We consider cocycles of isometries on spaces of non-positive curvature
. We show that the supremum of the drift over all invariant ergodic probability measures equals the infimum of the displacements of continuous sections under the cocycle dynamics. In particular, if a cocycle has uniform sublinear drift, then there are almost invariant sections, that is, sections that move arbitrarily little under the cocycle dynamics. If, in addition,
is a symmetric space, then we show that almost invariant sections can be made invariant by perturbing the cocycle.