Theoretical Guarantees for Minimum Bayes Risk Decoding
This provides theoretical justification for MBR decoding's empirical success, addressing a gap in understanding for researchers in natural language processing and machine learning, though it is incremental as it builds on prior empirical work.
The paper tackles the lack of theoretical understanding for Minimum Bayes Risk (MBR) decoding by proving that, under certain assumptions, MBR decoding approaches the optimal solution with high probability at a rate of O(n^{-1/2}) given a reference set size n, even when the language space is much larger, and shows it converges faster than MAP decoding in several cases.
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 $O\left(n^{-\frac{1}{2}}\right)$, under certain assumptions, even though the language space $Y$ is significantly larger $|Y|\gg n$. 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.