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The fairness-aware online learning framework has emerged as a potent tool within the context of continuous lifelong learning. In this scenario, the learner’s objective is to progressively acquire new tasks as they arrive over time, while also guaranteeing statistical parity among various protected sub-populations, such as race and gender when it comes to the newly introduced tasks. A significant limitation of current approaches lies in their heavy reliance on the i.i.d (independent and identically distributed) assumption concerning data, leading to a static regret analysis of the framework. Nevertheless, it’s crucial to note that achieving low static regret does not necessarily translate to strong performance in dynamic environments characterized by tasks sampled from diverse distributions. In this article, to tackle the fairness-aware online learning challenge in evolving settings, we introduce a unique regret measure, FairSAR, by incorporating long-term fairness constraints into a strongly adapted loss regret framework. Moreover, to determine an optimal model parameter at each time step, we introduce an innovative adaptive fairness-aware online meta-learning algorithm, referred to as FairSAOML. This algorithm possesses the ability to adjust to dynamic environments by effectively managing bias control and model accuracy. The problem is framed as a bi-level convex-concave optimization, considering both the model’s primal and dual parameters, which pertain to its accuracy and fairness attributes, respectively. Theoretical analysis yields sub-linear upper bounds for both loss regret and the cumulative violation of fairness constraints. Our experimental evaluation of various real-world datasets in dynamic environments demonstrates that our proposed FairSAOML algorithm consistently outperforms alternative approaches rooted in the most advanced prior online learning methods. 

Abstract Transition metal oxides are promising candidates for the next generation of spintronic devices due to their fascinating properties that can be effectively engineered by strain, defects, and microstructure. An excellent example can be found in ferroelastic LaCoO 3 with paramagnetism in bulk. In contrast, unexpected ferromagnetism is observed in tensile-strained LaCoO 3 films, however, its origin remains controversial. Here we simultaneously reveal the formation of ordered oxygen vacancies and previously unreported long-range suppression of CoO 6 octahedral rotations throughout LaCoO 3 films. Supported by density functional theory calculations, we find that the strong modification of Co 3 d -O 2 p hybridization associated with the increase of both Co-O-Co bond angle and Co-O bond length weakens the crystal-field splitting and facilitates an ordered high-spin state of Co ions, inducing an emergent ferromagnetic-insulating state. Our work provides unique insights into underlying mechanisms driving the ferromagnetic-insulating state in tensile-strained ferroelastic LaCoO 3 films while suggesting potential applications toward low-power spintronic devices.