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Prior-Free Competitive Ratios for Improving Bandits: Scale, Curvature and Horizon Are Free, but Not Jointly Under Noise
In the improving multi-armed bandits problem, each of $k$ arms has an unknown nondecreasing, discretely concave reward curve $f_i$, and pulling arm $i$ for the $t$-th time yields $f_i(t)$. For sufficiently long horizons, Blum and Ravichandran (ALT 2025) proved that randomized algorithms achieve an $
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