Screening classifiers are increasingly used to identify qualified candidates in a variety of selection processes. In this context, it has been recently shown that if a classifier is calibrated, one can identify the smallest set of candidates which contains, in expectation, a desired number of qualified candidates using a threshold decision rule. This lends support to focusing on calibration as the only requirement for screening classifiers. In this paper, we argue that screening policies that use calibrated classifiers may suffer from an understudied type of within-group unfairness—they may unfairly treat qualified members within demographic groups of interest. Further, we argue that this type of unfairness can be avoided if classifiers satisfy within-group monotonicity, a natural monotonicity property within each group. Then, we introduce an efficient post-processing algorithm based on dynamic programming to minimally modify a given calibrated classifier so that its probability estimates satisfy within-group monotonicity. We validate our algorithm using US Census survey data and show that within-group monotonicity can often be achieved at a small cost in terms of prediction granularity and shortlist size.

Whenever a clinician reflects on the efficacy of a sequence of treatment decisions for a patient, they may try to identify critical time steps where, had they made different decisions, the patient's health would have improved. While recent methods at the intersection of causal inference and reinforcement learning promise to aid human experts, as the clinician above, to *retrospectively* analyze sequential decision making processes, they have focused on environments with finitely many discrete states. However, in many practical applications, the state of the environment is inherently continuous in nature. In this paper, we aim to fill this gap. We start by formally characterizing a sequence of discrete actions and continuous states using finite horizon Markov decision processes and a broad class of bijective structural causal models. Building upon this characterization, we formalize the problem of finding counterfactually optimal action sequences and show that, in general, we cannot expect to solve it in polynomial time. Then, we develop a search method based on the A* algorithm that, under a natural form of Lipschitz continuity of the environment’s dynamics, is guaranteed to return the optimal solution to the problem. Experiments on real clinical data show that our method is very efficient in practice, and it has the potential to offer interesting insights for sequential decision making tasks.

Testing is recommended for all close contacts of confirmed COVID-19 patients. However, existing pooled testing methods are oblivious to the circumstances of contagion provided by contact tracing. Here, we build upon a well-known semi-adaptive pooled testing method, Dorfman's method with imperfect tests, and derive a simple pooled testing method based on dynamic programming that is specifically designed to use information provided by contact tracing. Experiments using a variety of reproduction numbers and dispersion levels, including those estimated in the context of the COVID-19 pandemic, show that the pools found using our method result in a significantly lower number of tests than those found using Dorfman's method. Our method provides the greatest competitive advantage when the number of contacts of an infected individual is small, or the distribution of secondary infections is highly overdispersed. Moreover, it maintains this competitive advantage under imperfect contact tracing and significant levels of dilution.

Methods to find counterfactual explanations have predominantly focused on one-step decision making processes. In this work, we initiate the development of methods to find counterfactual explanations for decision making processes in which multiple, dependent actions are taken sequentially over time. We start by formally characterizing a sequence of actions and states using finite horizon Markov decision processes and the Gumbel-Max structural causal model. Building upon this characterization, we formally state the problem of finding counterfactual explanations for sequential decision making processes. In our problem formulation, the counterfactual explanation specifies an alternative sequence of actions differing in at most k actions from the observed sequence that could have led the observed process realization to a better outcome. Then, we introduce a polynomial time algorithm based on dynamic programming to build a counterfactual policy that is guaranteed to always provide the optimal counterfactual explanation on every possible realization of the counterfactual environment dynamics. We validate our algorithm using both synthetic and real data from cognitive behavioral therapy and show that the counterfactual explanations our algorithm finds can provide valuable insights to enhance sequential decision making under uncertainty.

As data-driven predictive models are increasingly used to inform decisions, it has been argued that decision makers should provide explanations that help individuals understand what would have to change for these decisions to be beneficial ones. However, there has been little discussion on the possibility that individuals may use the above counterfactual explanations to invest effort strategically and maximize their chances of receiving a beneficial decision. In this paper, our goal is to find policies and counterfactual explanations that are optimal in terms of utility in such a strategic setting. We first show that, given a pre-defined policy, the problem of finding the optimal set of counterfactual explanations is NP-hard. Then, we show that the corresponding objective is nondecreasing and satisfies submodularity and this allows a standard greedy algorithm to enjoy approximation guarantees. In addition, we further show that the problem of jointly finding both the optimal policy and set of counterfactual explanations reduces to maximizing a non-monotone submodular function. As a result, we can use a recent randomized algorithm to solve the problem, which also offers approximation guarantees. Finally, we demonstrate that, by incorporating a matroid constraint into the problem formulation, we can increase the diversity of the optimal set of counterfactual explanations and incentivize individuals across the whole spectrum of the population to self improve. Experiments on synthetic and real lending and credit card data illustrate our theoretical findings and show that the counterfactual explanations and decision policies found by our algorithms achieve higher utility than several competitive baselines.