Transforming and Combining Rewards for Aligning Large Language Models
Authors: name: Zihao Wang, name: Chirag Nagpal, name: Jonathan Berant, name: Jacob Eisenstein, name: Alex D'Amour, name: Sanmi Koyejo, name: Victor Veitch

A common approach for aligning language models to human preferences is to
first learn a reward model from preference data, and then use this reward model
to update the language model. We study two closely related problems that arise
in this approach. First, any monotone transformation of the reward model
preserves preference ranking; is there a choice that is ``better'' than others?
Second, we often wish to align language models to multiple properties: how
should we combine multiple reward models? Using a probabilistic interpretation
of the alignment procedure, we identify a natural choice for transformation for
(the common case of) rewards learned from Bradley-Terry preference models. This
derived transformation has two important properties. First, it emphasizes
improving poorly-performing outputs, rather than outputs that already score
well. This mitigates both underfitting (where some prompts are not improved)
and reward hacking (where the model learns to exploit misspecification of the
reward model). Second, it enables principled aggregation of rewards by linking
summation to logical conjunction: the sum of transformed rewards corresponds to
the probability that the output is ``good'' in all measured properties, in a
sense we make precise. Experiments aligning language models to be both helpful
and harmless using RLHF show substantial improvements over the baseline
(non-transformed) approach.