New Algorithm Improves LLM Alignment Convergence and Stability

The Self-Improving Alignment (SAIL) algorithm has shown promise in addressing distribution shift within Large Language Models (LLMs) by simplifying a complex bilevel problem into a more manageable single-level method. Despite its empirical success, a rigorous theoretical analysis of SAIL's convergence properties has been absent. Researchers identified a critical theoretical weakness: the standard SAIL objective function lacks strong concavity, primarily due to unfavorable characteristics of its Hessian matrix. To overcome this limitation, a new regularized objective, termed SAIL-RevKL, has been proposed. This enhanced version integrates a reverse Kullback-Leibler (KL) divergence penalty, which significantly improves the optimization landscape. The core contribution of this work is the proof that SAIL-RevKL's regularized objective satisfies the Polyak-Lojasiewicz (PL) condition within a defined parameter space, thereby establishing global convergence guarantees with near-linear sample complexity. Empirical evaluations further confirm that SAIL-RevKL not only demonstrates greater effectiveness but also improved stability compared to the original SAIL algorithm across various benchmarks, including MuJoCo and LLM alignment tasks.