提出两种公平性优化方法，分别应对有无敏感属性场景。

Ensuring fairness has emerged as one of the primary concerns in AI and its related algorithms. Over time, the field of machine learning fairness has evolved to address these issues. This paper provides an extensive overview of this field and introduces two formal frameworks to tackle open questions in machine learning fairness. In one framework, operator-valued optimisation and min-max objectives are employed to address unfairness in time-series problems. This approach showcases state-of-the-art performance on the notorious COMPAS benchmark dataset, demonstrating its effectiveness in real-world scenarios. In the second framework, the challenge of lacking sensitive attributes, such as gender and race, in commonly used datasets is addressed. This issue is particularly pressing because existing algorithms in this field predominantly rely on the availability or estimations of such attributes to assess and mitigate unfairness. Here, a framework for a group-blind bias-repair is introduced, aiming to mitigate bias without relying on sensitive attributes. The efficacy of this approach is showcased through analyses conducted on the Adult Census Income dataset. Additionally, detailed algorithmic analyses for both frameworks are provided, accompanied by convergence guarantees, ensuring the robustness and reliability of the proposed methodologies.