Multi-Objective $\textit{min-max}$ Online Convex Optimization

In online convex optimization (OCO), a single loss function sequence is revealed over a time horizon of $T$, and an online algorithm has to choose its action at time $t$, before the loss function at time $t$ is revealed. The goal of the online algorithm is to incur minimal penalty (called $\textit{regret}$ compared to a static optimal action made by an optimal offline algorithm knowing all functions of the sequence in advance.