A Novel Class of Robust and Fast Algorithms for Online Allocation Problems A central problem in operations research is allocating limited resources sequentially to maximize cumulative rewards. Applications abound and include network revenue management and internet advertising among many others. Existing data-driven algorithms are tailored for convex settings with either adversarial or stochastic inputs. Many modern applications of online allocations problems, however, are nonconvex. Furthermore, algorithms for adversarial inputs may be too conservative in practice, whereas algorithms for stochastic inputs can perform poorly when the model is misspecified. In the paper “The Best of Many Worlds: Dual Mirror Descent for Online Allocation Problems,” Balseiro, Lu, and Mirrokni present a novel class of algorithms for nonconvex online allocation problems that attain good performance simultaneously in stochastic and adversarial input models and also in various nonstationary settings. The resulting algorithms are simple, fast, and robust to noise and corruption in the observations, in contrast to existing methods from the literature.
A d exchanges are emerging Internet markets where advertisers may purchase display ad placements, in real time and based on specific viewer information, directly from publishers via a simple auction mechanism. Advertisers join these markets with a prespecified budget and participate in multiple second-price auctions over the length of a campaign. This paper studies the competitive landscape that arises in ad exchanges and the implications for publishers' decisions. The presence of budgets introduces dynamic interactions among advertisers that need to be taken into account when attempting to characterize the bidding landscape or the impact of changes in the auction design. To this end, we introduce the notion of a fluid mean-field equilibrium (FMFE) that is behaviorally appealing and computationally tractable, and in some important cases, it yields a closed-form characterization. We establish that an FMFE approximates well the rational behavior of advertisers in these markets. We then show how this framework may be used to provide sharp prescriptions for key auction design decisions that publishers face in these markets. In particular, we show that ignoring budgets, a common practice in this literature, can result in significant profit losses for the publisher when setting the reserve price.
In online advertising markets, advertisers often purchase ad placements through bidding in repeated auctions based on realized viewer information. We study how budget-constrained advertisers may compete in such sequential auctions in the presence of uncertainty about future bidding opportunities and competition. We formulate this problem as a sequential game of incomplete information, in which bidders know neither their own valuation distribution nor the budgets and valuation distributions of their competitors. We introduce a family of practical bidding strategies we refer to as adaptive pacing strategies, in which advertisers adjust their bids according to the sample path of expenditures they exhibit, and analyze the performance of these strategies in different competitive settings. We establish the asymptotic optimality of these strategies when competitors’ bids are independent and identically distributed over auctions, but also when competing bids are arbitrary. When all the bidders adopt these strategies, we establish the convergence of the induced dynamics and characterize a regime (well motivated in the context of online advertising markets) under which these strategies constitute an approximate Nash equilibrium in dynamic strategies: the benefit from unilaterally deviating to other strategies, including ones with access to complete information, becomes negligible as the number of auctions and competitors grows large. This establishes a connection between regret minimization and market stability, by which advertisers can essentially follow approximate equilibrium bidding strategies that also ensure the best performance that can be guaranteed off equilibrium. This paper was accepted by Noah Gans, stochastic models and simulation.
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