Aniruddhan Ganesaraman, VIdyadhar Kulkarni
Imagine a building with hundreds of identical light bulbs. You replace any bulb the moment it dies, but you also swap out every bulb on a fixed schedule, and the question is how long to wait between those mass swaps. Wait too long and you pay for constant one-off replacements; swap too often and you bin working bulbs. The twist is that you don't know the bulbs' lifespan and only learn it by watching, including many still working when replaced.
The authors cast this as a bandit problem, where each candidate interval is a lever you can pull and learn from. Their confidence-bound algorithms home in on the cheapest interval at a rate matching the known theoretical best. A neat wrinkle: testing a short interval also reveals something about longer ones, letting a smarter variant avoid wasting trials on bad choices.
This is drawn from the abstract, so see the paper for the proofs and experiments.
We develop data-driven algorithms for maintaining $N$ independent identical machines under a \textit{block replacement policy}, in which each machine is replaced upon failure and all machines are jointly replaced at regular intervals of length $k$. The goal is to learn the cost-minimizing interval $k^*$ from operational data when the lifetime distribution is unknown. At each decision epoch, the operator selects $k \in \{1, 2, \ldots, K\}$, observes the resulting failure…
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