@inproceedings{mohsin-etal-2026-continuous,
title = "Continuous-Utility Direct Preference Optimization",
author = "Mohsin, Muhammad Ahmed and
Umer, Muhammad and
Fox, Emily",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.2410/",
pages = "54724--54768",
ISBN = "979-8-89176-459-0",
abstract = "Large language model reasoning is often treated as a monolithic capability, relying on binary preference supervision that fails to capture partial progress or fine-grained reasoning quality. We introduce continuous utility direct preference optimization CU-DPO, a framework that aligns models to a portfolio of prompt-based cognitive strategies by replacing binary labels with continuous scores that capture fine-grained reasoning quality, proving that learning with $K$ strategies yields a $\Theta(K \log K)$ improvement in sample complexity over binary preferences and that DPO converges to the entropy-regularized utility-maximizing policy. To exploit this signal, we propose a two-stage pipeline: (i)strategy selection, which optimizes the model to choose the best strategy via best-vs-all comparisons, and (ii){~}execution refinement, which trains correct execution using margin-stratified pairs. The framework is domain-agnostic: any task admitting cognitively distinct solution strategies and a decomposable continuous utility signal can be incorporated into the portfolio. On mathematical reasoning benchmarks, CU-DPO improves strategy selection accuracy from 35{--}46{\%} to 68{--}78{\%} across seven base models, yielding downstream reasoning gains of up to +6.6 points on in-distribution datasets with effective out-of-distribution transfer, and demonstrates consistent gains on code generation and causal reasoning benchmarks, confirming generalization beyond the mathematical domain."
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<abstract>Large language model reasoning is often treated as a monolithic capability, relying on binary preference supervision that fails to capture partial progress or fine-grained reasoning quality. We introduce continuous utility direct preference optimization CU-DPO, a framework that aligns models to a portfolio of prompt-based cognitive strategies by replacing binary labels with continuous scores that capture fine-grained reasoning quality, proving that learning with K strategies yields a Θ(K łog K) improvement in sample complexity over binary preferences and that DPO converges to the entropy-regularized utility-maximizing policy. To exploit this signal, we propose a two-stage pipeline: (i)strategy selection, which optimizes the model to choose the best strategy via best-vs-all comparisons, and (ii) execution refinement, which trains correct execution using margin-stratified pairs. The framework is domain-agnostic: any task admitting cognitively distinct solution strategies and a decomposable continuous utility signal can be incorporated into the portfolio. On mathematical reasoning benchmarks, CU-DPO improves strategy selection accuracy from 35–46% to 68–78% across seven base models, yielding downstream reasoning gains of up to +6.6 points on in-distribution datasets with effective out-of-distribution transfer, and demonstrates consistent gains on code generation and causal reasoning benchmarks, confirming generalization beyond the mathematical domain.</abstract>
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%0 Conference Proceedings
%T Continuous-Utility Direct Preference Optimization
%A Mohsin, Muhammad Ahmed
%A Umer, Muhammad
%A Fox, Emily
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F mohsin-etal-2026-continuous
%X Large language model reasoning is often treated as a monolithic capability, relying on binary preference supervision that fails to capture partial progress or fine-grained reasoning quality. We introduce continuous utility direct preference optimization CU-DPO, a framework that aligns models to a portfolio of prompt-based cognitive strategies by replacing binary labels with continuous scores that capture fine-grained reasoning quality, proving that learning with K strategies yields a Θ(K łog K) improvement in sample complexity over binary preferences and that DPO converges to the entropy-regularized utility-maximizing policy. To exploit this signal, we propose a two-stage pipeline: (i)strategy selection, which optimizes the model to choose the best strategy via best-vs-all comparisons, and (ii) execution refinement, which trains correct execution using margin-stratified pairs. The framework is domain-agnostic: any task admitting cognitively distinct solution strategies and a decomposable continuous utility signal can be incorporated into the portfolio. On mathematical reasoning benchmarks, CU-DPO improves strategy selection accuracy from 35–46% to 68–78% across seven base models, yielding downstream reasoning gains of up to +6.6 points on in-distribution datasets with effective out-of-distribution transfer, and demonstrates consistent gains on code generation and causal reasoning benchmarks, confirming generalization beyond the mathematical domain.
%U https://aclanthology.org/2026.emnlp-main.2410/
%P 54724-54768
Markdown (Informal)
[Continuous-Utility Direct Preference Optimization](https://aclanthology.org/2026.emnlp-main.2410/) (Mohsin et al., EMNLP 2026)
ACL
- Muhammad Ahmed Mohsin, Muhammad Umer, and Emily Fox. 2026. Continuous-Utility Direct Preference Optimization. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 54724–54768, Budapest, Hungary. Association for Computational Linguistics.