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arXiv 2103.09287cs.LGcs.AIcs.CYmath.OC
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在决策时确保公平性的算法挑战

Algorithmic Challenges in Ensuring Fairness at the Time of Decision

US Naval Academy(美国海军学院);Massachusetts Institute of Technology(麻省理工学院);University of Illinois Chicago(芝加哥伊利诺伊大学)

Jad Salem, Swati Gupta, Vijay Kamble

AI总结:

本文将无嫉妒性公平约束引入随机凸优化,提出一种坐标下降结构的无嫉妒算法,在满足 PL 不等式的光滑凸函数上实现近最优遗憾,并探讨了若干开放问题。

摘要:

社会情境中的算法决策,如零售定价、贷款管理、在线平台推荐等,可以被建模为基于老虎机反馈的随机优化问题,这通常需要为了学习而对不同决策进行实验。这种实验往往会导致受这些决策影响的人们产生不公平感;例如,最近已有数起诉讼指控部署算法定价做法的公司进行价格欺诈。受围绕算法决策不断变化的法律环境所驱动,我们将已被充分研究的公平性概念——无嫉妒性——引入到随机凸优化的情境中。我们的概念要求,在当下收到决策时,各个群体不会嫉妒任何其他群体在当下以及过去所收到的决策。这产生了一个新颖的轨迹约束随机优化问题,使得现有技术无法适用。\n\n本工作的主要技术贡献在于,展示了在施加无嫉妒性时,可实现遗憾(在忽略对数因子的意义上)不存在差距的问题设置。特别地,在我们的主要结果中,我们开发了一种近似最优的无嫉妒算法,对于满足 PL 不等式的光滑凸函数,该算法实现了 $\tilde{O}(\sqrt{T})$ 的遗憾。该算法具有坐标下降结构,我们仔细利用梯度信息来确保沿每个维度的单调采样,同时以高概率避免越过约束最优解。后一方面关键地利用了光滑性和无嫉妒性约束的结构,而 PL 不等式则保证了对最优解的充分推进。我们讨论了由该分析引出的若干开放问题,这些问题可能具有独立的研究意义。

英文摘要:

Algorithmic decision-making in societal contexts, such as retail pricing, loan administration, recommendations on online platforms, etc., can be framed as stochastic optimization under bandit feedback, which typically requires experimentation with different decisions for the sake of learning. Such experimentation often results in perceptions of unfairness among people impacted by these decisions; for instance, there have been several recent lawsuits accusing companies that deploy algorithmic pricing practices of price gouging. Motivated by the changing legal landscape surrounding algorithmic decision-making, we introduce the well-studied fairness notion of envy-freeness within the context of stochastic convex optimization. Our notion requires that upon receiving decisions in the present time, groups do not envy the decisions received by any of the other groups, both in the present as well as the past. This results in a novel trajectory-constrained stochastic optimization problem that renders existing techniques inapplicable. The main technical contribution of this work is to show problem settings where there is no gap in achievable regret (up to logarithmic factors) when envy-freeness is imposed. In particular, in our main result, we develop a near-optimal envy-free algorithm that achieves $\tilde{O}(\sqrt{T})$ regret for smooth convex functions that satisfy the PL inequality. This algorithm has a coordinate-descent structure, in which we carefully leverage gradient information to ensure monotonic sampling along each dimension, while avoiding overshooting the constrained optimum with high probability. This latter aspect critically uses smoothness and the structure of the envy-freeness constraints, while the PL inequality allows for sufficient progress towards the optimal solution. We discuss several open questions that arise from this analysis, which may be of independent interest.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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