Practice — Contextual Bandits for Personalization (5 questions)

Your team currently uses a plain (context-free) multi-armed bandit with 4 arms — send now, in 2h, in 6h, tomorrow morning — for notification send-time selection. A analysis shows the best arm differs substantially between "night owl" users (peak engagement 11pm–1am) and "early bird" users (peak engagement 6–8am), and these two segments are roughly equal in size.

1. Explain concretely what a plain bandit converges to in this situation, and quantify (qualitatively) how much value is left on the table.
2. Describe how you would restructure this as a contextual bandit, including a specific context feature vector.
3. A colleague argues "we could just run two separate plain bandits, one for night owls and one for early birds, and get the same benefit without learning a contextual model." Evaluate this proposal, including what breaks as you add more segments.