Yuan Deng
Yuan Deng is a Research Scientist at Google Research New York City. His research is broadly situated at the interface between economics and computer science (aka. algorithmic game theory), mainly including dynamic mechanism design (how to design auctions for online advertisement markets) and learning in economic environments (e.g. online pricing for strategic agents and/or learning agents).
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Non-uniform Bid-scaling and Equilibria for Different Auctions: An Empirical Study
Jieming Mao
Yifeng Teng
Song Zuo
Proceedings of the ACM on Web Conference 2024, 256–266
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In recent years, the growing adoption of autobidding has motivated the study of auction design with value-maximizing auto-bidders. It is known that under mild assumptions, uniform bid-scaling is an optimal bidding strategy in truthful auctions, e.g., Vickrey-Clarke-Groves auction (VCG), and the price of anarchy for VCG is 2. However, for other auction formats like First-Price Auction (FPA) and Generalized Second-Price auction (GSP), uniform bid-scaling may not be an optimal bidding strategy, and bidders have incentives to deviate to adopt strategies with non-uniform bid-scaling. Moreover, FPA can achieve optimal welfare if restricted to uniform bid-scaling, while its price of anarchy becomes 2 when non-uniform bid-scaling strategies are allowed.
All these price of anarchy results have been focused on welfare approximation in the worst-case scenarios. To complement theoretical understandings, we empirically study how different auction formats (FPA, GSP, VCG) with different levels of non-uniform bid-scaling perform in an autobidding world with a synthetic dataset for auctions. Our empirical findings include: * For both uniform bid-scaling and non-uniform bid-scaling, FPA is better than GSP and GSP is better than VCG in terms of both welfare and profit; * A higher level of non-uniform bid-scaling leads to lower welfare performance in both FPA and GSP, while different levels of non-uniform bid-scaling have no effect in VCG. Our methodology of synthetic data generation may be of independent interest.
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Individual Welfare Guarantees in the Autobidding World with Machine-learned Advice
Negin Golrezaei
Patrick Jaillet
Jason Cheuk Nam Liang
Proceedings of the ACM on Web Conference 2024, 267–275
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Online advertising channels commonly focus on maximizing total advertiser welfare to enhance channel health, and previous literature has studied augmenting ad auctions with machine learning predictions on advertiser values (also known asmachine-learned advice ) to improve total welfare. Yet, such improvements could come at the cost of individual bidders' welfare and do not shed light on how particular advertiser bidding strategies impact welfare. Motivated by this, we present an analysis on an individual bidder's welfare loss in the autobidding world for auctions with and without machine-learned advice, and also uncover how advertiser strategies relate to such losses. In particular, we demonstrate how ad platforms can utilize ML advice to improve welfare guarantee on the aggregate and individual bidder level by setting ML advice as personalized reserve prices when the platform consists ofautobidders who maximize value while respecting a return on ad spend (ROAS) constraint. Under parallel VCG auctions with such ML advice-based reserves, we present a worst-case welfare lower-bound guarantee for an individual autobidder, and show that the lower-bound guarantee is positively correlated with ML advice quality as well as the scale of bids induced by the autobidder's bidding strategies. Further, we show that no truthful, and possibly randomized mechanism with anonymous allocations can achieve universally better individual welfare guarantees than VCG, in the presence of personalized reserves based on ML-advice of equal quality. Moreover, we extend our individual welfare guarantee results to generalized first price (GFP) and generalized second price (GSP) auctions. Finally, we present numerical studies using semi-synthetic data derived from ad auction logs of a search ad platform to showcase improvements in individual welfare when setting personalized reserve prices with ML-advice.
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Efficiency of the Generalized Second-Price Auction for Value Maximizers
Jieming Mao
Hanrui Zhang
Song Zuo
Proceedings of the ACM on Web Conference 2024, 46–56
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We study the price of anarchy of the generalized second-price auction where bidders are value maximizers (i.e., autobidders). We show that in general the price of anarchy can be as bad as 0. For comparison, the price of anarchy of running VCG is 1/2 in the autobidding world. We further show a fined-grained price of anarchy with respect to the discount factors (i.e., the ratios of click probabilities between lower slots and the highest slot in each auction) in the generalized second-price auction, which highlights the qualitative relation between the smoothness of the discount factors and the efficiency of the generalized second-price auction.
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Optimal Pricing Schemes for an Impatient Buyer
Jieming Mao
Kangning Wang
Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms(2023), pp. 382-398
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A patient seller aims to sell a good to an impatient buyer (i.e., one who discounts utility over time).The buyer will remain in the market for a period of time T , and her private value is drawn from a publicly known distribution. What is the revenue-optimal pricing-curve (sequence of (price, time) pairs) for the seller? Is randomization of help here? Is the revenue-optimal pricing-curve computable in polynomial time? We answer these questions in this paper. We give an efficient algorithm for computing the revenue-optimal pricing curve. We show that pricing curves, that post a price at each point of time and let the buyer pick her utility maximizing time to buy, are revenue-optimal among a much broader class of sequential lottery mechanisms: namely, mechanisms that allow the seller to post a menu of lotteries at each point of time cannot get any higher revenue than pricing curves. We also show that the even broader class of mechanisms that allow the menu of lotteries to be adaptively set, can earn strictly higher revenue than that of pricing curves, and the revenue gap can be as big as the support size of the buyer’s value distribution.
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Autobidding Auctions in the Presence of User Costs
Jieming Mao
Hanrui Zhang
Song Zuo
Proceedings of the ACM Web Conference 2023, pp. 3428-3435
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Although costs are prevalent in ad auctions, not many auction theory works study auction design in the presence of cost in the classic settings. One reason is that most auctions design in the setting without cost directly generalize to the setting with cost when the bidders maximizing quasi-linear utility.
However, as auto-bidding becomes a major choice of advertisers in online advertising, the distinction from the underlying behavior model often leads to different solutions of many well-studied auctions. In the context of ad auctions with cost, VCG achieves optimal welfare with quasi-linear utility maximizing bidders, while has 0 welfare approximation guarantee with value maximizing bidders who follow the optimization behind common auto-bidding algorithms.
In this paper, we prove that the approximation welfare guarantee of VCG auction can be significantly improved by a minimal change --- introducing cost multipliers. We note that one can use either one multiplier per auction or one multiplier per bidder, but one global multiplier across all auctions and bidders does not work. Finally, to echo with our theoretical results, we conduct empirical evaluations using semi-synthetic data derived from real auction data of a major advertising platform.
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Multi-channel Autobidding with Budget and ROI Constraints
Negin Golrezaei
Patrick Jaillet
Jason Cheuk Nam Liang
Proceedings of the 40th International Conference on Machine Learning(2023), 7617–7644
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In digital online advertising, advertisers procure ad impressions simultaneously on multiple platforms, or so-called channels, such as Google Ads, Meta Ads Manager, etc., each of which consists of numerous ad auctions. We study how an advertiser maximizes total conversion (e.g. ad clicks) while satisfying aggregate return-on-investment (ROI) and budget constraints across all channels. In practice, an advertiser does not have control over, and thus cannot globally optimize, which individual ad auctions she participates in for each channel, and instead authorizes a channel to procure impressions on her behalf: the advertiser can only utilize two levers on each channel, namely setting a per-channel budget and per-channel target ROI. In this work, we first analyze the effectiveness of each of these levers for solving the advertiser's global multi-channel problem. We show that when an advertiser only optimizes over per-channel ROIs, her total conversion can be arbitrarily worse than what she could have obtained in the global problem. Further, we show that the advertiser can achieve the global optimal conversion when she only optimizes over per-channel budgets. In light of this finding, under a bandit feedback setting that mimics real-world scenarios where advertisers have limited information on ad auctions in each channels and how channels procure ads, we present an efficient learning algorithm that produces per-channel budgets whose resulting conversion approximates that of the global optimal problem. Finally, we argue that all our results hold for both single-item and multi-item auctions from which channels procure impressions on advertisers' behalf.
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Approximately Efficient Bilateral Trade
Jieming Mao
Kangning Wang
Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing(2022), 718–721
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We study bilateral trade between two strategic agents. The celebrated result of Myerson and Satterthwaite states that in general, no incentive-compatible, individually rational and weakly budget balanced mechanism can be efficient. I.e., no mechanism with these properties can guarantee a trade whenever buyer value exceeds seller cost. Given this, a natural question is whether there exists a mechanism with these properties that guarantees a constant fraction of the first-best gains-from-trade, namely a constant fraction of the gains-from-trade attainable whenever buyer’s value weakly exceeds seller’s cost. In this work, we positively resolve this long-standing open question on constant-factor approximation, mentioned in several previous works, using a simple mechanism that obtains a 1/8.23 ≈ 0.121 fraction of the first-best.
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We study posted price auctions and dynamic prior-independent mechanisms for (ROI-constrained) value maximizers. In contrast to classic (quasi-linear) utility maximizers, these agents aim to maximize their total value subject to a minimum ratio of value per unit of payment made. When personalized posted prices are allowed, posted price auctions for value maximizers can be reduced to posted price auctions for utility maximizers. However, for anonymous posted prices, the well-known 1/2 approximation for utility maximizers is impossible for value maximizers and we provide a posted price mechanism with 1/2 * (1 - 1/e) approximation. Moreover, we demonstrate how to apply our results to design prior-independent mechanisms in a dynamic environment; and to the best of our knowledge, this gives the first constant revenue approximation with multiple value maximizers. Finally, we provide an extension to combinatorial auctions with submodular / XOS agents.
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Optimal Mechanisms for Value Maximizers with Budget Constraints via Target Clipping
Jieming Mao
Song Zuo
Proceedings of the 23rd ACM Conference on Economics and Computation(2022), pp. 475
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We study the design of revenue-maximizing mechanisms for value-maximizing agents with budget constraints. Agents have return-on-spend constraints requiring a minimum amount of value per unit of payment made and budget constraints limiting their total payments. The agents' only private information are the minimum admissible ratios on the return-on-spend constraint, referred to as the target ratios.
Our work is motivated by internet advertising platforms, where automated bidders are increasingly being adopted by advertisers to purchase advertising opportunities on their behalf. Instead of specifying bids for each keyword, advertiser set high-level goals, such as maximizing clicks, and targets on cost-per-clicks or return-on-spend, and the platform automatically purchases opportunities by bidding in different auctions. We present a model that abstracts away the complexities of the auto-bidding procurement process that is general enough to accommodate many allocation mechanisms such as auctions, matchings, etc.
We reduce the mechanism design problem when agents have private target ratios to a challenging non-linear optimization problem with monotonicity constraints. We provide a novel decomposition approach to tackle this problem that yields insights into the structure of optimal mechanisms and show that surprising features stem from the interaction on budget and return-on-spend constraints. Our optimal mechanism, which we dub the target-clipping mechanism, has an appealing structure: it sets a threshold on the target ratio of each agent, targets above the threshold are allocated efficiently, and targets below are clipped to the threshold.
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Online Combinatorial Auctions
Debmalya Panigrahi
Hanrui Zhang
Proceedings of the ACM-SIAM Symposium on Discrete Algorithms(2021)
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We study combinatorial auctions in online environments with the goal of maximizing social welfare. In this problem, new items become available on each day and must be sold before their respective expiration dates. We design online auctions for the widely studied classes of submodular and XOS valuations, and show the following results:
– For submodular valuations, we give an O(log m)-competitive mechanism for adversarial valuations and an O(1)-competitive mechanism for Bayesian valuations, where m is the total number of items. Both these mechanisms are computationally efficient and universally truthful for myopic agents, i.e., agents with no knowledge of the future.
– For XOS valuations, we show that there is no online mechanism that can achieve a competitive ratio of o ((m/ log m)1/3) even in a Bayesian setting. Our lower bound holds even if we do not require truthfulness and/or computational efficiency of the mechanism.
This establishes a sharp separation between XOS valuations and its subclass of submodular valuations for online combinatorial auctions. In contrast, no such separation exists for offline auctions, where the best bounds for both submodular and XOS valuations are O((log log m)3) for adversarial settings (Assadi and Singla, FOCS 2019) and O(1) for Bayesian settings (Dütting et al., FOCS 2017).
In contrast to the above, if items do not expire and only need to be sold before the market closes, then we give a reduction from offline to online mechanisms that preserves the competitive ratio for all subadditive valuations (that includes XOS and submodular valuations), thereby achieving the same bounds as the respective best offline mechanisms.
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Auto-bidding has become one of the main options for bidding in online advertisements, in which advertisers only need to specify high-level objectives and leave the complex task of bidding to auto-bidders. In this paper, we propose a family of auctions with boosts to improve welfare for auto-bidders with both return on ad spend constraints and budget constraints. Our empirical results validate our theoretical findings and show that both the welfare and revenue can be improved by selecting the weight of the boosts properly.
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Non-Clairvoyant Dynamic Mechanism Design with Budget Constraints and Beyond
Song Zuo
Proceedings of the 22nd ACM Conference on Economics and Computation(2021), pp. 369
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We provide a general design framework for dynamic mechanisms under complex environments, coined Lossless History Compression mechanisms. Lossless history compression mechanisms compress the history into a state carrying the least historical information without losing any generality in terms of either revenue or welfare. In particular, the characterization works for almost arbitrary constraints on the outcomes, and any objective function defined on the historical reports, allocations, and the cumulative payments. We then apply our framework to design a non-clairvoyant dynamic mechanism under budget and ex-post individual rationality constraints that is dynamic incentive-compatible and achieves non-trivial revenue performance, even without any knowledge about the future. In particular, our dynamic mechanism obtains a constant approximation to the optimal dynamic mechanism having access to all information in advance. To the best of our knowledge, this is the first dynamic mechanism that achieves a constant approximation and strictly respects dynamic incentive-compatibility and budget constraints without relying on any forecasts of the future.
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We study prior-independent dynamic auction design with production costs for a value-maximizing buyer, a paradigm that is becoming prevalent recently following the development of automatic bidding algorithms in advertising platforms. In contrast to a utility-maximizing buyer, who maximizes the difference between her total value and total payment, a value-maximizing buyer aims to maximize her total value subject to a return on investment (ROI) constraint. Our main result is a dynamic mechanism with regret $\tilde{O}(T^{2/3})$, where $T$ is the time horizon, against the first-best benchmark, i.e., the maximum amount of revenue the seller can extract assuming all values of the buyer are publicly known.
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Robust Auction Design in the Auto-bidding World
Jieming Mao
Song Zuo
Advances in Neural Information Processing Systems(2021)
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In classic auction theory, reserve prices are known to be effective for improving revenue for the auctioneer against quasi-linear utility maximizing bidders. The introduction of reserve prices, however, usually do not help improve total welfare of the auctioneer and the bidders. In this paper, we focus on value maximizing bidders with return on spend constraints---a paradigm that has drawn considerable attention recently as more advertisers adopt auto-bidding algorithms in advertising platforms---and show that the introduction of reserve prices has a novel impact on the market. Namely, by choosing reserve prices appropriately the auctioneer can improve not only the total revenue but also the total welfare. Our results also demonstrate that reserve prices are robust to bidder types, i.e., reserve prices work well for different bidder types, such as value maximizers and utility maximizers, without using bidder type information. We generalize these results for a variety of auction mechanisms such as VCG, GSP, and first-price auctions. Moreover, we show how to combine these results with additive boosts to improve the welfare of the outcomes of the auction further. Finally, we complement our theoretical observations with an empirical study confirming the effectiveness of these ideas using data from online advertising auctions.
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Welfare-maximizing Guaranteed Dashboard Mechanisms
Jason Hartline
Jieming Mao
Proceedings of the 22nd ACM Conference on Economics and Computation(2021), pp. 370
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Bidding dashboards are used in online marketplaces to aid a bidder in computing good bidding strategies, particularly when the auction used by the marketplace is constrained to have the winners-pay-bid payment format. A dashboard predicts the outcome a bidder can expect to get at each possible bid. To convince a bidder to best respond to the information published in a dashboard, a dashboard mechanism should ensure either (a) that best responding maximizes the bidder's utility (a weaker requirement) or (b) that the mechanism implements the outcome published in the dashboard (a stronger requirement that subsumes (a)). Recent work by Hartline et al. EC'19 formalized the notion of dashboard mechanisms and designed winners-pay-bid mechanisms that guaranteed epsilon-optimal utility (an epsilon-approximate version of (a)), but not (b). I.e., the mechanism could end up implementing arbitrarily different outcomes from what was promised. While this guarantee is sufficient from a purely technical perspective, it is far from enough in the real world: it is hard to convince bidders to best respond to information which could be arbitrarily inaccurate, regardless of the theoretical promise of near-optimality. In this paper we study guaranteed dashboard mechanisms, namely, ones that are guaranteed to implement what they publish, and obtain good welfare. We study this question in a repeated auction setting for general single-dimensional valuations and give tight characterizations of the loss in welfare as a function of natural parameters upper bounding the difference in valuation profile across the rounds. In particular, we give three different characterizations, bounding the loss in welfare in terms of the 0 norm, 1 norm and infinite norm of difference in valuation profile across rounds. All the characterizations generalize at least up to matroid feasibility constraints, and the infinite norm characterization extends to general downward-closed feasibility constraints. We bring to bear different techniques for each of these characterizations, including connections to differential privacy and online convex optimizations.
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Revenue-Incentive Tradeoffs in Dynamic Reserve Pricing
Sébastien Lahaie
Song Zuo
International Conference on Machine Learning(2021), pp. 2601-2610
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Online advertisements are primarily sold via repeated auctions with reserve prices. In this paper, we study how to set reserves to boost revenue based on the historical bids of strategic buyers, while controlling the impact of such a policy on the incentive compatibility of the repeated auctions. Adopting an incentive compatibility metric which quantifies the incentives to shade bids, we propose a novel class of reserve pricing policies and provide analytical tradeoffs between their revenue performance and bid-shading incentives. The policies are inspired by the exponential mechanism from the literature on differential privacy, but our study uncovers mechanisms with significantly better revenue-incentive tradeoffs than the exponential mechanism in practice. We further empirically evaluate the tradeoffs on synthetic data as well as ad auction data from a major ad exchange to verify and support our theoretical findings.
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The Landscape of Autobidding Auctions: Value versus Utility Maximization
Jieming Mao
Song Zuo
Proceedings of the 22nd ACM Conference on Economics and Computation(2021), pp. 132-133
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Internet advertisers are increasingly adopting automated bidders to buy advertising opportunities. Automated bidders simplify the procurement process by allowing advertisers to specify their goals and then bidding on their behalf in the auctions that are used to sell advertising slots. One popular goal adopted by advertisers is to maximize their clicks (or conversions) subject to a return on spend (RoS) constraint, which imposes that the ratio of total value to total spend is greater than a target ratio specified by the advertisers. The emergence of automated bidders brings into question whether the standard mechanisms used to sold ads are still effective in this new landscape. Thus motivated, in this paper we study the problem of characterizing optimal mechanisms for selling an item to one of multiple agents with return on spend constraints when either the values or target ratios are private. We consider two objectives for the agents: value maximization, which is becoming the prevalent objective in advertising markets, and utility maximization, which is the de facto paradigm in economic theory. Our goal is to understand the impact of the agents' private information and their objectives on the seller's revenue, and determine whether the first-best revenue, which is the optimal revenue without private information, is achievable.
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Robust Pricing in Dynamic Mechanism Design
Sébastien Lahaie
International Conference on Machine Learning(2020), pp. 2494-2503
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Motivated by the repeated sale of online ads via auctions, optimal pricing in repeated auctions has attracted a large body of research. While dynamic mechanisms offer powerful techniques to improve on both revenue and efficiency by optimizing auctions across different items, their reliance on exact distributional information of buyers’ valuations (present and future) limits their use in practice. In this paper, we propose robust dynamic mechanism design. We develop a new framework to design dynamic mechanisms that are robust to both estimation errors in value distributions and strategic behavior. We apply the framework in learning environments, leading to the first policy that achieves provably low regret against the optimal dynamic mechanism in contextual auctions, where the dynamic benchmark has full and accurate distributional information.
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A Data-Driven Metric of Incentive Compatibility
Sébastien Lahaie
Song Zuo
Proceedings of The Web Conference(2020), pp. 1796-1806
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An incentive-compatible auction incentivizes buyers to truthfully reveal their private valuations. However, many ad auction mechanisms deployed in practice are not incentive-compatible, such as first-price auctions (for display advertising) and the generalized second-price auction (for search advertising). We introduce a new metric to quantify incentive compatibility in both static and dynamic environments. Our metric is data-driven and can be computed directly through black-box auction simulations without relying on reference mechanisms or complicated optimizations. We provide interpretable characterizations of our metric and prove that it is monotone in auction parameters for several mechanisms used in practice, such as soft floors and dynamic reserve prices. We empirically evaluate our metric on ad auction data from a major ad exchange and a major search engine to demonstrate its broad applicability in practice.
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Bayesian Repeated Zero-Sum Games with Persistent State, with Application to Security Games
Vincent Conitzer
Shaddin Dughmi
International Conference on Web and Internet Economics(2020), pp. 444-458
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We study infinitely-repeated two-player zero-sum games with one-sided private information and a persistent state. Here, only one of the two players learns the state of the repeated game. We consider two models: either the state is chosen by nature, or by one of the players. For the former, the equilibrium of the repeated game is known to be equivalent to that of a one-shot public signaling game, and we make this equivalence algorithmic. For the latter, we show equivalence to one-shot team max-min games, and also provide an algorithmic reduction. We apply this framework to repeated zero-sum security games with private information on the side of the defender and provide an almost complete characterization of their computational complexity.
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Strategizing against No-regret Learners
Advances in Neural Information Processing Systems(2019), pp. 1579-1587
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How should a player who repeatedly plays a game against a no-regret learner strategize to maximize his utility? We study this question and show that under some mild assumptions, the player can always guarantee himself a utility of at least what he would get in a Stackelberg equilibrium of the game. When the no-regret learner has only two actions, we show that the player cannot get any higher utility than the Stackelberg equilibrium utility. But when the no-regret learner has more than two actions and plays a mean-based no-regret strategy, we show that the player can get strictly higher than the Stackelberg equilibrium utility. We provide a characterization of the optimal game-play for the player against a mean-based no-regret learner as a solution to a control problem. When the no-regret learner's strategy also guarantees him a no-swap regret, we show that the player cannot get anything higher than a Stackelberg equilibrium utility.
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Prior-Free Dynamic Auctions with Low Regret Buyers
Advances in Neural Information Processing Systems(2019), pp. 4803-4813
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We study the problem of how to repeatedly sell to a buyer running a no-regret, mean-based algorithm. Previous work (Braverman et al., EC '18) shows that it is possible to design effective mechanisms in such a setting that extract almost all of the economic surplus, but these mechanisms require the buyer's values each round to be drawn iid from a fixed distribution. In this paper, we do away with this assumption and consider the {\it prior-free setting} where the buyer's value each round is chosen adversarially (possibly adaptively).
We show that even in this prior-free setting, it is possible to extract a $(1-\varepsilon)$-approximation of the full economic surplus for any $\varepsilon > 0$. The menu complexity of our mechanism (the number of options offered to a buyer in any round) scales independently of the number of rounds $T$ and polynomially in $\varepsilon$. We show that this is optimal up to a polynomial factor; any mechanism achieving this approximation factor, even when values are drawn stochastically, requires menu complexity at least $\Omega(1/\varepsilon)$.
Finally, we examine what is possible when we constrain our mechanism to a natural auction format where overbidding is dominated. Braverman et al. show that even when values are drawn from a known stochastic distribution supported on $[1/H, 1]$, it is impossible in general to extract more than $O(\log\log H / \log H)$ of the economic surplus. We show how to achieve the same approximation factor in the {\it prior-independent} setting (where the distribution is unknown to the seller), and an approximation factor of $O(1 / \log H)$ in the prior-free setting.
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Preferred Deals in General Environments
Sébastien Lahaie
Proceedings of the 28th International Joint Conference on Artificial Intelligence(2019), pp. 231-237
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A preferred deal is a special contract for selling impressions of display ad inventory. By accepting a deal, a buyer agrees to buy a minimum amount of impressions at a fixed price per impression, and is granted priority access to the impressions before they are sent to an open auction on an ad exchange. We consider the problem of designing preferred deals (inventory, price, quantity) in the presence of general convex constraints, including budget constraints, and propose an approximation algorithm to maximize the revenue obtained from the deals. We then evaluate our algorithm using auction data from a major advertising exchange and our empirical results show that the algorithm achieves around 95% of the optimal revenue.
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Testing Dynamic Incentive Compatibility in Display Ad Auctions
Sébastien Lahaie
Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining(2019), pp. 1616-1624
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The question of transparency has become a key point of contention between buyers and sellers of display advertising space: ads are allocated via complex, black-box auction systems whose mechanics can be difficult to model let alone optimize against. Motivated by this concern, this paper takes the perspective of a single advertiser and develops statistical tests to confirm whether an underlying auction mechanism is dynamically incentive compatible (IC), so that truthful bidding in each individual auction and across time is an optimal strategy. The most general notion of dynamic-IC presumes that the seller knows how buyers discount future surplus, which is questionable in practice. We characterize dynamic mechanisms that are dynamic-IC for all possible discounting factors according to two intuitive conditions: the mechanism should be IC at each stage in the usual sense, and expected present utility (under truthful bidding) should be independent of past bids. The conditions motivate two separate experiments based on bid perturbations that can be run simultaneously on the same impression traffic. We provide a novel statistical test of stage-IC along with a test for utility-independence that can detect lags in how the seller uses past bid information. We evaluate our tests on display ad data from a major ad exchange and show how they can accurately uncover evidence of first- or second-price auctions coupled with dynamic reserve prices, among other types of dynamic mechanisms.
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A Robust Non-Clairvoyant Dynamic Mechanism for Contextual Auctions
Sébastien Lahaie
Advances in Neural Information Processing Systems(2019), pp. 8657-8667
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Dynamic mechanisms offer powerful techniques to improve on both revenue and efficiency by linking sequential auctions using state information, but these techniques rely on exact distributional information of the buyers’ valuations (present and future), which limits their use in learning settings. In this paper, we consider the problem of contextual auctions where the seller gradually learns a model of the buyer's valuation as a function of the context (e.g., item features) and seeks a pricing policy that optimizes revenue. Building on the concept of a bank account mechanism---a special class of dynamic mechanisms that is known to be revenue-optimal---we develop a non-clairvoyant dynamic mechanism that is robust to both estimation errors in the buyer's value distribution and strategic behavior on the part of the buyer. We then tailor its structure to achieve a policy with provably low regret against a constant approximation of the optimal dynamic mechanism in contextual auctions. Our result substantially improves on previous results that only provide revenue guarantees against static benchmarks.
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Developing efficient and guaranteed nonconvex algorithms has been an important challenge in modern machine learning. Algorithms with good empirical performance such as stochastic gradient descent often lack theoretical guarantees. In this paper, we analyze the class of homotopy or continuation methods for global optimization of nonconvex functions. These methods start from an objective function that is efficient to optimize (e.g. convex), and progressively modify it to obtain the required objective, and the solutions are passed along the homotopy path. For the challenging problem of tensor PCA, we prove global convergence of the homotopy method in the “high noise” regime. The signal-to-noise requirement for our algorithm is tight in the sense that it matches the recovery guarantee for the \em best degree-4 sum-of-squares algorithm. In addition, we prove a phase transition along the homotopy path for tensor PCA. This allows us to simplify the homotopy method to a local search algorithm, viz., tensor power iterations, with a specific initialization and a noise injection procedure, while retaining the theoretical guarantees.
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