Theoretical guarantees on the best-of-n alignment policy

• URL: http://arxiv.org/abs/2401.01879v1
• Date: Wed, 3 Jan 2024 18:39:13 GMT
• Title: Theoretical guarantees on the best-of-n alignment policy
• Authors: Ahmad Beirami and Alekh Agarwal and Jonathan Berant and Alexander D'Amour, and Jacob Eisenstein and Chirag Nagpal and Ananda Theertha Suresh
• Abstract summary: We show that the KL divergence between the best-of-$n$ policy and the base policy is equal to $log (n) - (n-1)/n.$ We propose a new estimator for the KL divergence and empirically show that it provides a tight approximation through a few examples.
• Score: 110.21094183592358
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A simple and effective method for the alignment of generative models is the best-of-$n$ policy, where $n$ samples are drawn from a base policy, and ranked based on a reward function, and the highest ranking one is selected. A commonly used analytical expression in the literature claims that the KL divergence between the best-of-$n$ policy and the base policy is equal to $\log (n) - (n-1)/n.$ We disprove the validity of this claim, and show that it is an upper bound on the actual KL divergence. We also explore the tightness of this upper bound in different regimes. Finally, we propose a new estimator for the KL divergence and empirically show that it provides a tight approximation through a few examples.

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