Continuous-Utility Direct Preference Optimization

• URL: http://arxiv.org/abs/2602.00931v1
• Date: Sat, 31 Jan 2026 23:15:32 GMT
• Title: Continuous-Utility Direct Preference Optimization
• Authors: Muhammad Ahmed Mohsin, Muhammad Umer, Ahsan Bilal, Zihao He, Muhammad Usman Rafique, Asad Aali, Muhammad Ali Jamshed, John M. Cioffi, Emily Fox,
• Abstract summary: We introduce Continuous Utility Direct Preference Optimization (CU-DPO), a framework that aligns models to a portfolio of prompt-based cognitive strategies.<n>We prove that learning with K strategies yields a Theta(K log K) improvement in sample complexity over binary preferences.<n>We show that CU-DPO improves strategy selection accuracy from 35-46 percent to 68-78 percent across seven base models.
• Score: 14.867957084669497
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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. We prove 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 training pipeline: (i) strategy selection, which optimizes the model to choose the best strategy for a given problem via best-vs-all comparisons, and (ii) execution refinement, which trains the model to correctly execute the selected strategy using margin-stratified pairs. On mathematical reasoning benchmarks, CU-DPO improves strategy selection accuracy from 35-46 percent to 68-78 percent across seven base models, yielding consistent downstream reasoning gains of up to 6.6 points on in-distribution datasets with effective transfer to out-of-distribution tasks.

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