Personalized Generative Recourse via Conjugate Cost Priors and Inverted Sampling

Algorithmic recourse aims to provide individuals with actionable changes that yield a favorable prediction while remaining in-distribution and minimizing the cost of change. Recent generative recourse methods balance these criteria more robustly than inference-time optimization, but they fix a single cost function at training time, whereas the cost of a change is user-dependent. We present **ACCORD**, a generative diffusion model conditioned on the user's cost function, so that a single model can serve recourse tailored to each individual's notion of what a change costs. Rather than tilting a fixed generative model toward the user's cost at inference time, which is expensive and degenerates when that cost differs from the training cost, ACCORD amortizes training over a flexible conjugate prior that we design. Our cost prior linearly combines random cost curves and expresses the weighted, asymmetric, and range-dependent costs typical of recourse applications. Starting from only unpaired positive and negative instances, we exploit the conjugacy of the prior to invert the order in which (cost, target) training pairs are sampled, avoiding a search over positives for every drawn cost. We analyze the risk of the trained model and show that inverting the sampling lowers risk on costs well supported by the positive instances. Empirically, ACCORD outperforms both search-based recourse methods and diffusion guidance techniques under diverse user-specific costs.