On the Convergence of Self-Improving Online LLM Alignment
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...
| Authors | Xudong Wu, Pangpang Liu, Vaneet Aggarwal et al. |
|---|---|
| Primary category | cs.LG |
| Published | 30 June 2026 |
| Last updated at source | 30 June 2026 |
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