Robust Contextual Pricing

Anupam Gupta, Guru Guruganesh, Renato Paes Leme, Jon Schneider

Keywords: pricing, contextual search, corruptions, online learning

TL;DR: We provide improved upper and lower bounds for contextual pricing with adversarial corruptions.

Abstract:

We provide an algorithm with regret $O(C d \log \log T)$ for contextual pricing with $C$ corrupted rounds, improving over the previous bound of $O(d^3 C \log^2(T))$ of Krishnamurthy et al. The result is based on a reduction that calls the uncorrupted algorithm as a black-box, unlike the previous approach that modifies the inner workings of the uncorrupted algorithm. As a result, it leads to a conceptually simpler algorithm.

Finally, we provide a lower bound ruling out a $O(C + d\log \log T)$ algorithm. This shows that robustifying contextual pricing is harder than robustifying contextual search with $\epsilon$-ball losses, for which it is possible to design algorithms where corruptions add only an extra additive term $C$ to the regret.

Primary Area: Theory (e.g., control theory, learning theory, algorithmic game theory)

Submission Number: 18726