We study revenue optimization learning algorithms for repeated posted-price auctions where a seller interacts with a single strategic buyer that holds a fixed private valuation for a good and seeks to maximize his cumulative discounted surplus. We propose a novel algorithm that never decreases offered prices and has a tight strategic regret bound of Θ(log log T ). This result closes the open research question on the existence of a no-regret horizon-independent weakly consistent pricing. We also

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... show that the property of nondecreasing prices is nearly necessary for a weakly consistent algorithm to be a no-regret one.