Truthful Learning Mechanisms for Multi-Slot Sponsored Search Auctions with Externalities

Sponsored search auctions constitute one of the most successful applications of microeconomic mechanisms. In mechanism design, auctions are usually designed to incentivize advertisers to bid their truthful valuations and to assure both the advertisers and the auctioneer a non-negative utility. Nonetheless, in sponsored search auctions, the click-through-rates (CTRs) of the advertisers are often unknown to the auctioneer and thus standard truthful mechanisms cannot be directly applied and must be paired with an effective learning algorithm for the estimation of the CTRs. This introduces the critical problem of designing a learning mechanism able to estimate the CTRs at the same time as implementing a truthful mechanism with a revenue loss as small as possible compared to an optimal mechanism designed with the true CTRs. Previous work showed that, when dominant-strategy truthfulness is adopted, in single-slot auctions the problem can be solved using suitable exploration-exploitation mechanisms able to achieve a per-step regret (over the auctioneer's revenue) of order $O(T^{-1/3})$ (where T is the number of times the auction is repeated). It is also known that, when truthfulness in expectation is adopted, a per-step regret (over the social welfare) of order $O(T^{-1/2})$ can be obtained. In this paper we extend the results known in the literature to the case of multi-slot auctions. In this case, a model of the user is needed to characterize how the advertisers' valuations change over the slots. We adopt the cascade model that is the most famous model in the literature for sponsored search auctions. We prove a number of novel upper bounds and lower bounds both on the auctioneer's revenue loss and social welfare w.r.t. to the VCG auction and we report numerical simulations investigating the accuracy of the bounds in predicting the dependency of the regret on the auction parameters

A Truthful Learning Mechanism for Contextual Multi--Slot Sponsored Search Auctions with Externalities

International audienceSponsored search auctions constitute one of the most successful applications of \emph{microeconomic mechanisms}. In mechanism design, auctions are usually designed to incentivize advertisers to bid their truthful valuations and, at the same time, to assure both the advertisers and the auctioneer a non--negative utility. Nonetheless, in sponsored search auctions, the click--through--rates (CTRs) of the advertisers are often unknown to the auctioneer and thus standard incentive compatible mechanisms cannot be directly applied and must be paired with an effective learning algorithm for the estimation of the CTRs. This introduces the critical problem of designing a learning mechanism able to estimate the CTRs as the same time as implementing a truthful mechanism with a revenue loss as small as possible compared to an optimal mechanism designed with the true CTRs. Previous works showed that in single--slot auctions the problem can be solved using a suitable exploration--exploitation mechanism able to achieve a per--step regret of order $O(T^{-1/3})$ (where $T$ is the number of times the auction is repeated). In this paper we extend these results to the general case of contextual multi--slot auctions with position-- and ad--dependent externalities. In particular, we prove novel upper--bounds on the revenue loss w.r.t. to a VCG auction and we report numerical simulations investigating their accuracy in predicting the dependency of the regret on the number of rounds $T$, the number of slots $K$, and the number of advertisements $n$

An Incentive Compatible Multi-Armed-Bandit Crowdsourcing Mechanism with Quality Assurance

Consider a requester who wishes to crowdsource a series of identical binary labeling tasks to a pool of workers so as to achieve an assured accuracy for each task, in a cost optimal way. The workers are heterogeneous with unknown but fixed qualities and their costs are private. The problem is to select for each task an optimal subset of workers so that the outcome obtained from the selected workers guarantees a target accuracy level. The problem is a challenging one even in a non strategic setting since the accuracy of aggregated label depends on unknown qualities. We develop a novel multi-armed bandit (MAB) mechanism for solving this problem. First, we propose a framework, Assured Accuracy Bandit (AAB), which leads to an MAB algorithm, Constrained Confidence Bound for a Non Strategic setting (CCB-NS). We derive an upper bound on the number of time steps the algorithm chooses a sub-optimal set that depends on the target accuracy level and true qualities. A more challenging situation arises when the requester not only has to learn the qualities of the workers but also elicit their true costs. We modify the CCB-NS algorithm to obtain an adaptive exploration separated algorithm which we call { \em Constrained Confidence Bound for a Strategic setting (CCB-S)}. CCB-S algorithm produces an ex-post monotone allocation rule and thus can be transformed into an ex-post incentive compatible and ex-post individually rational mechanism that learns the qualities of the workers and guarantees a given target accuracy level in a cost optimal way. We provide a lower bound on the number of times any algorithm should select a sub-optimal set and we see that the lower bound matches our upper bound upto a constant factor. We provide insights on the practical implementation of this framework through an illustrative example and we show the efficacy of our algorithms through simulations

Dynamic Ad Allocation: Bandits with Budgets

We consider an application of multi-armed bandits to internet advertising (specifically, to dynamic ad allocation in the pay-per-click model, with uncertainty on the click probabilities). We focus on an important practical issue that advertisers are constrained in how much money they can spend on their ad campaigns. This issue has not been considered in the prior work on bandit-based approaches for ad allocation, to the best of our knowledge. We define a simple, stylized model where an algorithm picks one ad to display in each round, and each ad has a \emph{budget}: the maximal amount of money that can be spent on this ad. This model admits a natural variant of UCB1, a well-known algorithm for multi-armed bandits with stochastic rewards. We derive strong provable guarantees for this algorithm