GUIDE-FBO: Guidance via Uncertainty Intervention and Distributional Exchange for Federated Bayesian Optimization

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.

Federated bilevel optimization is widely used for nested learning problems across distributed clients, such as federated hyperparameter tuning and meta-learning under privacy and communication constraints. Most existing formulations assume fixed client data distributions, which can be violated by performativity, where deployed decisions reshape client behavior and data collection, inducing client-specific, decision-dependent distribution shift. We study federated bilevel performative prediction, where both upper-level (UL) and lower-level (LL) objectives are evaluated under client-dependent, decision-dependent distributions. We formalize the federated bilevel performatively stable (FBPS) point under a decoupled-risk perspective and provide sufficient conditions for its existence and uniqueness. We then develop two federated methods to compute the FBPS solution: FBi-RRM, which converges linearly under a contraction condition, and FBi-SGD, a communication-efficient stochastic method based on federated hypergradient estimation with convergence guarantees under diminishing step sizes when sensitivities are sufficiently small. Experiments on strategic regression and meta strategic classification validate the predicted stability thresholds and demonstrate improved meta-generalization over non-performative baselines, and CNN-based classification further demonstrates the practical effectiveness of the proposed methods in nonconvex neural network settings.

Gaussian-process Bayesian optimization (GP-BO) excels at black-box optimization of costly functions, e.g., hyperparameter optimization (HPO) and multi-agent system (MAS) design. Convergence-rate guarantees exist for select methods, notably GP upper confidence bound (GP-UCB), but require a fixed kernel. Critically, the kernel encodes how input proximity affects objective value similarity. When raw coordinates poorly match this geometry - as with log-scaled hyperparameters or localized peaks - input warping can greatly improve sample efficiency, yet known GP-UCB proofs require a fixed kernel. We propose Finite-Library Input-Warped Bayesian Optimization (FLIWBO), which selects warps from a finite library of smooth input maps by any history-dependent rule. It adapts the input geometry to accelerate learning while retaining high-probability convergence guarantees under mild hypotheses, with an explicit $\sqrt(N_\varepsilon)$ library-size cost. Controlled diagnostics show that finite-library warping repairs planted geometry mismatches and identify FLIWBO failure cases. Across four repeated benchmarks - warped synthetic objectives, a confidence-fence trap, and Fashion-MNIST HPO - FLIWBO-UCB beats raw-coordinate GP-UCB under misspecified geometry, escapes traps that defeat even oracle-warp expected improvement, and recovers much of the gain from manual log scaling, while leading the tested methods that admit a matching regret guarantee. A 20-dimensional MAS design study further shows feasibility under costly noisy evaluations. Code for experiments is available: https://github.com/edvin-ketabati/bogp-paper-experiments.