Optimal Contextual Pricing and Extensions
Allen Liu, Renato Paes Leme, Jon Schneider

TL;DR
This paper introduces efficient algorithms for contextual pricing and search problems with near-optimal regret bounds, utilizing novel geometric techniques and extending to noisy feedback scenarios.
Contribution
It presents a polynomial-time algorithm for contextual pricing with regret close to the lower bound and extends to generalized search and noisy feedback models.
Findings
Achieves $O(d \,\log\log T + d \log d)$ regret for pricing.
Provides a nearly optimal $O(d \log d)$ regret algorithm under symmetric loss.
Extends results to generalized functions and noisy feedback settings.
Abstract
In the contextual pricing problem a seller repeatedly obtains products described by an adversarially chosen feature vector in and only observes the purchasing decisions of a buyer with a fixed but unknown linear valuation over the products. The regret measures the difference between the revenue the seller could have obtained knowing the buyer valuation and what can be obtained by the learning algorithm. We give a poly-time algorithm for contextual pricing with regret which matches the lower bound up to the additive factor. If we replace pricing loss by the symmetric loss, we obtain an algorithm with nearly optimal regret of matching the lower bound up to . These algorithms are based on a novel technique of bounding the value of the Steiner polynomial of a convex region at…
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Taxonomy
TopicsAdvanced Bandit Algorithms Research · Machine Learning and Algorithms · Optimization and Search Problems
