We study the theoretical aspects of Reinforced Language Models (RLMs) from a bi-objective optimization perspective. Specifically, we consider the RLMs as a Pareto optimization problem that maximizes the two conflicting objectives, i.e., reward objective and likelihood objectives, simultaneously. Our main contribution consists of three parts. First, we establish the theoretical foundations of RLM as a Pareto optimization problem by presenting Reward Upper BOund (RUBO) and Pareto optimality. Our theoretical outcomes are supported by not only deductive proofs but also empirical results. Second, we propose Reward Dropout, a simple yet powerful method that guarantees to improve a bi-objective optimization of RLM. Lastly, we demonstrate that the Reward Dropout is consistently effective across five benchmark datasets and four benchmark LLMs, meaning that the Reward Dropout significantly improves the optimization performance of RLMs.

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