Algorithmic predictions are increasingly informing societal resource allocations by identifying individuals for targeting. Policymakers often build these systems with the assumption that by gathering more observations on individuals, they can improve predictive accuracy and, consequently, allocation efficiency. An overlooked yet consequential aspect of prediction-driven allocations is that of timing. The planner has to trade off relying on earlier and potentially noisier predictions to intervene before individuals experience undesirable outcomes, or they may wait to gather more observations to make more precise allocations. We examine this tension using a simple mathematical model, where the planner collects observations on individuals to improve predictions over time. We analyze both the ranking induced by these predictions and optimal resource allocation. We show that though individual prediction accuracy improves over time, counter-intuitively, the average ranking loss can worsen. As a result, the planner's ability to improve social welfare can decline. We identify inequality as a driving factor behind this phenomenon. Our findings provide a nuanced perspective and challenge the conventional wisdom that it is preferable to wait for more accurate predictions to ensure the most efficient allocations.

This tension in assumptions is readily apparent in standard human-AI alignment methods--such as reinforcement learning from human feedback (RLHF) [6, 7, 8] and direct preference optimization (DPO) [9]--which assume a single reward function captures the interests of the entire population. We examine the limits of the preference homogeneity assumption when individuals belong to user types, each characterized by a specific reward function. Recent work has shown that in this setting, the homogeneity assumption can lead to unexpected behavior [10, 11, 12]. One challenge is that, under this assumption, learning from human preferences becomes unrealizable, as a single reward function cannot capture the complexity of population preferences with multiple reward functions [13, 14]. Both RLHF and DPO rely on maximum likelihood estimation (MLE) to optimize the reward or policy. Unrealizability implies their likelihood functions cannot fully represent the underlying preference data distribution, resulting in a nontrivial optimal MLE solution. From another perspective, learning a universal reward or policy from a heterogeneous population inherently involves an aggregation of diverse interests, and this aggregation is nontrivial. In the quest for a single policy that accommodates a heterogeneous population with multiple user types, we show that the only universal reward yielding a well-defined alignment problem is an affine Equal contribution Work done while visiting Harvard Equal advising 1 arXiv:2502.16320v1

Algorithmic predictions are emerging as a promising solution concept for efficiently allocating societal resources. Fueling their use is an underlying assumption that such systems are necessary to identify individuals for interventions. We propose a principled framework for assessing this assumption: Using a simple mathematical model, we evaluate the efficacy of prediction-based allocations in settings where individuals belong to larger units such as hospitals, neighborhoods, or schools. We find that prediction-based allocations outperform baseline methods using aggregate unit-level statistics only when between-unit inequality is low and the intervention budget is high. Our results hold for a wide range of settings for the price of prediction, treatment effect heterogeneity, and unit-level statistics' learnability. Combined, we highlight the potential limits to improving the efficacy of interventions through prediction.

Counterfactual explanations provide individuals with cost-optimal actions that can alter their labels to desired classes. However, if substantial instances seek state modification, such individual-centric methods can lead to new competitions and unanticipated costs. Furthermore, these recommendations, disregarding the underlying data distribution, may suggest actions that users perceive as outliers. To address these issues, our work proposes a collective approach for formulating counterfactual explanations, with an emphasis on utilizing the current density of the individuals to inform the recommended actions. Our problem naturally casts as an optimal transport problem. Leveraging the extensive literature on optimal transport, we illustrate how this collective method improves upon the desiderata of classical counterfactual explanations. We support our proposal with numerical simulations, illustrating the effectiveness of the proposed approach and its relation to classic methods.

Most medical treatment decisions are sequential in nature. Hence, there is substantial hope that reinforcement learning may make it possible to formulate precise data-driven treatment plans. However, a key challenge for most applications in this field is the sparse nature of primarily mortality-based reward functions, leading to decreased stability of offline estimates. In this work, we introduce a deep Q-learning approach able to obtain more reliable critical care policies. This method integrates relevant but noisy intermediate biomarker signals into the reward specification, without compromising the optimization of the main outcome of interest (e.g. patient survival). We achieve this by first pruning the action set based on all available rewards, and second training a final model based on the sparse main reward but with a restricted action set. By disentangling accurate and approximated rewards through action pruning, potential distortions of the main objective are minimized, all while enabling the extraction of valuable information from intermediate signals that can guide the learning process. We evaluate our method in both off-policy and offline settings using simulated environments and real health records of patients in intensive care units. Our empirical results indicate that pruning significantly reduces the size of the action space while staying mostly consistent with the actions taken by physicians, outperforming the current state-of-the-art offline reinforcement learning method conservative Q-learning. Our work is a step towards developing reliable policies by effectively harnessing the wealth of available information in data-intensive critical care environments.

ImageNet was famously created from Flickr image search results. What if we recreated ImageNet instead by searching the massive LAION dataset based on image captions alone? In this work, we carry out this counterfactual investigation. We find that the resulting ImageNet recreation, which we call LAIONet, looks distinctly unlike the original. Specifically, the intra-class similarity of images in the original ImageNet is dramatically higher than it is for LAIONet. Consequently, models trained on ImageNet perform significantly worse on LAIONet. We propose a rigorous explanation for the discrepancy in terms of a subtle, yet important, difference in two plausible causal data-generating processes for the respective datasets, that we support with systematic experimentation. In a nutshell, searching based on an image caption alone creates an information bottleneck that mitigates the selection bias otherwise present in image-based filtering. Our explanation formalizes a long-held intuition in the community that ImageNet images are stereotypical, unnatural, and overly simple representations of the class category. At the same time, it provides a simple and actionable takeaway for future dataset creation efforts.

Dynamic benchmarks interweave model fitting and data collection in an attempt to mitigate the limitations of static benchmarks. In contrast to an extensive theoretical and empirical study of the static setting, the dynamic counterpart lags behind due to limited empirical studies and no apparent theoretical foundation to date. Responding to this deficit, we initiate a theoretical study of dynamic benchmarking. We examine two realizations, one capturing current practice and the other modeling more complex settings. In the first model, where data collection and model fitting alternate sequentially, we prove that model performance improves initially but can stall after only three rounds. Label noise arising from, for instance, annotator disagreement leads to even stronger negative results. Our second model generalizes the first to the case where data collection and model fitting have a hierarchical dependency structure. We show that this design guarantees strictly more progress than the first, albeit at a significant increase in complexity. We support our theoretical analysis by simulating dynamic benchmarks on two popular datasets. These results illuminate the benefits and practical limitations of dynamic benchmarking, providing both a theoretical foundation and a causal explanation for observed bottlenecks in empirical work. In response to concerns around the limitations of static datasets as benchmarks, researchers have proposed dynamic benchmarking--a setting where data collection and model building happen iteratively in tandem--as an alternative (Nie et al., 2020; Potts et al., 2021; Kiela et al., 2021; Ma et al., 2021; Gehrmann et al., 2021).