Advancing Ad Auction Realism: Practical Insights & Modeling Implications

This paper proposes a learning model of online ad auctions that allows for the following four key realistic characteristics of contemporary online auctions: (1) ad slots can have different values and click-through rates depending on users' search queries, (2) the number and identity of competing advertisers are unobserved and change with each auction, (3) advertisers only receive partial, aggregated feedback, and (4) payment rules are only partially specified. We model advertisers as agents governed by an adversarial bandit algorithm, independent of auction mechanism intricacies. Our objective is to simulate the behavior of advertisers for counterfactual analysis, prediction, and inference purposes. Our findings reveal that, in such richer environments, "soft floors" can enhance key performance metrics even when bidders are drawn from the same population. We further demonstrate how to infer advertiser value distributions from observed bids, thereby affirming the practical efficacy of our approach even in a more realistic auction setting

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

Dispersion for Data-Driven Algorithm Design, Online Learning, and Private Optimization

Data-driven algorithm design, that is, choosing the best algorithm for a specific application, is a crucial problem in modern data science. Practitioners often optimize over a parameterized algorithm family, tuning parameters based on problems from their domain. These procedures have historically come with no guarantees, though a recent line of work studies algorithm selection from a theoretical perspective. We advance the foundations of this field in several directions: we analyze online algorithm selection, where problems arrive one-by-one and the goal is to minimize regret, and private algorithm selection, where the goal is to find good parameters over a set of problems without revealing sensitive information contained therein. We study important algorithm families, including SDP-rounding schemes for problems formulated as integer quadratic programs, and greedy techniques for canonical subset selection problems. In these cases, the algorithm's performance is a volatile and piecewise Lipschitz function of its parameters, since tweaking the parameters can completely change the algorithm's behavior. We give a sufficient and general condition, dispersion, defining a family of piecewise Lipschitz functions that can be optimized online and privately, which includes the functions measuring the performance of the algorithms we study. Intuitively, a set of piecewise Lipschitz functions is dispersed if no small region contains many of the functions' discontinuities. We present general techniques for online and private optimization of the sum of dispersed piecewise Lipschitz functions. We improve over the best-known regret bounds for a variety of problems, prove regret bounds for problems not previously studied, and give matching lower bounds. We also give matching upper and lower bounds on the utility loss due to privacy. Moreover, we uncover dispersion in auction design and pricing problems

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

Optimal No-regret Learning in Repeated First-price Auctions

We study online learning in repeated first-price auctions with censored feedback, where a bidder, only observing the winning bid at the end of each auction, learns to adaptively bid in order to maximize her cumulative payoff. To achieve this goal, the bidder faces a challenging dilemma: if she wins the bid--the only way to achieve positive payoffs--then she is not able to observe the highest bid of the other bidders, which we assume is iid drawn from an unknown distribution. This dilemma, despite being reminiscent of the exploration-exploitation trade-off in contextual bandits, cannot directly be addressed by the existing UCB or Thompson sampling algorithms in that literature, mainly because contrary to the standard bandits setting, when a positive reward is obtained here, nothing about the environment can be learned. In this paper, by exploiting the structural properties of first-price auctions, we develop the first learning algorithm that achieves $O(\sqrt{T}\log^2 T)$ regret bound when the bidder's private values are stochastically generated. We do so by providing an algorithm on a general class of problems, which we call monotone group contextual bandits, where the same regret bound is established under stochastically generated contexts. Further, by a novel lower bound argument, we characterize an $\Omega(T^{2/3})$ lower bound for the case where the contexts are adversarially generated, thus highlighting the impact of the contexts generation mechanism on the fundamental learning limit. Despite this, we further exploit the structure of first-price auctions and develop a learning algorithm that operates sample-efficiently (and computationally efficiently) in the presence of adversarially generated private values. We establish an $O(\sqrt{T}\log^3 T)$ regret bound for this algorithm, hence providing a complete characterization of optimal learning guarantees for this problem

Selling to a No-Regret Buyer

We consider the problem of a single seller repeatedly selling a single item to a single buyer (specifically, the buyer has a value drawn fresh from known distribution $D$ in every round). Prior work assumes that the buyer is fully rational and will perfectly reason about how their bids today affect the seller's decisions tomorrow. In this work we initiate a different direction: the buyer simply runs a no-regret learning algorithm over possible bids. We provide a fairly complete characterization of optimal auctions for the seller in this domain. Specifically: - If the buyer bids according to EXP3 (or any "mean-based" learning algorithm), then the seller can extract expected revenue arbitrarily close to the expected welfare. This auction is independent of the buyer's valuation $D$, but somewhat unnatural as it is sometimes in the buyer's interest to overbid. - There exists a learning algorithm $\mathcal{A}$ such that if the buyer bids according to $\mathcal{A}$ then the optimal strategy for the seller is simply to post the Myerson reserve for $D$ every round. - If the buyer bids according to EXP3 (or any "mean-based" learning algorithm), but the seller is restricted to "natural" auction formats where overbidding is dominated (e.g. Generalized First-Price or Generalized Second-Price), then the optimal strategy for the seller is a pay-your-bid format with decreasing reserves over time. Moreover, the seller's optimal achievable revenue is characterized by a linear program, and can be unboundedly better than the best truthful auction yet simultaneously unboundedly worse than the expected welfare

Learning Prices for Repeated Auctions with Strategic Buyers

Inspired by real-time ad exchanges for online display advertising, we consider the problem of inferring a buyer's value distribution for a good when the buyer is repeatedly interacting with a seller through a posted-price mechanism. We model the buyer as a strategic agent, whose goal is to maximize her long-term surplus, and we are interested in mechanisms that maximize the seller's long-term revenue. We define the natural notion of strategic regret --- the lost revenue as measured against a truthful (non-strategic) buyer. We present seller algorithms that are no-(strategic)-regret when the buyer discounts her future surplus --- i.e. the buyer prefers showing advertisements to users sooner rather than later. We also give a lower bound on strategic regret that increases as the buyer's discounting weakens and shows, in particular, that any seller algorithm will suffer linear strategic regret if there is no discounting.Comment: Neural Information Processing Systems (NIPS 2013

Online learning in repeated auctions

Motivated by online advertising auctions, we consider repeated Vickrey auctions where goods of unknown value are sold sequentially and bidders only learn (potentially noisy) information about a good's value once it is purchased. We adopt an online learning approach with bandit feedback to model this problem and derive bidding strategies for two models: stochastic and adversarial. In the stochastic model, the observed values of the goods are random variables centered around the true value of the good. In this case, logarithmic regret is achievable when competing against well behaved adversaries. In the adversarial model, the goods need not be identical and we simply compare our performance against that of the best fixed bid in hindsight. We show that sublinear regret is also achievable in this case and prove matching minimax lower bounds. To our knowledge, this is the first complete set of strategies for bidders participating in auctions of this type