  We provide a setting and a general approach to fair online learning with
stochastic sensitive and non-sensitive contexts. The setting is a repeated game
between the Player and Nature, where at each stage both pick actions based on
the contexts. Inspired by the notion of unawareness, we assume that the Player
can only access the non-sensitive context before making a decision, while we
discuss both cases of Nature accessing the sensitive contexts and Nature
unaware of the sensitive contexts. Adapting Blackwell's approachability theory
to handle the case of an unknown contexts' distribution, we provide a general
necessary and sufficient condition for learning objectives to be compatible
with some fairness constraints. This condition is instantiated on (group-wise)
no-regret and (group-wise) calibration objectives, and on demographic parity as
an additional constraint. When the objective is not compatible with the
constraint, the provided framework permits to characterise the optimal
trade-off between the two.
