Time-Varying Multi-Objective Optimization: Tradeoff Regret Bounds

TL;DR

This paper investigates time-varying multi-objective optimization, providing theoretical regret bounds that quantify the tradeoffs and performance guarantees when adapting solutions over time under computational constraints.

Contribution

It introduces regret bounds for time-varying multi-objective optimization, offering a theoretical framework for understanding tradeoffs in dynamic settings.

Findings

Regret bounds for performance guarantees

Quantitative analysis of tradeoffs over time

Framework applicable under computational budgets

Abstract

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.