arXiv:2603.03099v1 Announce Type: cross Abstract: Despite Adam demonstrating faster empirical convergence than SGD in many applications, much of the existing theory yields guarantees essentially comparable to those of SGD, leaving the empirical performance gap insufficiently explained. In this paper, we uncover a key second-moment normalization in Adam and develop a stopping-time/martingale analysis that provably distinguishes Adam from SGD under the classical bounded variance model (a second moment assumption). In particular, we establish the first theoretical separation between the high-probability convergence behaviors of the two methods: Adam achieves a $\delta^{-1/2}$ dependence on the confidence parameter $\delta$, whereas corresponding high-probability guarantee for SGD necessarily incurs at least a $\delta^{-1}$ dependence.

arXiv:2505.02156v5 Announce Type: replace-cross Abstract: Effective social intelligence simulation requires language agents to dynamically adjust reasoning depth, a capability notably absent in current studies. Existing methods either lack explicit reasoning or employ lengthy Chain-of-Thought reasoning uniformly across all scenarios, resulting in excessive token usage and inflexible social behaviors in tasks such as negotiation or collaboration. To address this, we propose an $\textbf{A}$daptive $\textbf{S}$ocial $\textbf{L}$earning ($\textbf{ASL}$) framework in this paper, aiming to improve the adaptive reasoning ability of language agents in dynamic social interactions. To this end, we first identify the hierarchical reasoning modes under such context, ranging from intuitive response to deep deliberation based on the cognitive control theory. We then develop the $\textbf{A}$daptive $\textbf{M}$ode $\textbf{P}$olicy $\textbf{O}$ptimization ($\textbf{AMPO}$) algorithm to learn the context-aware mode adaptation and reasoning. Our framework advances existing research in three key aspects: (1) Multi-granular reasoning mode design, (2) Context-aware mode switching in rich social interaction, and (3) Token-efficient reasoning with depth adaptation. Extensive experiments on the benchmark social intelligence environment verify that ASL achieves 15.6% higher task performance than GPT-4o. Notably, our AMPO outperforms GRPO by 7.0% with 32.8% shorter thinking chains, demonstrating the advantages of our AMPO and the learned adaptive reasoning ability over GRPO's solution.