Jingyi Zhu

Zhenyu Ma, Yuyang Song, Chunyi Yang et al.

LLM-based autonomous agents perform well on general reasoning tasks but still struggle to reliably use task structure, key constraints, and prior experience in complex real-world settings. We propose a case-based learning framework that converts experience from past tasks into reusable knowledge assets, allowing agents to transfer prior case experience to new tasks and perform more structured analysis. Unlike methods based mainly on pretrained knowledge or static prompts, our framework emphasizes extracting and reusing task-relevant knowledge, analytical prompts, and operational skills from real cases. We evaluate the method on a unified benchmark of six complex task categories and compare it with Zero-Shot, Few-Shot, Checklist Prompt, and Rule Memory baselines. Results show that our method achieves consistently strong performance across all tasks and matches or outperforms the best baseline in every case, with especially clear gains on more complex tasks. Further analysis shows that the advantage of case-based learning increases with task complexity, and that practical knowledge acquired by one agent can be reused by others. These findings suggest that case-based learning offers a promising path for building professional agents for real-world work.

Jingyi Zhu, Long Wang, James C. Spall

Stochastic approximation (SA) algorithms have been widely applied in minimization problems when the loss functions and/or the gradient information are only accessible through noisy evaluations. Stochastic gradient (SG) descent---a first-order algorithm and a workhorse of much machine learning---is perhaps the most famous form of SA. Among all SA algorithms, the second-order simultaneous perturbation stochastic approximation (2SPSA) and the second-order stochastic gradient (2SG) are particularly efficient in handling high-dimensional problems, covering both gradient-free and gradient-based scenarios. However, due to the necessary matrix operations, the per-iteration floating-point-operations (FLOPs) cost of the standard 2SPSA/2SG is $O(p^3)$, where $p$ is the dimension of the underlying parameter. Note that the $O(p^3)$ FLOPs cost is distinct from the classical SPSA-based per-iteration $O(1)$ cost in terms of the number of noisy function evaluations. In this work, we propose a technique to efficiently implement the 2SPSA/2SG algorithms via the symmetric indefinite matrix factorization and show that the FLOPs cost is reduced from $O(p^3)$ to $O(p^2)$. The formal almost sure convergence and rate of convergence for the newly proposed approach are directly inherited from the standard 2SPSA/2SG. The improvement in efficiency and numerical stability is demonstrated in two numerical studies.