Stochastic Gradient Descent in Non-Convex Problems: Asymptotic Convergence with Relaxed Step-Size via Stopping Time Methods

Stochastic Gradient Descent (SGD) is widely used in machine learning research. Previous convergence analyses of SGD under the vanishing step-size setting typically require Robbins-Monro conditions. However, in practice, a wider variety of step-size schemes are frequently employed, yet existing convergence results remain limited and often rely on strong assumptions. This paper bridges this gap by introducing a novel analytical framework based on a stopping-time method, enabling asymptotic convergence analysis of SGD under more relaxed step-size conditions and weaker assumptions. In the non-convex setting, we prove the almost sure convergence of SGD iterates for step-sizes $ \{ \epsilon_t \}_{t \geq 1} $ satisfying $\sum_{t=1}^{+\infty} \epsilon_t = +\infty$ and $\sum_{t=1}^{+\infty} \epsilon_t^p < +\infty$ for some $p > 2$. Compared with previous studies, our analysis eliminates the global Lipschitz continuity assumption on the loss function and relaxes the boundedness requirements for higher-order moments of stochastic gradients. Building upon the almost sure convergence results, we further establish $L_2$ convergence. These significantly relaxed assumptions make our theoretical results more general, thereby enhancing their applicability in practical scenarios.

Demonstration of DB-GPT: Next Generation Data Interaction System Empowered by Large Language Models

The recent breakthroughs in large language models (LLMs) are positioned to transition many areas of software. The technologies of interacting with data particularly have an important entanglement with LLMs as efficient and intuitive data interactions are paramount. In this paper, we present DB-GPT, a revolutionary and product-ready Python library that integrates LLMs into traditional data interaction tasks to enhance user experience and accessibility. DB-GPT is designed to understand data interaction tasks described by natural language and provide context-aware responses powered by LLMs, making it an indispensable tool for users ranging from novice to expert. Its system design supports deployment across local, distributed, and cloud environments. Beyond handling basic data interaction tasks like Text-to-SQL with LLMs, it can handle complex tasks like generative data analysis through a Multi-Agents framework and the Agentic Workflow Expression Language (AWEL). The Service-oriented Multi-model Management Framework (SMMF) ensures data privacy and security, enabling users to employ DB-GPT with private LLMs. Additionally, DB-GPT offers a series of product-ready features designed to enable users to integrate DB-GPT within their product environments easily. The code of DB-GPT is available at Github(https://github.com/eosphoros-ai/DB-GPT) which already has over 10.7k stars. Please install DB-GPT for your own usage with the instructions(https://github.com/eosphoros-ai/DB-GPT#install) and watch a 5-minute introduction video on Youtube(https://youtu.be/n_8RI1ENyl4) to further investigate DB-GPT.