On the Convergence of Self-Improving Online LLM Alignment
Xudong Wu, Pangpang Liu, Vaneet Aggarwal, Jiayu Chen
cs.LG, cs.AI, stat.ML
Submitted: 2026-06-30
Comments: Accepted at UAI 2026
Code: https://github.com/xudongwu-0/SAIL_LLM
License: http://creativecommons.org/licenses/by/4.0/
The gist: The Self-Improving Alignment (SAIL) algorithm addresses distribution shift by reducing a bilevel formulation of the problem to an efficient, single-level method.
Terminology
Abstract
The Self-Improving Alignment (SAIL) algorithm addresses distribution shift by reducing a bilevel formulation of the problem to an efficient, single-level method. Empirically, SAIL has demonstrated strong performance on this task. However, a formal analysis of its convergence properties has been lacking. We identify a key theoretical challenge: the standard SAIL objective function is not guaranteed to be strongly concave due to unfavorable properties of its Hessian. To address this limitation, we propose a regularized objective, SAIL-RevKL, which incorporates a reverse Kullback-Leibler (KL) divergence penalty to improve the optimization landscape. Our central theoretical contribution is to prove that this regularized objective satisfies the Polyak-Lojasiewicz (PL) condition within a bounded parameter space. We establish global convergence guarantees, achieving a near-linear sample complexity. We further validate the effectiveness and stability of SAIL-RevKL through empirical evaluations, demonstrating that it outperforms the vanilla SAIL on both MuJoCo benchmarks and LLM alignment tasks.
Sources
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