Distributionally Robust Black Box Optimization-based Bidding Strategy in Auction-based Federated Learning

Auction-based Federated Learning (AFL) provides a market-based mechanism to incentivize decentralized data owners (DOs) to join FL model training initiated by data consumers (DCs). However, optimizing the DC's bidding strategy remains fundamentally challenging. Existing methods predominantly rely on Reinforcement Learning (RL), which suffers from severe instability caused by the mismatch between stepwise Markovian rewards and the trajectory-level, non-decomposable feedback inherent in AFL. To address this mismatch, we transition from the stepwise RL formulation to a distributionally robust black-box optimization framework. By treating the entire recruitment-to-training process as a single high-fidelity function evaluation, this transition eliminates the need for explicit reward decomposition. We propose DR-AFL , which accounts for market non-stationarity and data distribution shifts by optimizing policies against worst-case environments within a Wasserstein ambiguity set. Our approach further incorporates an adversarial reweighting scheme to enhance robustness, alongside a dynamic safety projection that leverages real-time cost feedback to enforce budget-aware exploration. We provide theoretical analysis showing that DR-AFL induces a smooth surrogate over the discontinuous auction landscape and guarantees a robust performance lower bound under distributional shifts. Extensive experiments on 6 widely adopted datasets show that DR-AFL consistently outperforms state-of-the-art RL-based baselines, achieving a 2.43% improvement in model accuracy while reducing the number of training cycles required to reach target accuracy by 62.3%.