Proportionality is an attractive fairness concept that has been applied to a range of problems including the facility location problem, a classic problem in social choice.

We establish new connections between LwEQ-TD and LfS-TD by studying LwEQ-TD for different learner models based on the richness of their query functions. We show that LwEQ-TD isthesameaswc-TD[18],RTD[22,24],andNCTD[27]forahypothesis class when restricting query functions to specific families.

The objective(1) can be extended to a weighted average, but we do not write out the weights and consider them as part ofℓn(x,ξ)andFn(x).

The first design helps the model focus more on the global context of the image as each patch could attend to the whole image areas. It reduces the local texture bias ofCNN.

Inaddition, there is a fixed distribution over types which sets the proportion of each type in the population of arms. The decision maker is oblivious to the type of any arm and to the aforementioned distribution over types, but perfectly knows the total number of types occurring in the population of arms.