  RL-based techniques can be used to search for prompts that when fed into a
target language model maximize a set of user-specified reward functions.
However, in many target applications, the natural reward functions are in
tension with one another -- for example, content preservation vs. style
matching in style transfer tasks. Current techniques focus on maximizing the
average of reward functions, which does not necessarily lead to prompts that
achieve balance across rewards -- an issue that has been well-studied in the
multi-objective and robust optimization literature. In this paper, we adapt
several techniques for multi-objective optimization to RL-based discrete prompt
optimization -- two that consider volume of the Pareto reward surface, and
another that chooses an update direction that benefits all rewards
simultaneously. We conduct an empirical analysis of these methods on two NLP
tasks: style transfer and machine translation, each using three competing
reward functions. Our experiments demonstrate that multi-objective methods that
directly optimize volume perform better and achieve a better balance of all
rewards than those that attempt to find monotonic update directions.
