical results with numerical simulations.

2021

1. Fairness, Welfare, and Equity in Personalized Pricing

   Nathan Kallus, and Angela Zhou

   ACM Conference on Fairness, Accountability, and Transparency (FAccT) 2021

   Abs arXiv

   We study the interplay of fairness, welfare, and equity considerations in personalized pricing based on customer features. Sellers are increasingly able to conduct price personalization based on predictive modeling of demand conditional on covariates: setting customized interest rates, targeted discounts of consumer goods, and personalized subsidies of scarce resources with positive externalities like vaccines and bed nets. These different application areas may lead to different concerns around fairness, welfare, and equity on different objectives: price burdens on consumers, price envy, firm revenue, access to a good, equal access, and distributional consequences when the good in question further impacts downstream outcomes of interest. We conduct a comprehensive literature review in order to disentangle these different normative considerations and propose a taxonomy of different objectives with mathematical definitions. We focus on observational metrics that do not assume access to an underlying valuation distribution which is either unobserved due to binary feedback or ill-defined due to overriding behavioral concerns regarding interpreting revealed preferences. In the setting of personalized pricing for the provision of goods with positive benefits, we discuss how price optimization may provide unambiguous benefit by achieving a "triple bottom line": personalized pricing enables expanding access, which in turn may lead to gains in welfare due to heterogeneous utility, and improve revenue or budget utilization. We empirically demonstrate the potential benefits of personalized pricing in two settings: pricing subsidies for an elective vaccine, and the effects of personalized interest rates on downstream outcomes in microcredit.

2. It’s COMPASlicated: The Messy Relationship between RAI Datasets and Algorithmic Fairness Benchmarks

   Michelle Bao, Angela Zhou, Samantha Zottola, and 5 more authors

   Advances in Neural Information Processing Systems, Datasets and Benchmarks 2021 2021

   Abs arXiv

   Risk assessment instrument (RAI) datasets, particularly ProPublica’s COMPAS dataset, are commonly used in algorithmic fairness papers due to benchmarking practices of comparing algorithms on datasets used in prior work. In many cases, this data is used as a benchmark to demonstrate good performance without accounting for the complexities of criminal justice (CJ) processes. We show that pretrial RAI datasets contain numerous measurement biases and errors inherent to CJ pretrial evidence and due to disparities in discretion and deployment, are limited in making claims about real-world outcomes, making the datasets a poor fit for benchmarking under assumptions of ground truth and real-world impact. Conventional practices of simply replicating previous data experiments may implicitly inherit or edify normative positions without explicitly interrogating assumptions. With context of how interdisciplinary fields have engaged in CJ research, algorithmic fairness practices are misaligned for meaningful contribution in the context of CJ, and would benefit from transparent engagement with normative considerations and values related to fairness, justice, and equality. These factors prompt questions about whether benchmarks for intrinsically socio-technical systems like the CJ system can exist in a beneficial and ethical way.

2020

1. Confounding-Robust Policy Evaluation in Infinite-Horizon Reinforcement Learning

   Nathan Kallus, and Angela Zhou

   Neurips 2020

   Abs arXiv Code

   Off-policy evaluation of sequential decision policies from observational data is necessary in applications of batch reinforcement learning such as education and healthcare. In such settings, however, observed actions are often confounded with transitions by unobserved variables, rendering exact evaluation of new policies impossible, ie, unidentifiable. We develop a robust approach that estimates sharp bounds on the (unidentifiable) value of a given policy in an infinite-horizon problem given data from another policy with unobserved confounding subject to a sensitivity model. We phrase the problem precisely as computing the support function of the set of all stationary state-occupancy ratios that agree with both the data and the sensitivity model. We show how to express this set using a new partially identified estimating equation and prove convergence to the sharp bounds, as we collect more confounded data. We prove that membership in the set can be checked by solving a linear program, while the support function is given by a difficult nonconvex optimization problem. We leverage an analytical solution for the finite-state-space case to develop approximations based on nonconvex projected gradient descent. We demonstrate the resulting bounds empirically.

2019

1. The fairness of risk scores beyond classification: Bipartite ranking and the xauc metric

   Nathan Kallus, and Angela Zhou

   Neurips 2019

   Abs arXiv Code

   Where machine-learned predictive risk scores inform high-stakes decisions, such as bail and sentencing in criminal justice, fairness has been a serious concern. Recent work has characterized the disparate impact that such risk scores can have when used for a binary classification task. This may not account, however, for the more diverse downstream uses of risk scores and their non-binary nature. To better account for this, in this paper, we investigate the fairness of predictive risk scores from the point of view of a bipartite ranking task, where one seeks to rank positive examples higher than negative ones. We introduce the xAUC disparity as a metric to assess the disparate impact of risk scores and define it as the difference in the probabilities of ranking a random positive example from one protected group above a negative one from another group and vice versa. We provide a decomposition of bipartite ranking loss into components that involve the discrepancy and components that involve pure predictive ability within each group. We use xAUC analysis to audit predictive risk scores for recidivism prediction, income prediction, and cardiac arrest prediction, where it describes disparities that are not evident from simply comparing within-group predictive performance.

2. Assessing Disparate Impact of Personalized Interventions: Identifiability and Bounds

   Nathan Kallus, and Angela Zhou

   Neurips 2019

   Abs arXiv Code

   Personalized interventions in social services, education, and healthcare leverage individual-level causal effect predictions in order to give the best treatment to each individual or to prioritize program interventions for the individuals most likely to benefit. While the sensitivity of these domains compels us to evaluate the fairness of such policies, we show that actually auditing their disparate impacts per standard observational metrics, such as true positive rates, is impossible since ground truths are unknown. Whether our data is experimental or observational, an individual’s actual outcome under an intervention different than that received can never be known, only predicted based on features. We prove how we can nonetheless point-identify these quantities under the additional assumption of monotone treatment response, which may be reasonable in many applications. We further provide a sensitivity analysis for this assumption via sharp partial-identification bounds under violations of monotonicity of varying strengths. We show how to use our results to audit personalized interventions using partially-identified ROC and xROC curves and demonstrate this in a case study of a French job training dataset.

3. Interval estimation of individual-level causal effects under unobserved confounding

   Nathan Kallus, Xiaojie Mao, and Angela Zhou

   AISTATS 2019

   Abs arXiv

   We study the problem of learning conditional average treatment effects (CATE) from observational data with unobserved confounders. The CATE function maps baseline covariates to individual causal effect predictions and is key for personalized assessments. Recent work has focused on how to learn CATE under unconfoundedness, ie, when there are no unobserved confounders. Since CATE may not be identified when unconfoundedness is violated, we develop a functional interval estimator that predicts bounds on the individual causal effects under realistic violations of unconfoundedness. Our estimator takes the form of a weighted kernel estimator with weights that vary adversarially. We prove that our estimator is sharp in that it converges exactly to the tightest bounds possible on CATE when there may be unobserved confounders. Further, we study personalized decision rules derived from our estimator and prove that they achieve optimal minimax regret asymptotically. We assess our approach in a simulation study as well as demonstrate its application in the case of hormone replacement therapy by comparing conclusions from a real observational study and clinical trial.

2018

1. Confounding-robust policy improvement

   Nathan Kallus, and Angela Zhou

   Neurips 2018

   arXiv
2. Policy Evaluation and Optimization with Continuous Treatments

   Nathan Kallus, and Angela Zhou

   AISTATS 2018

   Abs arXiv Code

   We study the problem of policy evaluation and learning from batched contextual bandit data when treatments are continuous, going beyond previous work on discrete treatments. Previous work for discrete treatment/action spaces focuses on inverse probability weighting (IPW) and doubly robust (DR) methods that use a rejection sampling approach for evaluation and the equivalent weighted classification problem for learning. In the continuous setting, this reduction fails as we would almost surely reject all observations. To tackle the case of continuous treatments, we extend the IPW and DR approaches to the continuous setting using a kernel function that leverages treatment proximity to attenuate discrete rejection. Our policy estimator is consistent and we characterize the optimal bandwidth. The resulting continuous policy optimizer (CPO) approach using our estimator achieves convergent regret and approaches the best-in-class policy for learnable policy classes. We demonstrate that the estimator performs well and, in particular, outperforms a discretization-based benchmark. We further study the performance of our policy optimizer in a case study on personalized dosing based on a dataset of Warfarin patients, their covariates, and final therapeutic doses. Our learned policy outperforms benchmarks and nears the oracle-best linear policy.

3. Residual Unfairness in Fair Machine Learning from Prejudiced Data

   Nathan Kallus, and Angela Zhou

   ICML 2018

   Abs arXiv

   Recent work in fairness in machine learning has proposed adjusting for fairness by equalizing accuracy metrics across groups and has also studied how datasets affected by historical prejudices may lead to unfair decision policies. We connect these lines of work and study the residual unfairness that arises when a fairness-adjusted predictor is not actually fair on the target population due to systematic censoring of training data by existing biased policies. This scenario is particularly common in the same applications where fairness is a concern. We characterize theoretically the impact of such censoring on standard fairness metrics for binary classifiers and provide criteria for when residual unfairness may or may not appear. We prove that, under certain conditions, fairness-adjusted classifiers will in fact induce residual unfairness that perpetuates the same injustices, against the same groups, that biased the data to begin with, thus showing that even state-of-the-art fair machine learning can have a" bias in, bias out" property. When certain benchmark data is available, we show how sample reweighting can estimate and adjust fairness metrics while accounting for censoring. We use this to study the case of Stop, Question, and Frisk (SQF) and demonstrate that attempting to adjust for fairness perpetuates the same injustices that the policy is infamous for.