Large language model (LLM) agents increasingly operate in private environments and accumulate valuable experience from task execution, tool use, feedback, and local knowledge. Yet such experience is distributed across organizations and cannot be directly shared because of privacy and proprietary constraints. Conventional federated learning is insufficient for this setting, as agent capabilities extend beyond model parameters to memory, tools, rewards, skills, and structured knowledge. In this paper, we formulate \textbf{Federated Agent Optimization (FAO)}, which studies how distributed agents can collaboratively improve through controlled information exchange while keeping raw data, complete trajectories, and private knowledge local. We define FAO as a multi-objective problem balancing agent utility, privacy leakage, and communication cost, and organize its optimization space across policy, memory, tool use, reward, and structured knowledge and skills. We further characterize how private experience can be abstracted, protected, aggregated, and adapted into transferable capabilities, providing a unified view of how agents can benefit from one another without direct experience sharing. Finally, we identify the key challenges of FAO and outline several promising directions for future research toward trustworthy federated agent systems.

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