Differentiable Learning Under Triage

Abstract

Multiple lines of evidence suggest that predictive models may benefit from algorithmic triage. Under algorithmic triage, a predictive model does not predict all instances but instead defers some of them to human experts. However, the interplay between the prediction accuracy of the model and the human experts under algorithmic triage is not well understood. In this work, we start by formally characterizing under which circumstances a predictive model may benefit from algorithmic triage. In doing so, we also demonstrate that models trained for full automation may be suboptimal under triage. Then, given any model and desired level of triage, we show that the optimal triage policy is a deterministic threshold rule in which triage decisions are derived deterministically by thresholding the difference between the model and human errors on a per-instance level. Building upon these results, we introduce a practical gradient-based algorithm that is guaranteed to find a sequence of triage policies and predictive models of increasing performance. Experiments on a wide variety of supervised learning tasks using synthetic and real data from two important applications-content moderation and scientific discovery-illustrate our theoretical results and show that the models and triage policies provided by our gradient-based algorithm outperform those provided by several competitive baselines.

A Unifying Framework for Combining Complementary Strengths of Humans and ML toward Better Predictive Decision-Making

“…However, empirical findings regarding the success and effectiveness of these proposals are mixed (Lai et al, 2021, and references therein). Simultaneously, a growing body of theoretical work has attempted to conceptualize and formalize these hybrid designs (Gao et al, 2021;Bordt and von Luxburg, 2020) and study optimal ways of aggregating human and ML judgments within them (Madras et al, 2018;Mozannar and Sontag, 2020;Wilder et al, 2020;Keswani et al, 2021;Raghu et al, 2019;Okati et al, 2021;Donahue et al, 2022;Steyvers et al, 2022). The existing theories, however, are hard to navigate and make sense of as a whole.…”

Who Should Predict? Exact Algorithms For Learning to Defer to Humans

“…Finally, Okati et al (2021) proposes a method that iteratively optimizes the classifier on points where it outperforms the human on the training sample, and then learns a post-hoc rejector to predict who between the human and the AI has higher error on each point. The setting when the cost of deferral is constant, has a long history in machine learning and goes by the name of rejection learning (Cortes et al, 2016;Chow, 1970;Bartlett and Wegkamp, 2008;Charoenphakdee et al, 2021) or selective classification (only predict on x% of data) (El-Yaniv and Wiener, 2010;Geifman and El-Yaniv, 2017;Gangrade et al, 2021;Acar et al, 2020).…”

“…Failure of Prior Approaches. Existing literature has focused on surrogate loss functions for deferral (Madras et al, 2018;Mozannar and Sontag, 2020;Verma and Nalisnick, 2022) and confidence based approaches (Raghu et al, 2019;Okati et al, 2021). We give a simple synthetic setting where all of these approaches fail to find a classifier/rejector pair with low system error.…”

Combining Human Predictions with Model Probabilities via Confusion Matrices and Calibration

“…In crowd-sourcing, classification models have been used to automatically filter examples to improve human annotation efficiency [17,38,2,5]. A similar line of research focuses on algorithmic deferral techniques where a model defers to human predictions based on the model's confidence [39,40], as well as work on adapting prediction models to the human decision maker [41,42,43,44]. The results in [41] in particular describe experiments with the same CIFAR-10H dataset that we use in this paper.…”