Orthogonalized Policy Optimization:Decoupling Sampling Geometry from Optimization Geometry in RLHF

• URL: http://arxiv.org/abs/2601.12415v2
• Date: Wed, 21 Jan 2026 14:54:54 GMT
• Title: Orthogonalized Policy Optimization:Decoupling Sampling Geometry from Optimization Geometry in RLHF
• Authors: Wang Zixian,
• Abstract summary: Large language model alignment objectives are often presented as a collection of distinct algorithms, such as PPO, DPO, IPO, and their variants.<n>In this work, we argue that this diversity obscures a simpler underlying structure.<n>We show that this entanglement is not merely a modeling convenience but a source of systematic instability.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Large language model alignment objectives are often presented as a collection of distinct algorithms, such as PPO, DPO, IPO, and their variants, each motivated by different derivations. In this work, we argue that this diversity obscures a simpler underlying structure. At a fundamental level, alignment objectives involve two independent design choices: (i) how training signals are sampled and weighted, and (ii) how deviations from a reference policy are geometrically penalized. Existing methods typically entangle these choices through a single divergence, most commonly the Kullback-Leibler divergence. We show that this entanglement is not merely a modeling convenience but a source of systematic instability. When the same divergence simultaneously determines sample weighting and optimization curvature, adjusting one aspect, such as exploration strength, inevitably alters the other, such as gradient geometry. This coupling is particularly problematic in preference-based reinforcement learning, where advantage signals are unbounded and high-confidence regimes are common. We propose a simple but structural remedy by formulating alignment as an orthogonal mirror descent problem, in which sampling geometry enters only as a linear driving force, while optimization geometry is determined independently by a mirror map. This perspective leads to a new alignment objective called Orthogonalized Policy Optimization (OPO), obtained by choosing a Euclidean mirror map in likelihood ratio space. The resulting objective admits a closed-form solution, linear and non-saturating gradient dynamics, and a well-conditioned trust region, while remaining fully compatible with standard large language model training pipelines.

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