Smoothed Online Optimization with Unreliable Predictions

We consider online optimization with switching costs in a normed vector space (X, ||·||) wherein, at each time t, a decision maker observes a non-convex hitting cost function ƒ : t X →[0, ∞] and must decide upon some xt∈X→, paying ƒt (xt) + || xt-xt-1||, where ||·|| characterizes the switching cost. Throughout, we assume that ƒt is globally α-polyhedral, i.e., ƒt has a unique minimizer υt ∈X, and, for all x ∈ X, ƒ t) (x) ≥ ƒt + α · ||x - υ t. Moreover, we assume that the decision maker has access to an untrusted prediction xt of the optimal decision during each round, such as the decision suggested by a black-box AI tool.