Prior-Free Competitive Ratios for Improving Bandits: Scale, Curvature and Horizon Are Free, but Not Jointly Under Noise
No prior is needed at all: a random-marginal probing algorithm reading neither the scale $m$, nor the concavity-envelope exponent $\beta$ of Blum, Garicano, Ravichandran and Sharma, nor the horizon $T, achieves the optimal $\Theta(k^{\beta/(1+\beta)}+k/T)$ simultaneously for every $\beta$ and every horizon.
Xuan-Jun Li
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