  When faced with multiple minima of an "inner-level" convex optimization
problem, the convex bilevel optimization problem selects an optimal solution
which also minimizes an auxiliary "outer-level" convex objective of interest.
Bilevel optimization requires a different approach compared to single-level
optimization problems since the set of minimizers for the inner-level objective
is not given explicitly. In this paper, we propose a new projection-free method
for convex bilevel optimization which require only a linear optimization oracle
over the base domain. We establish $O(t^{-1/2})$ convergence rate guarantees
for our method in terms of both inner- and outer-level objectives, and
demonstrate how additional assumptions such as quadratic growth and strong
convexity result in accelerated rates of up to $O(t^{-1})$ and $O(t^{-2/3})$
for inner- and outer-levels respectively. Lastly, we conduct a numerical study
to demonstrate the performance of our method.
