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Abstract: Opinion control under the Friedkin-Johnsen (FJ) model has traditionally focused on modifying individual users, for example by changing their opinions or susceptibility to social influence. We study a complementary problem: can collective outcomes be steered by modifying the interaction network instead? We formulate structural median control as an edge-addition problem aimed at moving the equilibrium median beyond a target threshold. We show that the problem is NP-hard even under highly restricted settings and propose both continuous optimization methods and computationally lighter opinion-aware heuristics for selecting edge additions. Experiments on synthetic and real-world networks reveal that intervention success depends jointly on network topology, the placement of favorable opinions, and user susceptibility. Structural interventions produce the largest shifts when opinion placement and network structure allow added edges to create useful influence pathways toward the target outcome. Finally, under a homogeneous reference setting, we compare structural and node-level interventions using normalized budgets and a degree-weighted cost model. We show that, although node interventions often appear stronger under normalized budgets, structural interventions become competitive and frequently more cost-effective once the higher cost of targeting high-reach users is taken into account.

Abstract: Real-world systems often serve many objectives but can deploy only a few options, whose performance must be learned from noisy feedback. Modeling each option as an arm in a multi-objective bandit, we introduce \emph{few-for-many best-arm identification}, which seeks a small set of arms minimizing the worst weighted degradation from the objective-wise optima, rather than the best arm for every objective. We consider both known objective groups and latent groups specified only by a representative budget, and propose \textsc{GFM-Elim} and \textsc{AFM-Elim} with instance-dependent sample-complexity guarantees. For Gaussian rewards, we further derive a lower bound for the latent-group setting and show that it is asymptotically attainable with high probability by an oracle-based Track-and-Stop procedure. Our results show that sharing observations across objectives and ignoring irrelevant objective-wise distinctions can substantially reduce the sampling cost, as confirmed by experiments on synthetic and real-world tasks.