Fed-MOZOO: Federated Multi-Objective Online Zeroth-Order Optimization with Intermittent Communication

Federated online learning provides a promising framework for sequential decision-making over distributed data, but its effectiveness is challenged by communication constraints, heterogeneous local data, and dynamically changing objectives. When multiple objectives must be optimized simultaneously, existing federated online methods mainly rely on first-order gradient information, which may be unavailable in black-box or gradient-inaccessible environments. This motivates the study of federated multi-objective online optimization with limited function-value feedback and intermittent communication. To this end, we propose \FedMOZOO, a two-point zeroth-order method that performs local preference-based scalarization and projected updates, followed by periodic model aggregation. For convex $G$-Lipschitz losses over a radius-$B$ domain, we establish a dimension- and communication-dependent regret guarantee for the virtual global model: $\mathcal{O}(BG(\sqrt{d/T}+d^{1/4}/\sqrt{R}+1/T))$, where $T$ is the online horizon and $R$ is the number of communication rounds. The bound characterizes the effects of zeroth-order feedback and intermittent communication, and recovers the standard $\mathcal{O}(BG\sqrt{d/T})$ scaling when communication occurs at every round. Experiments on synthetic and convex multi-objective learning tasks evaluate regret, communication–accuracy trade-offs, preference tracking, Pareto-front quality, and the scaling behavior with dimension and communication frequency.