Compound AI systems integrating multiple components, such as Large Language Models, specialized tools, and traditional machine learning models, are increasingly deployed to solve complex real-world tasks. However, optimizing compound systems remains challenging due to their non-differentiable structures and diverse configuration types across components, including prompts, hyperparameters, and model parameters. To address this challenge, we propose Optimas, a unified framework for effective optimization of compound systems. The core idea of Optimas is to maintain one Local Reward Function (LRF) per component, each satisfying a local-global alignment property, i.e., each component's local reward correlates with the global system performance. In each iteration, Optimas efficiently adapts the LRFs to maintain this property while simultaneously maximizing each component's local reward. This approach enables independent updates of heterogeneous configurations using the designated optimization method, while ensuring that local improvements consistently lead to performance gains. We present extensive evaluations across five real-world compound systems to demonstrate that Optimas outperforms strong baselines by an average improvement of 11.92%, offering a general and effective approach for improving compound systems. Our website is at https://optimas.stanford.edu.

Large Language Model (LLM) based multi-agent systems (MAS) show remarkable potential in collaborative problem-solving, yet they still face critical challenges: low communication efficiency, poor scalability, and a lack of effective parameter-updating optimization methods. We present Optima, a novel framework that addresses these issues by significantly enhancing both communication efficiency and task effectiveness in LLM-based MAS through LLM training. Optima employs an iterative generate, rank, select, and train paradigm with a reward function balancing task performance, token efficiency, and communication readability. We explore various RL algorithms, including Supervised Fine-Tuning, Direct Preference Optimization, and their hybrid approaches, providing insights into their effectiveness-efficiency trade-offs. We integrate Monte Carlo Tree Search-inspired techniques for DPO data generation, treating conversation turns as tree nodes to explore diverse interaction paths. Evaluated on common multi-agent tasks, including information-asymmetric question answering and complex reasoning, Optima shows consistent and substantial improvements over single-agent baselines and vanilla MAS based on Llama 3 8B, achieving up to 2.8x performance gain with less than 10\% tokens on tasks requiring heavy information exchange. Moreover, Optima's efficiency gains open new possibilities for leveraging inference-compute more effectively, leading to improved inference-time scaling laws. By addressing fundamental challenges in LLM-based MAS, Optima shows the potential towards scalable, efficient, and effective MAS (https://chenweize1998.github.io/optima-project-page).