Provably Convergent Primal-Dual DPO for Constrained LLM Alignment

The widespread application of large language models (LLMs) raises increasing demands on ensuring safety or imposing constraints, such as reducing harmful content and adhering to predefined rules. While there have been several works studying LLM safety alignment, these works either need to train three models and incur high memory costs, or require prior knowledge on the optimal solution. Witnessing this fact, we investigate the constrained alignment problem for LLMs, i.e., maximizing the reward of outputs while restricting the cost to stay below a threshold. We propose a novel primal-dual direct preference optimization (DPO) approach, which first trains a model using standard DPO on reward preference data to provide reward information, and then adopts a rearranged Lagrangian DPO objective utilizing the provided reward information to fine-tune LLMs. Our approach only needs to train two models rather than three, which significantly saves memory costs, and does not require extra prior knowledge. Moreover, we establish rigorous suboptimality and constraint violation guarantees. We also extend our approach to enable online exploration and drop the data coverage dependence in the results. Experiments on the PKU-SafeRLHF and TruthfulQA datasets demonstrate the state-of-the-art performance of our approach.