Online Long-run Constrained Optimization

In this paper, a novel Follow-the-Perturbed-Leader type algorithm is proposed and analyzed for solving general long-term constrained optimization problems in online manner, where the objective and constraints are not necessarily convex. In each period, random linear perturbation and strongly concave perturbation are incorporated in primal and dual directions, respectively, to the offline oracle, and a global minimax point is searched as solution. Based on two particular definitions of expected static cumulative regret, we derive the first sublinear $O(T^{8/9})$ regret complexity for this class of problems. The proposed algorithm is applied to tackle a long-term (risk) constrained river pollutant source identification problem, demonstrating the validity of the theoretical results and exhibiting superior performance compared to existing method.