Learning Fair Policies for Multi-stage Selection Problems from Observational Data

We consider the problem of learning fair policies for multi-stage selection problems from observational data. This problem arises in several high-stakes domains such as company hiring, loan approval, or bail decisions where outcomes (e.g., career success, loan repayment, recidivism) are only observed for those selected. We propose a multi-stage framework that can be augmented with various fairness constraints, such as demographic parity or equal opportunity. This problem is a highly intractable infinite chance-constrained program involving the unknown joint distribution of covariates and outcomes. Motivated by the potential impact of selection decisions on people's lives and livelihoods, we propose to focus on interpretable linear selection rules. Leveraging tools from causal inference and sample average approximation, we obtain an asymptotically consistent solution to this selection problem by solving a mixed binary conic optimization problem, which can be solved using standard off-the-shelf solvers. We conduct extensive computational experiments on a variety of datasets adapted from the UCI repository on which we show that our proposed approaches can achieve an 11.6% improvement in precision and a 38% reduction in the measure of unfairness compared to the existing selection policy.

Learning Optimal and Fair Policies for Online Allocation of Scarce Societal Resources from Data Collected in Deployment

We study the problem of allocating scarce societal resources of different types (e.g., permanent housing, deceased donor kidneys for transplantation, ventilators) to heterogeneous allocatees on a waitlist (e.g., people experiencing homelessness, individuals suffering from end-stage renal disease, Covid-19 patients) based on their observed covariates. We leverage administrative data collected in deployment to design an online policy that maximizes expected outcomes while satisfying budget constraints, in the long run. Our proposed policy waitlists each individual for the resource maximizing the difference between their estimated mean treatment outcome and the estimated resource dual-price or, roughly, the opportunity cost of using the resource. Resources are then allocated as they arrive, in a first-come first-serve fashion. We demonstrate that our data-driven policy almost surely asymptotically achieves the expected outcome of the optimal out-of-sample policy under mild technical assumptions. We extend our framework to incorporate various fairness constraints. We evaluate the performance of our approach on the problem of designing policies for allocating scarce housing resources to people experiencing homelessness in Los Angeles based on data from the homeless management information system. In particular, we show that using our policies improves rates of exit from homelessness by 1.9% and that policies that are fair in either allocation or outcomes by race come at a very low price of fairness.

Learning Optimal Classification Trees Robust to Distribution Shifts

We consider the problem of learning classification trees that are robust to distribution shifts between training and testing/deployment data. This problem arises frequently in high stakes settings such as public health and social work where data is often collected using self-reported surveys which are highly sensitive to e.g., the framing of the questions, the time when and place where the survey is conducted, and the level of comfort the interviewee has in sharing information with the interviewer. We propose a method for learning optimal robust classification trees based on mixed-integer robust optimization technology. In particular, we demonstrate that the problem of learning an optimal robust tree can be cast as a single-stage mixed-integer robust optimization problem with a highly nonlinear and discontinuous objective. We reformulate this problem equivalently as a two-stage linear robust optimization problem for which we devise a tailored solution procedure based on constraint generation. We evaluate the performance of our approach on numerous publicly available datasets, and compare the performance to a regularized, non-robust optimal tree. We show an increase of up to 12.48% in worst-case accuracy and of up to 4.85% in average-case accuracy across several datasets and distribution shifts from using our robust solution in comparison to the non-robust one.

ODTlearn: A Package for Learning Optimal Decision Trees for Prediction and Prescription

ODTLearn is an open-source Python package that provides methods for learning optimal decision trees for high-stakes predictive and prescriptive tasks based on the mixed-integer optimization (MIO) framework proposed in Aghaei et al. (2019) and several of its extensions. The current version of the package provides implementations for learning optimal classification trees, optimal fair classification trees, optimal classification trees robust to distribution shifts, and optimal prescriptive trees from observational data. We have designed the package to be easy to maintain and extend as new optimal decision tree problem classes, reformulation strategies, and solution algorithms are introduced. To this end, the package follows object-oriented design principles and supports both commercial (Gurobi) and open source (COIN-OR branch and cut) solvers. The package documentation and an extensive user guide can be found at https://d3m-research-group.github.io/odtlearn/. Additionally, users can view the package source code and submit feature requests and bug reports by visiting https://github.com/D3M-Research-Group/odtlearn.

Deploying a Robust Active Preference Elicitation Algorithm: Experiment Design, Interface, and Evaluation for COVID-19 Patient Prioritization

Preference elicitation leverages AI or optimization to learn stakeholder preferences in settings ranging from marketing to public policy. The online robust preference elicitation procedure of arXiv:2003.01899 has been shown in simulation to outperform various other elicitation procedures in terms of effectively learning individuals' true utilities. However, as with any simulation, the method makes a series of assumptions that cannot easily be verified to hold true beyond simulation. Thus, we propose to validate the robust method's performance in deployment, focused on the particular challenge of selecting policies for prioritizing COVID-19 patients for scarce hospital resources during the pandemic. To this end, we develop an online platform for preference elicitation where users report their preferences between alternatives over a moderate number of pairwise comparisons chosen by a particular elicitation procedure. We recruit Amazon Mechanical Turk workers ($n$ = 193) to report their preferences and demonstrate that the robust method outperforms asking random queries by 21%, the next best performing method in the simulated results of arXiv:2003.01899, in terms of recommending policies with a higher utility.

Fairness in Contextual Resource Allocation Systems: Metrics and Incompatibility Results

We study critical systems that allocate scarce resources to satisfy basic needs, such as homeless services that provide housing. These systems often support communities disproportionately affected by systemic racial, gender, or other injustices, so it is crucial to design these systems with fairness considerations in mind. To address this problem, we propose a framework for evaluating fairness in contextual resource allocation systems that is inspired by fairness metrics in machine learning. This framework can be applied to evaluate the fairness properties of a historical policy, as well as to impose constraints in the design of new (counterfactual) allocation policies. Our work culminates with a set of incompatibility results that investigate the interplay between the different fairness metrics we propose. Notably, we demonstrate that: 1) fairness in allocation and fairness in outcomes are usually incompatible; 2) policies that prioritize based on a vulnerability score will usually result in unequal outcomes across groups, even if the score is perfectly calibrated; 3) policies using contextual information beyond what is needed to characterize baseline risk and treatment effects can be fairer in their outcomes than those using just baseline risk and treatment effects; and 4) policies using group status in addition to baseline risk and treatment effects are as fair as possible given all available information. Our framework can help guide the discussion among stakeholders in deciding which fairness metrics to impose when allocating scarce resources.

Learning Resource Allocation Policies from Observational Data with an Application to Homeless Services Delivery

We study the problem of learning, from observational data, fair and interpretable policies that effectively match heterogeneous individuals to scarce resources of different types. We model this problem as a multi-class multi-server queuing system where both individuals and resources arrive stochastically over time. Each individual, upon arrival, is assigned to a queue where they wait to be matched to a resource. The resources are assigned in a first come first served (FCFS) fashion according to an eligibility structure that encodes the resource types that serve each queue. We propose a methodology based on techniques in modern causal inference to construct the individual queues as well as learn the matching outcomes and provide a mixed-integer optimization (MIO) formulation to optimize the eligibility structure. The MIO problem maximizes policy outcome subject to wait time and fairness constraints. It is very flexible, allowing for additional linear domain constraints. We conduct extensive analyses using synthetic and real-world data. In particular, we evaluate our framework using data from the U.S. Homeless Management Information System (HMIS). We obtain wait times as low as an FCFS policy while improving the rate of exit from homelessness for underserved or vulnerable groups (7% higher for the Black individuals and 15% higher for those below 17 years old) and overall.

Learning Optimal Fair Classification Trees

The increasing use of machine learning in high-stakes domains -- where people's livelihoods are impacted -- creates an urgent need for interpretable and fair algorithms. In these settings it is also critical for such algorithms to be accurate. With these needs in mind, we propose a mixed integer optimization (MIO) framework for learning optimal classification trees of fixed depth that can be conveniently augmented with arbitrary domain specific fairness constraints. We benchmark our method against the state-of-the-art approach for building fair trees on popular datasets; given a fixed discrimination threshold, our approach improves out-of-sample (OOS) accuracy by 2.3 percentage points on average and obtains a higher OOS accuracy on 88.9% of the experiments. We also incorporate various algorithmic fairness notions into our method, showcasing its versatile modeling power that allows decision makers to fine-tune the trade-off between accuracy and fairness.

Learning Optimal Prescriptive Trees from Observational Data

We consider the problem of learning an optimal prescriptive tree (i.e., a personalized treatment assignment policy in the form of a binary tree) of moderate depth, from observational data. This problem arises in numerous socially important domains such as public health and personalized medicine, where interpretable and data-driven interventions are sought based on data gathered in deployment, through passive collection of data, rather than from randomized trials. We propose a method for learning optimal prescriptive trees using mixed-integer optimization (MIO) technology. We show that under mild conditions our method is asymptotically exact in the sense that it converges to an optimal out-of-sample treatment assignment policy as the number of historical data samples tends to infinity. This sets us apart from existing literature on the topic which either requires data to be randomized or imposes stringent assumptions on the trees. Based on extensive computational experiments on both synthetic and real data, we demonstrate that our asymptotic guarantees translate to significant out-of-sample performance improvements even in finite samples.

Strong Optimal Classification Trees

Decision trees are among the most popular machine learning models and are used routinely in applications ranging from revenue management and medicine to bioinformatics. In this paper, we consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in mixed-integer optimization (MIO) technology. Yet, existing MIO-based approaches from the literature do not leverage the power of MIO to its full extent: they rely on weak formulations, resulting in slow convergence and large optimality gaps. To fill this gap in the literature, we propose an intuitive flow-based MIO formulation for learning optimal binary classification trees. Our formulation can accommodate side constraints to enable the design of interpretable and fair decision trees. Moreover, we show that our formulation has a stronger linear optimization relaxation than existing methods. We exploit the decomposable structure of our formulation and max-flow/min-cut duality to derive a Benders' decomposition method to speed-up computation. We propose a tailored procedure for solving each decomposed subproblem that provably generates facets of the feasible set of the MIO as constraints to add to the main problem. We conduct extensive computational experiments on standard benchmark datasets on which we show that our proposed approaches are 31 times faster than state-of-the art MIO-based techniques and improve out of sample performance by up to 8%.