  We consider a generic min-max multi-objective bilevel optimization problem
with applications in robust machine learning such as representation learning
and hyperparameter optimization. We design MORBiT, a novel single-loop gradient
descent-ascent bilevel optimization algorithm, to solve the generic problem and
present a novel analysis showing that MORBiT converges to the first-order
stationary point at a rate of $\widetilde{\mathcal{O}}(n^{1/2} K^{-2/5})$ for a
class of weakly convex problems with $n$ objectives upon $K$ iterations of the
algorithm. Our analysis utilizes novel results to handle the non-smooth min-max
multi-objective setup and to obtain a sublinear dependence in the number of
objectives $n$. Experimental results on robust representation learning and
robust hyperparameter optimization showcase (i) the advantages of considering
the min-max multi-objective setup, and (ii) convergence properties of the
proposed MORBiT. Our code is at https://github.com/minimario/MORBiT.
