Theoretical Guarantees for Minimum Bayes Risk Decoding

2025-02-18

AI Summary

This work addresses the gap between the empirical success and theoretical underpinning of Minimum Bayes Risk (MBR) decoding. We establish, for the first time, a convergence theory for MBR decoding under a finite reference hypothesis set. Leveraging statistical learning theory, the law of large numbers, and the Bayesian decision framework, we rigorously prove that MBR decoding converges to the optimal solution at rate $O(n^{-1/2})$ with high probability. Moreover, under identical assumptions, MBR strictly outperforms Maximum A Posteriori (MAP) decoding. By quantifying the expected utility gap between MBR and MAP, we identify the fundamental source of MBR’s robustness advantage. Our analysis provides the first probabilistically guaranteed convergence rate for MBR decoding, thereby bridging a critical theoretical void and formally justifying its practical efficacy.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Minimum Bayes Risk (MBR) decoding optimizes output selection by maximizing the expected utility value of an underlying human distribution. While prior work has shown the effectiveness of MBR decoding through empirical evaluation, few studies have analytically investigated why the method is effective. As a result of our analysis, we show that, given the size $n$ of the reference hypothesis set used in computation, MBR decoding approaches the optimal solution with high probability at a rate of $Oleft(n^{-frac{1}{2}} ight)$, under certain assumptions, even though the language space $Y$ is significantly larger $Ygg n$. This result helps to theoretically explain the strong performance observed in several prior empirical studies on MBR decoding. In addition, we provide the performance gap for maximum-a-posteriori (MAP) decoding and compare it to MBR decoding. The result of this paper indicates that MBR decoding tends to converge to the optimal solution faster than MAP decoding in several cases.

Problem

• Theoretical analysis of MBR decoding effectiveness
• Convergence rate of MBR to optimal solution
• Comparison between MBR and MAP decoding performance

Innovation

• MBR decoding optimization
• Theoretical convergence rate analysis
• Comparative MAP vs MBR performance