A Black Box Optimization-based Bidding Strategy for Data Consumers in Auction-based Federated Learning

Auction-based Federated Learning (AFL) has emerged as a robust paradigm for incentivizing Data Owners (DOs) to contribute their private resources to a global model. However, determining optimal bidding strategies for Data Consumers (DCs) remains a fundamental challenge. Existing approaches typically rely on Reinforcement Learning (RL), which suffers from severe credit assignment ambiguity and non-stationarity due to the structural mismatch between stepwise Markovian rewards and the delayed, trajectory-level utility inherent in FL training. In this paper, we depart from the stepwise MDP paradigm and reformulate AFL bidding as a Black-Box Optimization (BBO) problem. By treating the entire recruitment-to-training pipeline as a single function evaluation, we bypass the need for intractable reward decomposition. To address the prohibitive cost of policy sampling in real-world markets, we propose BBO-AFL (Budget-Efficient BBO for DC in AFL). Our core innovation is a Budget-Aware Exploration mechanism that decouples high-frequency market cost signals from low-frequency model utility feedback. BAE employs a fast-frequency cost surrogate to project risky strategy perturbations onto a safe financial manifold via a closed-form KKT solution, preventing premature budget exhaustion during the learning phase. Theoretical analysis demonstrates that BBO-AFL asymptotically recovers the standard convergence rate of zeroth-order methods while strictly maintaining financial safety throughout the optimization trajectory. Extensive experiments on benchmark datasets demonstrate that BBO-AFL significantly outperforms state-of-the-art RL baselines. Specifically, it achieves a 2.1% improvement in model accuracy while exhibiting superior economic sample efficiency, reducing the number of training cycles required to reach target accuracy by 60%.