Ad exchanges are widely used in platforms for online display advertising. Autonomous agents operating in these exchanges must learn policies for interacting profitably with a diverse, continually changing, but unknown market. We consider this problem from the perspective of a publisher, strategically interacting with an advertiser through a posted price mechanism. The learning problem for this agent is made difficult by the fact that information is censored, i.e., the publisher knows if an impression is sold but no other quantitative information. We address this problem using the Harsanyi-Bellman Ad Hoc Coordination (HBA) algorithm [1, 3], which conceptualises this interaction in terms of a Stochastic Bayesian Game and arrives at optimal actions by best responding with respect to probabilistic beliefs maintained over a candidate set of opponent behaviour profiles. We adapt and apply HBA to the censored information setting of ad exchanges. Also, addressing the case of stochastic opponents, we devise a strategy based on a Kaplan-Meier estimator for opponent modelling. We evaluate the proposed method using simulations wherein we show that HBA-KM achieves substantially better competitive ratio and lower variance of return than baselines, including a Q-learning agent and a UCB-based online learning agent, and comparable to the offline optimal algorithm.
From the advertiser's perspective, @cite_15 study budget optimisation for sponsored search auctions. The authors cast the problem of budget optimisation as a Markov Decision Process (MDP) with censored observations and propose a learning algorithm based on Kaplan-Meier estimators. The authors also perform a large scale empirical demonstration on auction data from Microsoft, in order to demonstrate that their algorithm is extremely effective in practice. Another take on the advertiser's optimisation problem is the one by @cite_18 who study the design of a bidding agent in a marketplace for displaying ads. They provide algorithms and performance guarantees for both settings, while also experimentally evaluating their performance on a fitted log-normal distribution from data observed from the Right Media Exchange.
@cite_15 @cite_18
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We consider the budget optimization problem faced by an advertiser participating in repeated sponsored search auctions, seeking to maximize the number of clicks attained under that budget. We cast the budget optimization problem as a Markov Decision Process (MDP) with censored observations, and propose a learning algorithm based on the wellknown Kaplan-Meier or product-limit estimator. We validate the performance of this algorithm by comparing it to several others on a large set of search auction data from Microsoft adCenter, demonstrating fast convergence to optimal performance. Motivated by the emergence of auction-based marketplaces for display ads such as the Right Media Exchange, we study the design of a bidding agent that implements a display advertising campaign by bidding in such a marketplace. The bidding agent must acquire a given number of impressions with a given target spend, when the highest external bid in the marketplace is drawn from an unknown distribution P. The quantity and spend constraints arise from the fact that display ads are usually sold on a CPM basis. We consider both the full information setting, where the winning price in each auction is announced publicly, and the partially observable setting where only the winner obtains information about the distribution; these differ in the penalty incurred by the agent while attempting to learn the distribution. We provide algorithms for both settings, and prove performance guarantees using bounds on uniform closeness from statistics, and techniques from online learning. We experimentally evaluate these algorithms: both algorithms perform very well with respect to both target quantity and spend; further, our algorithm for the partially observable case performs nearly as well as that for the fully observable setting despite the higher penalty incurred during learning.