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.

翻译：本文提出并分析了一种新颖的“跟随扰动领导者”型算法，用于在线求解通用长期约束优化问题，其中目标函数和约束条件可任意生成且不必然为凸函数。在每个周期中，算法分别沿原始方向和对偶方向向离线预言机注入随机线性扰动与强凹扰动（strongly concave perturbation），并搜索全局极小极大点作为解。基于所提出的期望静态累积遗憾，我们针对此类问题推导出首个次线性的$O(T^{8/9})$遗憾复杂度。将该算法应用于解决长期（极值）约束的河流污染源识别问题，验证了理论结果，并展现出相较现有方法的优越性能。