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Follow the Herd: A Data-Driven Approach for Actionable Recourse

Nishtha Madaan, Srikanta Bedathur

arXiv:2610.36580v1cs.AI

TL;DR

Action recourse needs to offer plausible ways to reach favorable decisions, but existing approaches rely on costly human supervision to specify action costs. DDAR learns user-trajectory dynamics from historical data and searches for recourse; experiments find it achieves desired decisions at low cost compared with baselines.

  • Problem

    Action recourse requires plausible, actionable recommendations, while existing approaches rely on costly human effort to specify action costs and domain knowledge.

    Source: Introduction · p. 1

  • Method

    DDAR learns a dynamics model from historical user trajectories and searches for recourse, treating more likely next states as lower-cost actions.

    Source: Introduction · p. 1, Framework · p. 2

  • Results

    Across experiments, DDAR generates recourse that achieves desired decisions at low cost compared with baselines.

    Source: Introduction · p. 1, Conclusion · p. 7

  • Takeaways & Limitations

    The paper concludes that DDAR generates recourse without costly human-provided common-sense knowledge.

    Source: Conclusion · p. 7

    DDAR assumes its user model can generate samples and evaluate density, depending on the optimization approach.

    Source: Framework · p. 2

Abstract

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As machine learning systems make increasingly greater decisions about people's lives, it is critical to provide users with actionable recourse about how they can achieve their desired outcomes. This problem is currently tackled by relying on expensive human supervision which involves hand-designing a cost function before searching for low-cost actions that achieve the desired outcome. In this paper, we propose \textit{``Data-Driven Action Recourse"} (DDAR), the first approach for providing action recourse without requiring costly supervision from humans about action costs. We build upon the notion that highly likely trajectories in the historical user data should be associated with lower costs. With this, DDAR first builds a dynamics model of historical user trajectories. Under this model, it then searches for trajectories that achieve the desired outcome. In experiments, we find that this simple approach recommends plausible action recourse without requiring human supervision, achieving lower action costs than the existing approaches.

Introduction

Action recourse can help people respond to unfavorable decisions, but existing approaches rely on human-specified costs. DDAR learns from historical user trajectories to generate actionable recourse without human supervision.

  • Actionable recourse is important when decisions in areas such as criminal justice, loan approval, and healthcare produce unfavorable outcomes for users.For example, a rejected loan applicant may need a plausible path to acceptance.Source: Introduction · p. 1
  • Existing action-recourse methods formulate finding the lowest-cost change that crosses a decision boundary as constrained optimization, given a decision model and cost function (Wachter, Mittelstadt, and Russell 2017; Mothilal, Sharma, and Tan 2020; Ustun, Spangher, and Liu 2019).Source: Introduction · p. 1
  • Existing approaches rely on human supervision to identify mutable attributes and encode common-sense costs, while historical data may capture domain constraints and typical actions without such supervision.The paper states that prior work had not acquired action costs from data in an unsupervised manner.Source: Introduction · p. 1
  • DDAR trains a diffusion model on historical user-trajectory logs to predict future states and guide actionable, low-cost recourse toward the desired outcome.It samples possible next recourse states guided by the trajectory dynamics model.Source: Introduction · p. 1
  • DDAR is introduced as the first data-driven action recourse framework, learning plausible recourse from the underlying data distribution and its characteristics.The paper also extends the framework to generate K-step recourse.Source: Introduction · p. 1
  • In experiments, DDAR significantly outperforms baselines on various metrics, producing low-cost recourse with a high recourse rate.Source: Introduction · p. 1

Framework

DDAR seeks a next user state that achieves the desired label while minimizing a cost estimated from observational user trajectories. Its framework uses a user model conditioned on the current state and allows optimization methods to search for recourse.

DDAR Objective

  • DDAR seeks a next state that minimizes user cost while achieving the desired label.The recourse objective is defined relative to the user's previous state and a decision model.Source: Framework · pp. 1–2

Framework Overview

  • Unlike nearest-recourse and plausibility-focused formulations, DDAR accounts for recourse cost conditioned on the individual's current state without costly human supervision.The figure contrasts DDAR with Wachter, Mittelstadt, and Russell (2017), which seeks the nearest recourse, and Madaan and Bedathur (2024), which emphasizes plausibility but ignores user cost.Source: Figure 1 · p. 2, Framework · p. 2

A Data-Driven Cost Function

  • DDAR approximates low-cost actions as likely next states, using observational trajectory data to estimate transition probability conditional on the current state.The paper motivates this data-driven cost function as an alternative to an expensive manual process.Source: Framework · p. 2

User Model and Optimization

  • The user model must support sampling and density evaluation; an optimization method can sample candidate trajectories, score them, and rank those achieving the desired label.The framework permits any optimization approach given the user model, decision model, and score function; higher scores indicate greater likelihood of crossing the decision boundary.Source: Framework · p. 2

Conditional Guided Diffusion for DDAR

DDAR models user-state transitions with diffusion and guides denoising toward a desired decision label to generate recourse.

Conditional Guided Diffusion for DDAR

  • DDAR combines a diffusion-based user model with guided diffusion to produce recourse aimed at the desired outcome.The architecture encodes the input state, denoises a recourse embedding, and applies decision-model gradients during denoising.Source: Conditional Guided Diffusion for DDAR · p. 2, Figure 2 · p. 3

Encoder

  • The encoder maps each K-integer user-state tuple to a latent representation by applying a learned D-dimensional embedding dictionary to each item.For tabular data, the paper describes quantizing each cell to an integer before embedding it.Source: Encoder · p. 2

Conditional Diffusion as the User Model

  • The conditional diffusion model predicts the next latent user state through T denoising steps, starting from Gaussian noise and using a cosine variance schedule.Its denoiser is a 12-layer, 768-hidden-size transformer with 12 heads; it is trained to predict the clean state using cross-entropy on categorical labels, which the authors found superior to L2 loss.Source: Conditional Diffusion as the User Model · pp. 2–3

Recourse Generation

  • At each denoising step, recourse generation adds the gradient of cross-entropy between the decision model’s output and the desired label to steer the sample.The guiding loss is Lguide(z, y*) = CE(f(z), y*).Source: Recourse Generation · p. 3, Figure 2 · p. 3

Datasets

DDAR is evaluated on two synthetic datasets, LoanSynth and GradSynth, and the semi-realistic AdultIncome++ dataset. Each represents users as evolving trajectories with outcome labels.

Datasets

  • The evaluation uses LoanSynth and GradSynth as synthetic datasets and AdultIncome++ as a semi-realistic dataset.Source: Datasets · p. 3

LoanSynth Dataset

  • LoanSynth trajectories contain 30 yearly rows of user attributes, including education, occupation, finances, and credit score, plus a loan-approval label.The dataset is generated from an initial user-state distribution and causal dynamics.Source: LoanSynth Dataset · p. 3

GradSynth: A Synthetic Dataset for Graduate School Applications

Adult Income ++ Benchmark

  • Adult Income++ trajectories contain four rows of adult demographic, employment, and financial attributes, plus a label indicating whether income exceeds $50K.Source: Adult Income ++ Benchmark · p. 3

Related Work

The related work identifies a gap in action recourse: existing methods do not learn user action costs from data. It also distinguishes this focus from robustness research and reviews diffusion models’ varied uses in tabular data.

Action Recourse

  • To the authors’ knowledge, existing action-recourse methods do not acquire action costs in a data-driven manner, and counterfactual methods do not explicitly model user costs.Some counterfactual approaches encourage proximity or diversity, while robustness of recourse and explanations is described as orthogonal to this work.Source: Related Work · p. 4
  • Robustness methods address a separate issue, though future work could combine advances in robust action recourse with data-driven recourse.The passage also notes methods for handling corrupted data.Source: Related Work · p. 4

Diffusion in Tabular Data

  • Tabular diffusion research spans mixed-type table modeling, conditional imputation, time-series synthesis, missing-value imputation, and anomaly detection.The cited work also applies diffusion-based density modeling to unsupervised anomaly detection.Source: Related Work · p. 4

Experiments

Across three datasets, DDAR outperforms baselines on RR-AUC and cost. Multi-step recourse and best-of-N sampling further increase recourse rates.

Setup

  • The experiments use LoanSynth and GradSynth for loan and admission decisions, respectively, plus Adult-Income++, a synthetic Adult Income extension with evolving attributes and an income-over-$50K decision.The structured user states include immutable attributes such as gender and race.Source: Setup · p. 4

Metrics

  • Evaluation reports recourse rate under an allowable-cost threshold and its area under the curve (RR-AUC), average cost, conditional negative log-likelihood (CNLL), and unconditional negative log-likelihood (UNLL).CNLL evaluates recourses given the previous user state; UNLL evaluates them under a marginal density over user states.Source: Metrics · pp. 4–5

Baselines

  • Baselines include optimization-based Wachter and DiCE, graph-path FACE, and SCD, a density-modeling counterfactual explainer without a user trajectory model.FACE avoids sparse regions along its paths; SCD models the data distribution with a VAE or diffusion model.Source: Baselines · pp. 5–6

Can DDAR effectively provide low-cost recourse?

  • RR-AUC reached 4.142 on LoanSynth and 48.98 on GradSynth, versus under 1.0 and under 6.0 for baselines; Adult Income++ reached 4.142 with cost 1.25.DDAR also achieves remarkably low costs across all three datasets, while baselines perform significantly worse when no method has explicit cost-function knowledge.Source: Table 4 · p. 6, Can DDAR effectively provide low-cost… · p. 6
  • CNLL was 29.26, 16.42, and 40.17 for DDAR versus 71.45, 38.83, and 53.20 for the next-best baseline on LoanSynth, GradSynth, and Adult Income++, respectively.DDAR also outperforms baselines on unconditional negative log-likelihood; qualitatively, it avoids changing immutable fields such as race or sex, which many baselines alter.Source: Table 5 · p. 6, Can DDAR effectively provide low-cost… · p. 6, Table 6 · p. 6

Benefits of Multi-Step Recourse

Best-of-N Recourse.

  • With N=5 or 10, DDAR’s recourse rate improves across datasets; on LoanSynth, it reaches 1.0 at allowable cost 2.0, versus 0.12 for the next-best baseline.Other baselines are deterministic or show a smaller increase with greater N.Source: Figure 5 · p. 7, Best-of-N Recourse · p. 7

Conclusion

DDAR generates recourses that achieve the desired decision while maintaining low cost compared with baselines, without requiring costly common-sense knowledge from humans. The work also contributes three datasets for generating data-driven recourse.

  • DDAR recourses achieve the desired decision while maintaining low cost compared with baselines.The paper reports this result through experiments.Source: Conclusion · p. 7
  • The paper introduces DDAR, a data-driven framework for generating recourse without costly common-sense knowledge from humans.The authors describe it as the first such framework.Source: Conclusion · p. 7
  • The work contributes three datasets—LoanSynth, GradSynth, and Adult Income++—for generating data-driven recourse.Source: Conclusion · p. 7
  • Future work could incorporate user-defined constraints into the data-driven paradigm.Source: Conclusion · p. 7

Additional Details of the Method

The section specifies the diffusion model’s training schedule and hyperparameters, and explains how its scalar time input is represented as a vector embedding.

Denoiser Model and Training Hyperparameters

Sinusoidal Time Embeddings

  • The denoiser’s scalar time input is embedded as a vector using sinusoidal embeddings.The embedding uses H = D/2 and ω_k = exp(−log(max_period)k/H), with max_period = 10000.Source: Sinusoidal Time Embeddings · p. 9

Cost Functions

The section describes human-defined cost functions for evaluating two benchmarks, while noting that evaluated models are not given these costs and are trained unsupervised on historical user logs.

  • Algorithms 1 and 2 provide human-defined cost-function pseudocode for evaluating the two benchmarks; evaluated models do not receive these costs and instead train unsupervised on historical user-log data.Source: Cost Functions · p. 9

Benchmark Datasets

The benchmark datasets are documented through separate data-generation procedures in Algorithms 3, 4, and 5.

LoanSynth Generation

GradeSynth Generation

Adult Income ++ Generation

Qualitative Samples

The qualitative samples compare DDAR with baselines on LoanSynth and GradSynth, and report that other methods sometimes change immutable attributes while DDAR does not.

Qualitative Samples

  • Qualitative comparisons cover LoanSynth and GradSynth, marking changes and invalid immutable changes in cyan and red, respectively.The section identifies these comparisons in Tables 9 and 10.Source: Qualitative Samples · p. 9, Table 9 · p. 11, Table 10 · p. 12
  • DDAR input-output samples are provided, including LoanSynth recourse with K = 10.Table 7 presents the LoanSynth samples as user states over time; Table 11 also provides DDAR input-output pairs.Source: Table 7 · p. 10, Table 11 · p. 13
  • Other baselines sometimes change immutable attributes such as gender, institute tier, and college GPA, while DDAR does not.The GradSynth comparison highlights changes in cyan and wrongly changed immutable attributes in red.Source: Table 12 · p. 13
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