Local Duality for Sparse Support Vector Machines

Due to the rise of cardinality minimization in optimization, sparse support vector machines (SSVMs) have attracted much attention lately and show certain empirical advantages over convex SVMs. A common way to derive an SSVM is to add a cardinality function such as $\ell_0$-norm to the dual problem of a convex SVM. However, this process lacks theoretical justification. This paper fills the gap by developing a local duality theory for such an SSVM formulation and exploring its relationship with the hinge-loss SVM (hSVM) and the ramp-loss SVM (rSVM). In particular, we prove that the derived SSVM is exactly the dual problem of the 0/1-loss SVM, and the linear representer theorem holds for their local solutions. The local solution of SSVM also provides guidelines on selecting hyperparameters of hSVM and rSVM. {Under specific conditions, we show that a sequence of global solutions of hSVM converges to a local solution of 0/1-loss SVM. Moreover, a local minimizer of 0/1-loss SVM is a local minimizer of rSVM.} This explains why a local solution induced by SSVM outperforms hSVM and rSVM in the prior empirical study. We further conduct numerical tests on real datasets and demonstrate potential advantages of SSVM by working with locally nice solutions proposed in this paper.

Accelerating RLHF Training with Reward Variance Increase

Reinforcement learning from human feedback (RLHF) is an essential technique for ensuring that large language models (LLMs) are aligned with human values and preferences during the post-training phase. As an effective RLHF approach, group relative policy optimization (GRPO) has demonstrated success in many LLM-based applications. However, efficient GRPO-based RLHF training remains a challenge. Recent studies reveal that a higher reward variance of the initial policy model leads to faster RLHF training. Inspired by this finding, we propose a practical reward adjustment model to accelerate RLHF training by provably increasing the reward variance and preserving the relative preferences and reward expectation. Our reward adjustment method inherently poses a nonconvex optimization problem, which is NP-hard to solve in general. To overcome the computational challenges, we design a novel $O(n \log n)$ algorithm to find a global solution of the nonconvex reward adjustment model by explicitly characterizing the extreme points of the feasible set. As an important application, we naturally integrate this reward adjustment model into the GRPO algorithm, leading to a more efficient GRPO with reward variance increase (GRPOVI) algorithm for RLHF training. As an interesting byproduct, we provide an indirect explanation for the empirical effectiveness of GRPO with rule-based reward for RLHF training, as demonstrated in DeepSeek-R1. Experiment results demonstrate that the GRPOVI algorithm can significantly improve the RLHF training efficiency compared to the original GRPO algorithm.

A Survey on Large Language Model-based Agents for Statistics and Data Science

In recent years, data science agents powered by Large Language Models (LLMs), known as "data agents," have shown significant potential to transform the traditional data analysis paradigm. This survey provides an overview of the evolution, capabilities, and applications of LLM-based data agents, highlighting their role in simplifying complex data tasks and lowering the entry barrier for users without related expertise. We explore current trends in the design of LLM-based frameworks, detailing essential features such as planning, reasoning, reflection, multi-agent collaboration, user interface, knowledge integration, and system design, which enable agents to address data-centric problems with minimal human intervention. Furthermore, we analyze several case studies to demonstrate the practical applications of various data agents in real-world scenarios. Finally, we identify key challenges and propose future research directions to advance the development of data agents into intelligent statistical analysis software.

LAMBDA: A Large Model Based Data Agent

We introduce ``LAMBDA," a novel open-source, code-free multi-agent data analysis system that that harnesses the power of large models. LAMBDA is designed to address data analysis challenges in complex data-driven applications through the use of innovatively designed data agents that operate iteratively and generatively using natural language. At the core of LAMBDA are two key agent roles: the programmer and the inspector, which are engineered to work together seamlessly. Specifically, the programmer generates code based on the user's instructions and domain-specific knowledge, enhanced by advanced models. Meanwhile, the inspector debugs the code when necessary. To ensure robustness and handle adverse scenarios, LAMBDA features a user interface that allows direct user intervention in the operational loop. Additionally, LAMBDA can flexibly integrate external models and algorithms through our knowledge integration mechanism, catering to the needs of customized data analysis. LAMBDA has demonstrated strong performance on various machine learning datasets. It has the potential to enhance data science practice and analysis paradigm by seamlessly integrating human and artificial intelligence, making it more accessible, effective, and efficient for individuals from diverse backgrounds. The strong performance of LAMBDA in solving data science problems is demonstrated in several case studies, which are presented at \url{https://www.polyu.edu.hk/ama/cmfai/lambda.html}.