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Abstract Stochastic bilevel optimization finds widespread applications in machine learning, including meta-learning, hyperparameter optimization, and neural architecture search. To extend stochastic bilevel optimization to distributed data, several decentralized stochastic bilevel optimization algorithms have been developed. However, existing methods often suffer from slow convergence rates and high communication costs in heterogeneous settings, limiting their applicability to real-world tasks. To address these issues, we propose two novel decentralized stochastic bilevel gradient descent algorithms based on simultaneous and alternating update strategies. Our algorithms can achieve faster convergence rates and lower communication costs than existing methods. Importantly, our convergence analyses do not rely on strong assumptions regarding heterogeneity. More importantly, our theoretical analyses clearly disclose how the computation and communication regarding the Hessian-inverse-vector product under the heterogeneous setting affects the convergence rate. To the best of our knowledge, this is the first time such favorable theoretical results have been achieved with mild assumptions in the heterogeneous setting. Furthermore, we demonstrate how to establish the convergence rate for the alternating update strategy when combined with the variance-reduced gradient. Finally, experimental results confirm the efficacy of our algorithms. 

Group Fairness-aware Continual Learning (GFCL) aims to eradicate discriminatory predictions against certain demographic groups in a sequence of diverse learning tasks.This paper explores an even more challenging GFCL problem – how to sustain a fair classifier across a sequence of tasks with covariate shifts and unlabeled data. We propose the MacFRL solution, with its key idea to optimizethe sequence of learning tasks. We hypothesize that high-confident learning can be enabled in the optimized task sequence, where the classifier learns from a set of prioritized tasks to glean knowledge, thereby becoming more capable to handle the tasks with substantial distribution shifts that were originally deferred. Theoretical and empirical studies substantiate that MacFRL excels among its GFCL competitors in terms of prediction accuracy and group fair-ness metrics.