aiqbench analysis
This research addresses a critical theoretical bottleneck in AI alignment, demonstrating how to enforce fairness axioms like Pareto Optimality in linear reward models by introducing controlled slack variables. The authors provide tight bounds on the cost of satisfying these constraints and propose a practical method that minimizes violations while maintaining linear scalability for unseen responses. This work is essential for developers building reliable preference-based alignment systems who need to balance mathematical rigor with deployment feasibility.
Axiom Satisfiability of Linear Rewards in Alignment
arXiv:2610.06892v1 Announce Type: cross Abstract: Learning from human preference data is the dominant route to aligning language models with human values. In linear social choice, where rewards are linear in a fixed feature representation of prompt-response pairs, Ge et al.[2024] show that fitting such a reward by minimizing any non-decreasing convex loss, including BTL, fails PO and PMC. Moreover, no rule that reads only the majority relation can satisfy PO once the output is required to be linearly induced. We ask what it costs to enforce these axioms anyway. To this end, we relax the linear model to allow per-candidate slack. We compute the relaxed linear reward with the smallest total slack that satisfies the axioms with a margin $\eta$, the minimum required difference between two reward values. Our solution satisfies the axioms under no assumptions about the voters or how comparisons were collected. We bound the optimal total slack by $O(1)$ when $\eta$ is at most $O(\frac{1}{m^2})$ for $m$ candidates. Furthermore, we exhibit an instance that forces this bound, concluding that the rate is tight up to constants. In practice, the no. of candidates far exceeds the feature dimension, and only a linear reward can be evaluated on unseen responses. We therefore introduce a new method that charges the linear part for each comparison it gets wrong. It simultaneously minimizes the total slack and the no. of violations, with a parameter $\lambda$ trading off between them. We show that the total slack is monotone but saturating in $\lambda$: raising it reduces the violations of the deployed linear reward and increases the slack, yet the slack stays below $(\eta+\Delta\sqrt{d})\lfloor m^2/4\rfloor$, where $\Delta$ and $d$ are the diameter and dimension of the features, respectively. Experiments on both synthetic and real-life preference data corroborate our theory and show that the linear reward output by our method beats linear BTL.
Abstract:Learning from human preference data is the dominant route to aligning language models with human values. In linear social choice, where rewards are linear in a fixed feature representation of prompt-response pairs, Ge et al.[2024] show that fitting such a reward by minimizing any non-decreasing convex loss, including BTL, fails PO and PMC. Moreover, no rule that reads only the majority relation can satisfy PO once the output is required to be linearly induced. We ask what it costs to enforce these axioms anyway. To this end, we relax the linear model to allow per-candidate slack. We compute the relaxed linear reward with the smallest total slack that satisfies the axioms with a margin $\eta$, the minimum required difference between two reward values. Our solution satisfies the axioms under no assumptions about the voters or how comparisons were collected. We bound the optimal total slack by $O(1)$ when $\eta$ is at most $O(\frac{1}{m^2})$ for $m$ candidates. Furthermore, we exhibit an instance that forces this bound, concluding that the rate is tight up to constants. In practice, the no. of candidates far exceeds the feature dimension, and only a linear reward can be evaluated on unseen responses. We therefore introduce a new method that charges the linear part for each comparison it gets wrong. It simultaneously minimizes the total slack and the no. of violations, with a parameter $\lambda$ trading off between them. We show that the total slack is monotone but saturating in $\lambda$: raising it reduces the violations of the deployed linear reward and increases the slack, yet the slack stays below $(\eta+\Delta\sqrt{d})\lfloor m^2/4\rfloor$, where $\Delta$ and $d$ are the diameter and dimension of the features, respectively. Experiments on both synthetic and real-life preference data corroborate our theory and show that the linear reward output by our method beats linear BTL.
Computer Science and Game Theory (cs.GT); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Multiagent Systems (cs.MA)
arXiv:2610.06892 [cs.GT]
(or arXiv:2610.06892v1 [cs.GT] for this version)
https://doi.org/10.48550/arXiv.2610.06892 Focus to learn more arXiv-issued DOI via DataCite
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