Abstract
This paper studies algorithmic decision-making in the presence of strategic individual behaviors, where an ML model is used to make decisions about human agents and the latter can adapt their behavior strategically to improve their future data. Existing results on strategic learning have largely focused on the linear setting where agents with linear labeling functions best respond to a (noisy) linear decision policy. Instead, this work focuses on general non-linear settings where agents respond to the decision policy with only "local information" of the policy. Moreover, we simultaneously consider the objectives of maximizing decision-maker welfare (model prediction accuracy), social welfare (agent improvement caused by strategic behaviors), and agent welfare (the extent that ML underestimates the agents). We first generalize the agent best response model in previous works to the non-linear setting, then reveal the compatibility of welfare objectives. We show the three welfare can attain the optimum simultaneously only under restrictive conditions which are challenging to achieve in non-linear settings. The theoretical results imply that existing works solely maximizing the welfare of a subset of parties inevitably diminish the welfare of the others. We thus claim the necessity of balancing the welfare of each party in non-linear settings and propose an irreducible optimization algorithm suitable for general strategic learning. Experiments on synthetic and real data validate the proposed algorithm.
Abstract (translated)
本文研究了在战略个体行为存在的情况下，使用机器学习模型进行人代理决策的问题，其中后一个可以战略性地调整其行为以提高其未来的数据。现有结果大部分集中在线性设置下，具有线性标记函数的代理商对（噪声）线性决策策略的最好反应。相反，本文关注的是通用非线性设置，在这种设置下，代理商仅对策略的局部信息做出反应。此外，我们还同时考虑了最大化决策者福利（模型预测准确性）、社会福利（由战略行为导致的代理商改进）和代理商福利（ML低估代理商的程度）。我们首先将之前工作的代理商最佳响应模型在非线性设置中进行一般化，然后揭示了福利目标的可行性。我们证明了只有在不确定条件下，三个福利才能达到最优解，这在非线性设置中是很难实现的。理论结果表明，仅最大化部分参与方福利的工作会不可避免地削弱其他参与方的福利。因此，我们声称在非线性设置中平衡每个参与方的福利是必要的，并提出了一个适合一般战略学习的不还原优化算法。对于合成和真实数据的实验验证了所提出的算法。
URL
https://arxiv.org/abs/2405.01810
