Tail-Aware Information-Theoretic Generalization for RLHF and SGLD

Researchers develop a new information-theoretic framework that handles heavy-tailed data distributions, addressing limitations in classical generalization bounds used in machine learning. The work applies specifically to reinforcement learning from human feedback (RLHF) and stochastic gradient optimization, where traditional KL-divergence tools fail due to non-existent moment generating functions.

This research tackles a fundamental problem in modern machine learning theory: classical generalization bounds assume well-behaved data distributions with finite moment generating functions, but real-world systems—particularly RLHF pipelines and robust learning systems—often produce heavy-tailed losses and rewards that violate these assumptions. The researchers introduce a tail-dependent framework using sub-Weibull distributions, parameterized by a tail index θ that elegantly captures the spectrum from sub-Gaussian (θ=2) through sub-exponential (θ=1) to genuinely heavy-tailed regimes (0<θ<1).

The technical innovation centers on a decorrelation lemma using shifted-log f_θ-divergence, which enables meaningful bounds without relying on MGF arguments. This breakthrough allows the team to establish sharp maximal inequalities and complexity bounds for sub-Weibull processes that scale with log^(1/θ), providing tighter analysis as tail heaviness increases. The framework directly addresses pain points in contemporary AI systems: RLHF models trained on human-generated reward signals often exhibit heavy tails due to inherent noise and outliers, while stochastic gradient Langevin dynamics used in Bayesian deep learning can suffer from heavy-tailed gradient noise.

For practitioners, this work provides theoretical justification for algorithm design choices in systems that naturally generate heavy-tailed data. The Rényi-regularized RLHF analysis suggests practical modifications to improve robustness when dealing with unreliable reward signals. The research bridges an important gap between statistical theory and engineering reality, offering both understanding and tools for principled algorithm design in modern deep learning applications.

• →New framework handles heavy-tailed distributions where classical information-theoretic bounds fail due to non-existent moment generating functions
• →Sub-Weibull tail index θ provides unified treatment of Gaussian, exponential, and genuinely heavy-tailed regimes
• →Sharp complexity bounds scale as log^(1/θ) and entropy^(1/θ), enabling tighter analysis for problematic data distributions
• →Direct applications to RLHF systems improve theoretical understanding of reward learning with noisy or outlier-rich feedback
• →Stochastic gradient Langevin dynamics gains new generalization guarantees under heavy-tailed gradient noise conditions