  Reinforcement Learning with Human Feedback (RLHF) is at the core of
fine-tuning methods for generative AI models for language and images. Such
feedback is often sought as rank or preference feedback from human raters, as
opposed to eliciting scores since the latter tends to be very noisy. On the
other hand, RL theory and algorithms predominantly assume that a reward
feedback is available. In particular, approaches for online learning that can
be helpful in adaptive data collection via active learning cannot incorporate
offline preference data. In this paper, we adopt a finite-armed linear bandit
model as a prototypical model of online learning. We consider an offline
preference dataset to be available generated by an expert of unknown
'competence'. We propose $\texttt{warmPref-PS}$, a posterior sampling algorithm
for online learning that can be warm-started with an offline dataset with noisy
preference feedback. We show that by modeling the competence of the expert that
generated it, we are able to use such a dataset most effectively. We support
our claims with novel theoretical analysis of its Bayesian regret, as well as
extensive empirical evaluation of an approximate algorithm which performs
substantially better (almost 25 to 50% regret reduction in our studies) as
compared to baselines.
