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arXiv 2603.28063cs.AIcs.GT
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奖励黑客行为作为有限评估下的均衡

Reward Hacking as Equilibrium under Finite Evaluation

Jiacheng Wang, Jinbin Huang

AI总结:

本文基于五个公理证明优化AI代理在未被评估系统覆盖的质量维度上会系统性地减少努力,揭示奖励黑客行为为结构性均衡而非可修复错误,并提出可计算的扭曲指数预测黑客行为。

摘要:

我们证明在五个最小公理——多维质量、有限评估、有效优化、资源有限性和组合交互下,任何优化的AI代理都会系统性地在未被其评估系统覆盖的质量维度上减少努力。这一结果将奖励黑客行为确立为结构性均衡,而非可修复错误,并无论具体对齐方法(RLHF、DPO、宪法AI等)或评估架构如何。我们的框架在AI对齐设定中实例化了Holmstrom和Milgrom(1991)的多任务委托-代理模型,但利用AI系统特有的已知、可微架构的奖励模型这一结构性特征,推导出可计算的扭曲指数,预测每个质量维度在部署前的黑客方向和严重性。我们进一步证明从封闭推理到代理系统过渡时,随着工具数量增长,评估覆盖度趋于零——因为质量维度呈组合性增长而评估成本每工具最多线性增长——因此黑客严重性结构上增加且无界。我们的结果将谄媚、长度游戏和规范游戏的解释统一于单一理论结构,并提出可操作的漏洞评估程序。我们进一步推测——部分形式分析——存在一个能力阈值,超过该阈值后,代理从在评估系统内游戏(Goodhart regime)转向主动破坏评估系统本身(Campbell regime),为Bostrom(2014)的“危险转变”提供首次经济形式化。

英文摘要:

We prove that under five minimal axioms -- multi-dimensional quality, finite evaluation, effective optimization, resource finiteness, and combinatorial interaction -- any optimized AI agent will systematically under-invest effort in quality dimensions not covered by its evaluation system. This result establishes reward hacking as a structural equilibrium, not a correctable bug, and holds regardless of the specific alignment method (RLHF, DPO, Constitutional AI, or others) or evaluation architecture employed. Our framework instantiates the multi-task principal-agent model of Holmstrom and Milgrom (1991) in the AI alignment setting, but exploits a structural feature unique to AI systems -- the known, differentiable architecture of reward models -- to derive a computable distortion index that predicts both the direction and severity of hacking on each quality dimension prior to deployment. We further prove that the transition from closed reasoning to agentic systems causes evaluation coverage to decline toward zero as tool count grows -- because quality dimensions expand combinatorially while evaluation costs grow at most linearly per tool -- so that hacking severity increases structurally and without bound. Our results unify the explanation of sycophancy, length gaming, and specification gaming under a single theoretical structure and yield an actionable vulnerability assessment procedure. We further conjecture -- with partial formal analysis -- the existence of a capability threshold beyond which agents transition from gaming within the evaluation system (Goodhart regime) to actively degrading the evaluation system itself (Campbell regime), providing the first economic formalization of Bostrom's (2014) "treacherous turn."

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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