  Recent studies show that Large Language Models (LLMs) with safety alignment
can be jail-broken by fine-tuning on a dataset mixed with harmful data. First
time in the literature, we show that the jail-broken effect can be mitigated by
separating states in the finetuning stage to optimize the alignment and user
datasets. Unfortunately, our subsequent study shows that this simple Bi-State
Optimization (BSO) solution experiences convergence instability when steps
invested in its alignment state is too small, leading to downgraded alignment
performance. By statistical analysis, we show that the \textit{excess drift}
towards consensus could be a probable reason for the instability. To remedy
this issue, we propose \textbf{L}azy(\textbf{i}) \textbf{s}afety
\textbf{a}lignment (\textbf{Lisa}), which introduces a proximal term to
constraint the drift of each state. Theoretically, the benefit of the proximal
term is supported by the convergence analysis, wherein we show that a
sufficient large proximal factor is necessary to guarantee Lisa's convergence.
Empirically, our results on four downstream finetuning tasks show that Lisa
with a proximal term can significantly increase alignment performance while
maintaining the LLM's accuracy on the user tasks. Code is available at
\url{https://github.com/git-disl/Lisa}.
