Training Large Language Model (LLM) agents via Reinforcement Learning (RL) in federated settings faces fundamental challenges, including model heterogeneity across clients, prohibitive communication costs and severe data heterogeneity. We propose a semantic federated learning framework called SemFed that addresses all challenges by communicating behavioral patterns rather than model parameters. Each client extracts compact semantic policy summaries from local training trajectories, which are aggregated at the server into shared, elite and anti-patterns. These aggregated patterns are injected back into local training through different complementary channels. Since the communicated objects are structured behavioral abstractions, SemFed supports heterogeneous model architectures while reducing per-round communication to kilobytes. Experiments on ALFWorld and WebShop across multiple heterogeneous LLM backbones demonstrate that SemFed consistently surpasses strong federated baselines in task success while reducing communication overhead by orders of magnitude.