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.

Related papers

• Statistical Analysis of Policy Space Compression Problem [54.1754937830779]
  Policy search methods are crucial in reinforcement learning, offering a framework to address continuous state-action and partially observable problems. Reducing the policy space through policy compression emerges as a powerful, reward-free approach to accelerate the learning process. This technique condenses the policy space into a smaller, representative set while maintaining most of the original effectiveness.
  arXiv  Detail & Related papers  (2024-11-15T02:46:55Z)
• Information Theoretic Guarantees For Policy Alignment In Large Language Models [19.315342870604113]
  We show that the $sqrtmathsfKL$ information theoretic upper bound holds if the reward under the reference policy has sub-gaussian tails. We also prove for the best of $n$ policy, that the $mathsfKL$ upper bound can be obtained for any $f$-divergence.
  arXiv  Detail & Related papers  (2024-06-09T18:41:50Z)
• Policy Gradient with Active Importance Sampling [55.112959067035916]
  Policy gradient (PG) methods significantly benefit from IS, enabling the effective reuse of previously collected samples. However, IS is employed in RL as a passive tool for re-weighting historical samples. We look for the best behavioral policy from which to collect samples to reduce the policy gradient variance.
  arXiv  Detail & Related papers  (2024-05-09T09:08:09Z)
• Asymptotics of Language Model Alignment [27.37118975691123]
  We show that the optimal KL-constrained RL solution satisfies a large deviation principle. We also show that the rate of growth of the scaled cumulants of the reward is characterized by proper Renyi cross entropy.
  arXiv  Detail & Related papers  (2024-04-02T08:40:07Z)
• Thompson Exploration with Best Challenger Rule in Best Arm Identification [66.33448474838342]
  We study the fixed-confidence best arm identification problem in the bandit framework. We propose a novel policy that combines Thompson sampling with a computationally efficient approach known as the best challenger rule.
  arXiv  Detail & Related papers  (2023-10-01T01:37:02Z)
• Estimating Optimal Policy Value in General Linear Contextual Bandits [50.008542459050155]
  In many bandit problems, the maximal reward achievable by a policy is often unknown in advance. We consider the problem of estimating the optimal policy value in the sublinear data regime before the optimal policy is even learnable. We present a more practical, computationally efficient algorithm that estimates a problem-dependent upper bound on $V*$.
  arXiv  Detail & Related papers  (2023-02-19T01:09:24Z)
• The Role of Baselines in Policy Gradient Optimization [83.42050606055822]
  We show that the emphstate value baseline allows on-policy. emphnatural policy gradient (NPG) to converge to a globally optimal. policy at an $O (1/t) rate gradient. We find that the primary effect of the value baseline is to textbfreduce the aggressiveness of the updates rather than their variance.
  arXiv  Detail & Related papers  (2023-01-16T06:28:00Z)
• On Gap-dependent Bounds for Offline Reinforcement Learning [40.92345387517103]
  This paper presents a systematic study on gap-dependent sample complexity in offline reinforcement learning. Under the optimal policy coverage assumption, the rate can be improved to $Oleft(frac1epsilonright)$ when there is a positive sub-optimality gap in the optimal $Q$-function. We show when the visitation probabilities of the behavior policy are uniformly lower bounded for states where an optimal policy's visitation probabilities are positive, the sample complexity of identifying an optimal policy is independent of $frac1epsilon$.
  arXiv  Detail & Related papers  (2022-06-01T01:44:12Z)
• Differentiable Bandit Exploration [38.81737411000074]
  We learn such policies for an unknown distribution $mathcalP$ using samples from $mathcalP$. Our approach is a form of meta-learning and exploits properties of $mathcalP$ without making strong assumptions about its form.
  arXiv  Detail & Related papers  (2020-02-17T05:07:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.