Imagine a world where AI systems design and refine themselves, learning and adapting without constant human intervention. This isn't science fiction, but the emerging reality of LLM-based optimization of compound AI systems. These systems, combining components like language models, retrievers, and code interpreters, are traditionally painstakingly optimized by hand. However, a new wave of research is exploring how to use LLMs themselves as optimizers, offering a powerful alternative. Instead of manually tweaking parameters, developers can now prompt an LLM to analyze the system's performance and generate improved instructions, tools, or even entire reasoning structures. This approach is particularly efficient because LLMs can handle complex, heterogeneous parameters without needing computationally expensive gradient calculations. One way LLMs achieve this is through a process analogous to program analysis. They can either analyze the system's design statically, without running it, or dynamically, by observing its runtime behavior and learning from its successes and failures. This dynamic approach allows the LLM to provide targeted feedback at different stages, much like a human supervisor guiding a complex process. Credit assignment, the challenge of identifying each component's contribution to the overall outcome, is tackled through techniques like backpropagation and trace propagation. These methods allow the LLM to understand which parts of the system need adjustment based on the observed performance. This ability is being applied to diverse areas like enhancing question-answering systems, solving complex math problems, and even improving sequential decision-making in interactive environments. The implications are far-reaching. LLM-based optimization not only automates the tedious process of system tuning but also opens doors to more controllable and interpretable AI. By breaking down complex tasks into smaller, manageable components, these systems offer greater transparency and make it easier to identify and mitigate potential safety concerns. While the field is still in its early stages, LLM-based optimization represents a significant leap towards more autonomous, adaptable, and ultimately more powerful AI systems.