We study resource allocation problems in which a central planner allocates resources among strategic agents with private cost functions in order to minimize a social cost, defined as an aggregate of the agents' costs. This setting poses two main challenges: (i) the agents' cost functions may be unknown to them or difficult to specify explicitly, and (ii) agents may misreport their costs strategically. To address these challenges, we propose an algorithm that combines preference-based learning with Vickrey-Clarke-Groves (VCG) payments to incentivize truthful reporting. Our algorithm selects informative preference queries via D-optimal design, estimates cost parameters through maximum likelihood, and computes VCG allocations and payments based on these estimates. In a one-shot setting, we prove that the mechanism is approximately truthful, individually rational, and efficient up to an error of $\tilde{\mathcal O}(K^{-1/2})$ for $K$ preference queries per agent. In an online setting, these guarantees hold asymptotically with sublinear regret at a rate of $\tilde{\mathcal O}(T^{2/3})$ after $T$ rounds. Finally, we validate our approach through a numerical case study on demand response in local electricity markets.

翻译：我们研究资源分配问题，其中中央规划者根据具有私有成本函数的策略性代理分配资源，以最小化社会成本（定义为代理成本的总和）。该设定面临两个主要挑战：（i）代理的成本函数可能未知或难以显式指定；（ii）代理可能策略性地虚报成本。为解决这些挑战，我们提出一种算法，将偏好学习与Vickrey-Clarke-Groves（VCG）支付相结合以激励真实报告。该算法通过D-最优设计选择信息性偏好查询，通过最大似然估计成本参数，并基于这些估计计算VCG分配与支付。在单次设定中，我们证明该机制具有近似真实性、个体理性及有效性，误差为$\tilde{\mathcal O}(K^{-1/2})$（其中$K$为每个代理的偏好查询次数）。在在线设定中，这些保证渐近成立，经过$T$轮后具有次线性遗憾率$\tilde{\mathcal O}(T^{2/3})$。最后，我们通过本地电力市场中需求响应的数值案例研究验证了所提方法。