Exploring Effective Strategies for Building a Customised GPT Agent for Coding Classroom Dialogues

This study investigates effective strategies for developing a customised GPT agent to code classroom dialogue. While classroom dialogue is widely recognised as a crucial element of education, its analysis remains challenging due to the need for a nuanced understanding of dialogic functions and the labour-intensive nature of manual transcript coding. Recent advancements in large language models offer promising avenues for automating this process. However, existing studies predominantly focus on training large-scale models or evaluating pre-trained models with fixed codebooks, which are often not applicable or replicable for dialogue researchers working with small datasets or customised coding schemes. Using GPT-4's MyGPT agent as a case, this study evaluates its baseline performance in coding classroom dialogue with a human codebook and examines how performance varies with different example inputs through a variable control method. Through a design-based research approach, it identifies a set of practical strategies, based on MyGPT's unique features, for configuring effective agents with limited data. The findings suggest that, despite some limitations, a MyGPT agent developed with these strategies can serve as a useful coding assistant by generating coding suggestions.

Anderson Acceleration in Nonsmooth Problems: Local Convergence via Active Manifold Identification

Anderson acceleration is an effective technique for enhancing the efficiency of fixed-point iterations; however, analyzing its convergence in nonsmooth settings presents significant challenges. In this paper, we investigate a class of nonsmooth optimization algorithms characterized by the active manifold identification property. This class includes a diverse array of methods such as the proximal point method, proximal gradient method, proximal linear method, proximal coordinate descent method, Douglas-Rachford splitting (or the alternating direction method of multipliers), and the iteratively reweighted $\ell_1$ method, among others. Under the assumption that the optimization problem possesses an active manifold at a stationary point, we establish a local R-linear convergence rate for the Anderson-accelerated algorithm. Our extensive numerical experiments further highlight the robust performance of the proposed Anderson-accelerated methods.

Avoiding strict saddle points of nonconvex regularized problems

We introduce a strict saddle property for $\ell_p$ regularized functions, and propose an iterative reweighted $\ell_1$ algorithm to solve the $\ell_p$ regularized problems. The algorithm is guaranteed to converge only to local minimizers when randomly initialized. The strict saddle property is shown generic on these sparse optimization problems. Those analyses as well as the proposed algorithm can be easily extended to general nonconvex regularized problems.