  Path integral contour deformations have been shown to mitigate sign and
signal-to-noise problems associated with phase fluctuations in lattice field
theories. We define a family of contour deformations applicable to $SU(N)$
lattice gauge theory that can reduce sign and signal-to-noise problems
associated with complex actions and complex observables. For observables, these
contours can be used to define deformed observables with identical expectation
value but different variance. As a proof-of-principle, we apply machine
learning techniques to optimize the deformed observables associated with Wilson
loops in two dimensional $SU(2)$ and $SU(3)$ gauge theory. We study loops
consisting of up to 64 plaquettes and achieve variance reduction of up to 4
orders of magnitude.
