Learning Where It Matters: Geometric Anchoring for Robust Preference Alignment

TL;DR

This paper introduces GAPO, a dynamic geometric anchoring method for preference alignment in language models that enhances robustness against noisy supervision by adaptively weighting preference signals.

Contribution

GAPO replaces static references with a geometry-aware, adversarial anchor, enabling adaptive reweighting and improved robustness in preference optimization.

Findings

GAPO outperforms static reference methods under noisy conditions.

It maintains or improves alignment and reasoning benchmark performance.

The Anchor Gap correlates with local margin degradation, guiding robust optimization.

Abstract

Direct Preference Optimization (DPO) and related methods align large language models from pairwise preferences by regularizing updates against a fixed reference policy. As the policy drifts, a static reference, however, can become increasingly miscalibrated, leading to distributional mismatch and amplifying spurious preference signals under noisy supervision. Conversely, reference-free variants avoid mismatch but often suffer from unconstrained reward drift. We propose Geometric Anchor Preference Optimization (GAPO), which replaces the fixed reference with a dynamic, geometry-aware anchor: an adversarial local perturbation of the current policy within a small radius that serves as a pessimistic baseline. This anchor enables an adaptive reweighting mechanism, modulating the importance of each preference pair based on its local sensitivity. We further introduce the Anchor Gap, the reward discrepancy between the policy and its anchor, and show under smoothness conditions that it approximates worst-case local margin degradation. Optimizing a logistic objective weighted by this gap downweights geometrically brittle instances while emphasizing robust preference signals. Across diverse noise settings, GAPO consistently improves robustness while matching or improving performance on standard LLM alignment and reasoning benchmarks.