Time-Varying Multi-Objective Optimization: Tradeoff Regret Bounds

Multi-objective optimization studies the process of seeking multiple competing desiderata in some operation. Solution techniques highlight marginal tradeoffs associated with weighing one objective over others. In this paper, we consider time-varying multi-objective optimization, in which the objectives are parametrized by a continuously varying parameter and a prescribed computational budget is available at each time instant to algorithmically adjust the decision variables to accommodate for the changes. We prove regret bounds indicating the relative guarantees on performance for the competing objectives.