Tail-Aware Information-Theoretic Generalization for RLHF and SGLD
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917401622216704 |
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| author | Zhang, Huiming Li, Binghan Tian, Wan Sun, Qiang |
| author_facet | Zhang, Huiming Li, Binghan Tian, Wan Sun, Qiang |
| contents | Classical information-theoretic generalization bounds typically control the generalization gap through KL-based mutual information and therefore rely on boundedness or sub-Gaussian tails via the moment generating function (MGF). In many modern pipelines, such as robust learning, RLHF, and stochastic optimization, losses and rewards can be heavy-tailed, and MGFs may not exist, rendering KL-based tools ineffective. We develop a tail-dependent information-theoretic framework for sub-Weibull data, where the tail parameter $θ$ controls the tail heaviness: $θ=2$ corresponds to sub-Gaussian, $θ=1$ to sub-exponential, and $0<θ<1$ to genuinely heavy tails. Our key technical ingredient is a decorrelation lemma that bounds change-of-measure expectations using a shifted-log $f_θ$-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 tail index $θ$, with complexity scaling as $\log^{1/θ}$ and entropy$^{1/θ}$. These tools yield expected and high-probability PAC-Bayes generalization bounds, as well as an information-theoretic chaining inequality based on multiscale Rényi mutual information. We illustrate the consequences in Rényi-regularized RLHF under heavy-tailed rewards and in stochastic gradient Langevin dynamics with heavy-tailed gradient noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10727 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tail-Aware Information-Theoretic Generalization for RLHF and SGLD Zhang, Huiming Li, Binghan Tian, Wan Sun, Qiang Machine Learning Artificial Intelligence Probability Statistics Theory Classical information-theoretic generalization bounds typically control the generalization gap through KL-based mutual information and therefore rely on boundedness or sub-Gaussian tails via the moment generating function (MGF). In many modern pipelines, such as robust learning, RLHF, and stochastic optimization, losses and rewards can be heavy-tailed, and MGFs may not exist, rendering KL-based tools ineffective. We develop a tail-dependent information-theoretic framework for sub-Weibull data, where the tail parameter $θ$ controls the tail heaviness: $θ=2$ corresponds to sub-Gaussian, $θ=1$ to sub-exponential, and $0<θ<1$ to genuinely heavy tails. Our key technical ingredient is a decorrelation lemma that bounds change-of-measure expectations using a shifted-log $f_θ$-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 tail index $θ$, with complexity scaling as $\log^{1/θ}$ and entropy$^{1/θ}$. These tools yield expected and high-probability PAC-Bayes generalization bounds, as well as an information-theoretic chaining inequality based on multiscale Rényi mutual information. We illustrate the consequences in Rényi-regularized RLHF under heavy-tailed rewards and in stochastic gradient Langevin dynamics with heavy-tailed gradient noise. |
| title | Tail-Aware Information-Theoretic Generalization for RLHF and SGLD |
| topic | Machine Learning Artificial Intelligence Probability Statistics Theory |
| url | https://arxiv.org/abs/2604.10727 |