  We consider a fair representation learning perspective, where optimal
predictors, on top of the data representation, are ensured to be invariant with
respect to different sub-groups. Specifically, we formulate this intuition as a
bi-level optimization, where the representation is learned in the outer-loop,
and invariant optimal group predictors are updated in the inner-loop. Moreover,
the proposed bi-level objective is demonstrated to fulfill the sufficiency
rule, which is desirable in various practical scenarios but was not commonly
studied in the fair learning. Besides, to avoid the high computational and
memory cost of differentiating in the inner-loop of bi-level objective, we
propose an implicit path alignment algorithm, which only relies on the solution
of inner optimization and the implicit differentiation rather than the exact
optimization path. We further analyze the error gap of the implicit approach
and empirically validate the proposed method in both classification and
regression settings. Experimental results show the consistently better
trade-off in prediction performance and fairness measurement.
