Jianhao Ma
Publications
Preconditioning Benefits of Spectral Orthogonalization in Muon
The Muon optimizer, a matrix-structured algorithm that leverages spectral orthogonalization of gradients, is a milestone in the pretraining of large language models. However, the underlying mechanisms of Muon -- particularly the role of gradient orthogonalization -- remain poorly understood, with very few works providing end-to-end analyses that rigorously explain its advantages in concrete applications. We take a step by studying the effectiveness of a simplified variant of Muon through two case studies: matrix factorization, and in-context learning of linear transformers. For both problems, we prove that simplified Muon converges linearly with iteration complexities independent of the relevant condition number, provably outperforming gradient descent and Adam. Our analysis reveals that the Muon dynamics decouple into a collection of independent scalar sequences in the spectral domain, each exhibiting similar convergence behavior. Our theory formalizes the preconditioning effect induced by spectral orthogonalization, offering insight into Muon's effectiveness in these matrix optimization problems and potentially beyond.
LIBRA: Language Model Informed Bandit Recourse Algorithm for Personalized Treatment Planning
We introduce a unified framework that seamlessly integrates algorithmic recourse, contextual bandits, and large language models (LLMs) to support sequential decision-making in high-stakes settings such as personalized medicine. We first introduce the recourse bandit problem, where a decision-maker must select both a treatment action and a feasible, minimal modification to mutable patient features. To address this problem, we develop the Generalized Linear Recourse Bandit (GLRB) algorithm. Building on this foundation, we propose LIBRA, a Language Model-Informed Bandit Recourse Algorithm that strategically combines domain knowledge from LLMs with the statistical rigor of bandit learning. LIBRA offers three key guarantees: (i) a warm-start guarantee, showing that LIBRA significantly reduces initial regret when LLM recommendations are near-optimal; (ii) an LLM-effort guarantee, proving that the algorithm consults the LLM only $O(\log^2 T)$ times, where $T$ is the time horizon, ensuring long-term autonomy; and (iii) a robustness guarantee, showing that LIBRA never performs worse than a pure bandit algorithm even when the LLM is unreliable. We further establish matching lower bounds that characterize the fundamental difficulty of the recourse bandit problem and demonstrate the near-optimality of our algorithms. Experiments on synthetic environments and a real hypertension-management case study confirm that GLRB and LIBRA improve regret, treatment quality, and sample efficiency compared with standard contextual bandits and LLM-only benchmarks. Our results highlight the promise of recourse-aware, LLM-assisted bandit algorithms for trustworthy LLM-bandits collaboration in personalized high-stakes decision-making.