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Semiparametric Preference Optimization: Your Language Model is Secretly a Single-Index Model

Nathan Kallus

arXiv 26 Dec 2025 · Machine Learning

arXiv:2512.21917 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Aligning large language models (LLMs) to preference data typically assumes a known link function between observed preferences and latent rewards (e.g., a logistic Bradley-Terry link). Misspecification of this link can bias inferred rewards and misalign learned policies. We study preference alignment under an unknown and unrestricted link function. We show that realizability of $f$-divergence-constrained reward maximization in a policy class induces a semiparametric single-index binary choice model, where a scalar policy-dependent index captures all dependence on demonstrations and the remaining preference distribution is unrestricted. Rather than assuming this model has identifiable finite-dimensional structural parameters and estimating them, as in econometrics, we focus on policy learning with the reward function implicit, analyzing error to the optimal policy and allowing for unidentifiable nonparametric indices. We develop preference optimization algorithms robust to the unknown link and prove convergence guarantees in terms of generic function complexity measures. We demonstrate this empirically on LLM alignment. Code is available at https://github.com/causalml/spo/

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69
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Roger W. Klein and Richard H. Spady (1993) An efficient semiparametric estimator for binary response models1.00075100%
2Joel L. Horowitz (1992) A smoothed maximum score estimator for the binary response model1.00074100%
3Stephen R. Cosslett (1983) Distribution-free maximum likelihood estimator of the binary choice model1.00055100%
4Jae-Young Kim and David Pollard (1990) Cube root asymptotics1.00053100%
5Robert Sherman (1993) The limiting distribution of the maximum rank correlation estimator0.92844100%
6Aaron K. Han (1987) Non-parametric estimation of a binary choice model by maximum rank correlation0.84333100%
7Charles F. Manski (1975) Maximum score estimation of the stochastic utility model of choice0.84333100%
8Charles F. Manski (1985) Semiparametric analysis of discrete response: Asymptotic properties of the maximum score estimator0.84333100%
9Rafael Rafailov, Archit Sharma, Eric Mitchell, Stefano Ermon, Chelse… (2023) Direct preference optimization: Your language model is secretly a reward model0.81142100%
10Daniel M. Ziegler, Nisan Stiennon, Jeffrey Wu, Tom B. Brown, Alec Ra… (2019) Fine-tuning language models from human preferences0.81142100%

Showing the top 10 of 69 scored citations.