Revenue maximization learning curves converge arbitrarily slowly without restrictions, at rate roughly 1/sqrt(n) when optimal revenue uses a finite price, and almost exponentially for discrete valuation supports.
Zhiyi Huang, Yishay Mansour, and Tim Roughgarden
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On the Learning Curves of Revenue Maximization
Revenue maximization learning curves converge arbitrarily slowly without restrictions, at rate roughly 1/sqrt(n) when optimal revenue uses a finite price, and almost exponentially for discrete valuation supports.