aiqbench analysis
This research introduces a novel information-theoretic framework specifically designed for large language models facing heavy-tailed reward distributions, addressing the limitations of standard KL-regularization in RLHF scenarios. By leveraging shifted-log divergences and Rényi regularization, the study provides finite reward guarantees that mitigate catastrophic Goodhart effects where conventional methods fail under token-space attacks or extreme outliers. The work advances theoretical safety boundaries for AI alignment by establishing sharp maximal inequalities applicable to sub-Weibull processes beyond traditional Gaussian assumptions.
Tail-Aware Information-Theoretic Bounds for LLM Alignment under Heavy-Tailed Rewards
arXiv:2604.10727v2 Announce Type: replace-cross Abstract: Classical information-theoretic learning bounds typically rely on KL mutual information and moment-generating-function (MGF) arguments, which are well matched to bounded or sub-Gaussian losses but can be ineffective when losses or rewards are heavy-tailed. We develop a tail-aware information-theoretic framework for sub-Weibull data, where the tail parameter $\theta$ controls the tail heaviness: $\theta=2$ corresponds to sub-Gaussian, $\theta=1$ to sub-exponential, and $0<\theta<1$ to genuinely heavy tails. Our key technical ingredient is a decorrelation lemma that bounds change-of-measure expectations using a shifted-log $f_\theta$-divergence, which admits explicit comparisons to R\'enyi divergence without MGF arguments. On the empirical-process side, we establish sharp maximal inequalities and a Dudley-type chaining bound for sub-Weibull processes, with logarithmic and entropy terms raised to the power $1/\theta$. These tools yield tail-adaptive selection bounds and a multiscale information-theoretic Dudley inequality based on shifted-log and R\'enyi mutual information. We apply our theory to large language models (LLMs) in the context of reward hacking within reinforcement learning from human feedback (RLHF). We show that R\'enyi-regularized alignment provides finite reward guarantees and ensures that best-of-N policies remain well-controlled, thereby mitigating the catastrophic Goodhart effects where standard KL-regularization fails. We illustrate R\'enyi-regularized RLHF by experiments, including controlled heavy-tailed rewards and token-space reward attacks.
Abstract:Classical information-theoretic learning bounds typically rely on KL mutual information and moment-generating-function (MGF) arguments, which are well matched to bounded or sub-Gaussian losses but can be ineffective when losses or rewards are heavy-tailed. We develop a tail-aware information-theoretic framework for sub-Weibull data, where the tail parameter $\theta$ controls the tail heaviness: $\theta=2$ corresponds to sub-Gaussian, $\theta=1$ to sub-exponential, and $0<\theta<1$ to genuinely heavy tails. Our key technical ingredient is a decorrelation lemma that bounds change-of-measure expectations using a shifted-log $f_\theta$-divergence, which admits explicit comparisons to Rényi divergence without MGF arguments. On the empirical-process side, we establish sharp maximal inequalities and a Dudley-type chaining bound for sub-Weibull processes, with logarithmic and entropy terms raised to the power $1/\theta$. These tools yield tail-adaptive selection bounds and a multiscale information-theoretic Dudley inequality based on shifted-log and Rényi mutual information. We apply our theory to large language models (LLMs) in the context of reward hacking within reinforcement learning from human feedback (RLHF). We show that Rényi-regularized alignment provides finite reward guarantees and ensures that best-of-N policies remain well-controlled, thereby mitigating the catastrophic Goodhart effects where standard KL-regularization fails. We illustrate Rényi-regularized RLHF by experiments, including controlled heavy-tailed rewards and token-space reward attacks.
Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Probability (math.PR); Statistics Theory (math.ST)
arXiv:2604.10727 [stat.ML]
(or arXiv:2604.10727v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2604.10727 Focus to learn more arXiv-issued DOI via DataCite
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