Direct Nash Optimization: Teaching Language Models to Self-Improve with
  General Preferences
Authors: name: Corby Rosset, name: Ching-An Cheng, name: Arindam Mitra, name: Michael Santacroce, name: Ahmed Awadallah, name: Tengyang Xie

This paper studies post-training large language models (LLMs) using
preference feedback from a powerful oracle to help a model iteratively improve
over itself. The typical approach for post-training LLMs involves Reinforcement
Learning from Human Feedback (RLHF), which traditionally separates reward
learning and subsequent policy optimization. However, such a reward
maximization approach is limited by the nature of "point-wise" rewards (such as
Bradley-Terry model), which fails to express complex intransitive or cyclic
preference relations. While advances on RLHF show reward learning and policy
optimization can be merged into a single contrastive objective for stability,
they yet still remain tethered to the reward maximization framework. Recently,
a new wave of research sidesteps the reward maximization presumptions in favor
of directly optimizing over "pair-wise" or general preferences. In this paper,
we introduce Direct Nash Optimization (DNO), a provable and scalable algorithm
that marries the simplicity and stability of contrastive learning with
theoretical generality from optimizing general preferences. Because DNO is a
batched on-policy algorithm using a regression-based objective, its
implementation is straightforward and efficient. Moreover, DNO enjoys monotonic
improvement across iterations that help it improve even over a strong teacher
(such as GPT-4). In our experiments, a resulting 7B parameter Orca-2.5 model
aligned by DNO achieves the state-of-the-art win-rate against GPT-4-Turbo of
33% on AlpacaEval 2.0 (even after controlling for response length), an absolute
gain of 26% (7% to 33%) over the initializing model. It outperforms models with
far more parameters, including Mistral Large, Self-Rewarding LM (70B
parameters), and older versions of GPT-4.