{"ID":5438829,"CreatedAt":"2026-07-01T01:17:58.482524686Z","UpdatedAt":"2026-07-03T11:20:51.789462812Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.31524","arxiv_id":"2606.31524","title":"On the Convergence of Self-Improving Online LLM Alignment","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.","short_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 k...","url_abs":"https://arxiv.org/abs/2606.31524","url_pdf":"https://arxiv.org/pdf/2606.31524v1","authors":"[\"Xudong Wu\",\"Pangpang Liu\",\"Vaneet Aggarwal\",\"Jiayu Chen\"]","published":"2026-06-30T11:36:41Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\",\"stat.ML\"]","methods":"[\"Large Language Model\"]","has_code":false}