Characterizing Truthful Multi-Armed Bandit Mechanisms

TL;DR

This paper studies truthful mechanisms in multi-armed bandit settings for online advertising, revealing structural constraints and higher regret compared to non-strategic algorithms, and proposes mechanisms that approach theoretical regret bounds.

Contribution

It characterizes the structural properties of truthful bandit mechanisms and provides a near-optimal mechanism with regret close to the lower bound.

Findings

Truthful mechanisms must separate exploration from exploitation.

Such mechanisms incur higher regret than non-strategic algorithms.

A mechanism is proposed that nearly matches the regret lower bound.

Abstract

We consider a multi-round auction setting motivated by pay-per-click auctions for Internet advertising. In each round the auctioneer selects an advertiser and shows her ad, which is then either clicked or not. An advertiser derives value from clicks; the value of a click is her private information. Initially, neither the auctioneer nor the advertisers have any information about the likelihood of clicks on the advertisements. The auctioneer's goal is to design a (dominant strategies) truthful mechanism that (approximately) maximizes the social welfare. If the advertisers bid their true private values, our problem is equivalent to the "multi-armed bandit problem", and thus can be viewed as a strategic version of the latter. In particular, for both problems the quality of an algorithm can be characterized by "regret", the difference in social welfare between the algorithm and the benchmark which always selects the same "best" advertisement. We investigate how the design of multi-armed bandit algorithms is affected by the restriction that the resulting mechanism must be truthful. We find that truthful mechanisms have certain strong structural properties -- essentially, they must separate exploration from exploitation -- and they incur much higher regret than the optimal multi-armed bandit algorithms. Moreover, we provide a truthful mechanism which (essentially) matches our lower bound on regret.