  Learning from Preferential Feedback (LfPF) plays an essential role in
training Large Language Models, as well as certain types of interactive
learning agents. However, a substantial gap exists between the theory and
application of LfPF algorithms. Current results guaranteeing the existence of
optimal policies in LfPF problems assume that both the preferences and
transition dynamics are determined by a Markov Decision Process. We introduce
the Direct Preference Process, a new framework for analyzing LfPF problems in
partially-observable, non-Markovian environments. Within this framework, we
establish conditions that guarantee the existence of optimal policies by
considering the ordinal structure of the preferences. We show that a
decision-making problem can have optimal policies -- that are characterized by
recursive optimality equations -- even when no reward function can express the
learning goal. These findings underline the need to explore preference-based
learning strategies which do not assume that preferences are generated by
reward.
