🤖 AI Summary
This paper studies online non-convex optimization under adversarial environments, where both the objective function and long-term non-convex constraints are time-varying and coupled. To address this challenge, we propose a novel Follow-the-Perturbed-Leader (FPL) algorithm incorporating stochastic linear perturbations on primal variables and strongly concave perturbations on dual variables; each round invokes an offline oracle to compute a global minimax point. We establish, for the first time, an expected static regret analysis framework for such non-convex, constrained online settings, achieving an optimal $O(T^{8/9})$ sublinear cumulative regret bound—breaking both the conventional convexity assumption and short-term constraint restrictions. Empirical evaluation on river pollution source identification—featuring extreme-value constraints—demonstrates that our method significantly improves long-term constraint satisfaction and decision quality over state-of-the-art baselines, simultaneously attaining low regret and strong feasibility.
📝 Abstract
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 arbitrarily generated and 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 the solution. Based on a proposed 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 (extreme value) constrained river pollutant source identification problem, validate the theoretical results and exhibit superior performance compared to existing methods.
