Towards a theory of inference-time alignment with unknown rewards

2026-08-15

AI Summary

This study addresses the absence of statistical learning theory for inference-time alignment under unknown rewards by formulating it as a weak-to-strong learning process. We introduce the concept of "alignment dimension" and prove that it fully characterizes learnability in this setting. By integrating the PAC learning framework with single-inclusion graph algorithms, we achieve effective alignment without reward estimation. This work establishes a comprehensive theoretical foundation for inference-time alignment in unknown reward scenarios, bridging critical gaps in learnability characterization and theoretical guarantees. Consequently, it provides a rigorous statistical basis for developing alignment algorithms, ensuring their reliability even when ground-truth rewards are inaccessible during inference.

Abstract

Generative model alignment has received broad interest, and significant progress has been made in supervised fine-tuning and inference-time computation. Yet, alignment has remained poorly understood from a statistical learning perspective. We formulate inference-time alignment as a weak-to-strong learning problem, where a reference policy (weak learner) is assumed to be fairly good and the goal is to produce a strong learner that predicts a good response at test time with arbitrarily high probability. Our problem is formulated as learning from scratch --- everything is learned from data rather than assuming access to a good reward estimate, and thus differs from the existing inference-time alignment theory. Our model shares similarity to the recent work of arXiv:2510.15464, where for each prompt, there could be multiple good responses. Our definition of the alignment learnability follows the PAC learning principle. We introduce a novel combinatorial dimension of the reward class which we call the alignment dimension, and show that it completely characterizes the alignment learnability --- a reward class is alignment learnable if and only if its alignment dimension is finite. The core of our learning procedure works by invoking the ordinary one-inclusion graph algorithm to run a tournament over all pairs of label sets satisfying that neither is a subset of the other. We believe our results might shed light on establishing a complete theoretical understanding towards alignment.

Problem

• Inference-time alignment
• Unknown rewards
• Statistical learning theory
• Alignment learnability
• Weak-to-strong learning

Innovation

• Inference-time Alignment
• Weak-to-Strong Learning
• Alignment Dimension
• PAC Learning
• One-Inclusion Graph Algorithm