Its central concept is the fractal dimension that measures the distributive irregularity of a spatial point set.

We study the linear contextual bandit problem where an agent has to select one candidate from a pool and each candidate belongs to a sensitive group. In this setting,candidates' rewardsmaynotbedirectly comparable between groups,for example when the agent is an employer hiring candidates from different ethnic groups and some groups have a lower reward due to discriminatory bias and/or socialinjustice.

We consider the framework of non-stationary stochastic optimization [Besbes et al., 2015] with squared error losses and noisy gradient feedback where the dynamic regret ofanonline learner against atime varying comparator sequence isstudied.