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From Search To Sampling: Generative Models For Robust Algorithmic Recourse

Prateek Garg, Lokesh Nagalapatti, Sunita Sarawagi

TL;DR

This work tackles algorithmic recourse by jointly optimizing three core criteria—validity, proximity, and plausibility—through a generative recourse model, GenRe. GenRe trains a recourse likelihood ${\mathcal{R}}_\theta(x^+|x)$ using paired supervision synthesized from unlabeled data via a pairing strategy, and performs forward sampling during inference to generate high-quality recourse candidates. The authors prove consistency of their estimator with rate ${\mathcal{O}}(1/N_+)$ and demonstrate superior performance across three real datasets against eight baselines, including robustness to cost magnitudes and superior data-manifold plausibility. Empirically, GenRe outperforms nearest-neighbor, diffusion-guided, and other plausibility-based methods on cost, validity, and latent density metrics, highlighting the practical impact of jointly trained generative recourse. The approach advances recourse research by providing a scalable, sampling-based mechanism with theoretical guarantees and strong empirical results, accompanied by open-source code.

Abstract

Algorithmic Recourse provides recommendations to individuals who are adversely impacted by automated model decisions, on how to alter their profiles to achieve a favorable outcome. Effective recourse methods must balance three conflicting goals: proximity to the original profile to minimize cost, plausibility for realistic recourse, and validity to ensure the desired outcome. We show that existing methods train for these objectives separately and then search for recourse through a joint optimization over the recourse goals during inference, leading to poor recourse recommendations. We introduce GenRe, a generative recourse model designed to train the three recourse objectives jointly. Training such generative models is non-trivial due to lack of direct recourse supervision. We propose efficient ways to synthesize such supervision and further show that GenRe's training leads to a consistent estimator. Unlike most prior methods, that employ non-robust gradient descent based search during inference, GenRe simply performs a forward sampling over the generative model to produce minimum cost recourse, leading to superior performance across multiple metrics. We also demonstrate GenRe provides the best trade-off between cost, plausibility and validity, compared to state-of-art baselines. Our code is available at: https://github.com/prateekgargx/genre.

From Search To Sampling: Generative Models For Robust Algorithmic Recourse

TL;DR

This work tackles algorithmic recourse by jointly optimizing three core criteria—validity, proximity, and plausibility—through a generative recourse model, GenRe. GenRe trains a recourse likelihood using paired supervision synthesized from unlabeled data via a pairing strategy, and performs forward sampling during inference to generate high-quality recourse candidates. The authors prove consistency of their estimator with rate and demonstrate superior performance across three real datasets against eight baselines, including robustness to cost magnitudes and superior data-manifold plausibility. Empirically, GenRe outperforms nearest-neighbor, diffusion-guided, and other plausibility-based methods on cost, validity, and latent density metrics, highlighting the practical impact of jointly trained generative recourse. The approach advances recourse research by providing a scalable, sampling-based mechanism with theoretical guarantees and strong empirical results, accompanied by open-source code.

Abstract

Algorithmic Recourse provides recommendations to individuals who are adversely impacted by automated model decisions, on how to alter their profiles to achieve a favorable outcome. Effective recourse methods must balance three conflicting goals: proximity to the original profile to minimize cost, plausibility for realistic recourse, and validity to ensure the desired outcome. We show that existing methods train for these objectives separately and then search for recourse through a joint optimization over the recourse goals during inference, leading to poor recourse recommendations. We introduce GenRe, a generative recourse model designed to train the three recourse objectives jointly. Training such generative models is non-trivial due to lack of direct recourse supervision. We propose efficient ways to synthesize such supervision and further show that GenRe's training leads to a consistent estimator. Unlike most prior methods, that employ non-robust gradient descent based search during inference, GenRe simply performs a forward sampling over the generative model to produce minimum cost recourse, leading to superior performance across multiple metrics. We also demonstrate GenRe provides the best trade-off between cost, plausibility and validity, compared to state-of-art baselines. Our code is available at: https://github.com/prateekgargx/genre.
Paper Structure (32 sections, 2 theorems, 11 equations, 5 figures, 13 tables, 2 algorithms)

This paper contains 32 sections, 2 theorems, 11 equations, 5 figures, 13 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Related Work
  4. Our Approach
  5. Creating Training Pairs
  6. Architecture and Training of the Generative Model
  7. Inference
  8. Theoretical Analysis
  9. Experimental Results
  10. Experimental Setup
  11. Overall comparison with baselines
  12. Generating recourse from a recourse likelihood model Vs Optimizing jointly during inference.
  13. Ablation: Role of conditional likelihood
  14. Comparison with Nearest Neighbor Search
  15. Comparison with Pre-trained Diffusion Models
  16. ...and 17 more sections

Key Result

Theorem 4.1

Let $f({\bm{x}}^+,{\bm{x}})$ be any function of $({\bm{x}}^+,{\bm{x}})$. For $Q({\bm{x}}^+|{\bm{x}})$ defined in Equation eq:Q and $R({\bm{x}}^+|{\bm{x}})$ defined in Equation eq:idealL, let $\mu = \mathbb{E}_R[f]$ and $\hat{\mu}=\mathbb{E}_Q[f]$. Then $\hat{\mu}$ is a consistent estimate of $\mu$ w

Figures (5)

  • Figure 1: The recourse pipeline starts with any instance ${\bm{x}}$ that received an unfavorable label $h({\bm{x}}) = y^-$. The recourse mechanism outputs an alternative ${\bm{x}}^+$ such that $h({\bm{x}}^+) = y^+$. The user is satisfied as long as ${\bm{x}}^+$ (1) is valid i.e., achieves the desired label from $P(y^+|{\bm{x}}^+)$, (2) is plausible and actionable in real-life, and (3) is proximal to the original ${\bm{x}}$ to incur low cost.
  • Figure 2: Comparison of different classes of recourse methods. Training instances are shown in light red and blue colors. Recourse is sought on instances marked in dark red color and they are connected by an edge to the recourse instance they were mapped to. From left to right:(1)Wachter, a cost minimizing method maps instances to classifier boundaries away from the blue data distribution.(2) PROBE, a robust recourse method, maps instances away from the boundary and from the blue data distribution. (3) CRUDS, a likelihood based method suffers mode collapse and for the circles dataset strays away from data distribution. to train (4) GenRe(our method) produces plausible recourse instances by being on the blue cloud while also minimizing cost. Recourse instances are also diverse.
  • Figure 3: Overview of GenRe. We define an empirical distribution of instance pairs $({\bm{x}}, {\bm{x}}^+)$ using training data ${\mathcal{D}}$, classifier $h$, cost function $C$ and balance parameter $\lambda$ to train the recourse model $\mathcal{R}_\theta$, an encoder-decoder model. During inference, the given negative instance ${\bm{x}}$ is fed to the decoder, and recourse instances sampled from the decoder auto-regressively.
  • Figure 4: Comparing GenRe with CRUDS for different values of balance parameter $\lambda \in \{0.5,1.0,2.5,5.0,10.0\}$. Note that $x$-axis is on exponential scale. Top: Comparing soft validity. Bottom: Comparing fraction of recourse instances that were inliers. GenRe provides better trade-offs than CRUDS with changing cost: GenRe always returns plausible instances and tradesoff validity gradually with cost. CRUDS shows huge swings in validity and plausibility with changing $\lambda$.
  • Figure 5: Visual Comparison between contours of density learned by conditional model (odd positions) and unconditional model (even positions)

Theorems & Definitions (4)

  • Theorem 4.1
  • proof
  • Theorem 4.2
  • proof