Weinan Zhang, Kan Ren, Jun Wang
This note is a complementary material for the solution of optimal real-time bidding function in paper "Optimal Real-Time Bidding for Display Advertising, KDD 2014", where the estimated cost is taken as the bid price, i.e., the upper bound of the true cost. Here we discuss a more general bid optimisation framework with various utility and cost functions.
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Bidding under Uncertainty: Theory and Experiments
本文介绍了一种研究代理投标策略，假设组合估价的互补性和可替代的商品，在三个拍卖环境：顺序拍卖，同时拍卖，和交易代理竞争（TAC）经典酒店拍卖设计，顺序拍卖和同时拍卖的混合。将序列拍卖中的投标问题转化为一个MDP问题，并证明了期望边际效用投标是最优投标策略。将同时拍卖中的投标问题表示为一个随机规划问题，并通过实例说明，即使在确定性条件下，边际效用投标也不是最优投标策略.两种替代方法近似的解决方案，这个随机程序：第一种方法，它依赖于期望值，是最佳的确定性环境中，第二种方法，采样的非确定性环境中，是渐近最佳的样本的数量趋于无穷大。最后，这些不同的投标政策的实验中描述的TAC经典设置。
Discrete All-Pay Bidding Games
在全付拍卖中，只有一个投标人获胜，但所有投标人都必须向拍卖人付款。全付费竞价博弈是在传统的组合博弈中附加一个类似的竞价结构来决定下一个博弈者。与单一支付投标博弈的既定理论相反，最优博弈涉及从某种概率分布中选择投标，以保证获胜的概率最小。在这种方式下，全付费投标博弈结合了经济学和组合博弈的基本概念。我们提出了几个结果，在这些游戏中的最优策略的结构。然后，我们给出了一个快速算法计算这样的策略，为一大类的所有支付投标游戏。所提出的方法提供了一个框架，为进一步发展的理论全支付投标游戏。
We analyze the problem of how to optimally bid for ad spaces in online ad auctions. For this we consider the general case of multiple ad campaigns with overlapping targeting criteria. In our analysis we first characterize the structure of an optimal bidding strategy. In particular, we show that an optimal bidding strategies decomposes the problem into disjoint sets of campaigns and targeting groups. In addition, we show that pure bidding strategies that use only a single bid value for each campaign are not optimal when the supply curves are not continuous. For this case, we derive a lower-boun…
A Dynamic Programming Model for Determining Bidding Strategies in Sequential Auctions: Quasi-linear Utility and Budget Constraints
本文利用动态规划技术，提出了一种求解序列拍卖中最优投标策略的新方法。现有的方法假设用户的效用是以加法的形式表示的。因此，在每个状态下，剩余的货币禀赋必须被显式地表示，并且当初始货币禀赋m变大时，最优投标策略的计算变得耗时。在本文中，我们开发了一个新的问题形式化，通过假设用户的效用可以用准线性形式表示，并将支付表示为状态转换成本，从而避免显式地表示剩余禀赋。实验结果表明，我们可以获得超过m倍的计算时间的加速。在此基础上，提出了一种在预算约束下获得半最优报价策略的方法，并通过实验验证了该方法的有效性。
Small operators who take part in secondary wireless spectrum markets typically have strict budget limits. In this paper, we study the bidding problem of a budget constrained operator in repeated secondary spectrum auctions. In existing truthful auctions, truthful bidding is the optimal strategy of a bidder. However, budget limits impact bidding behaviors and make bidding decisions complicated, since bidders may behave differently to avoid running out of money. We formulate the problem as a dynamic auction game between operators, where knowledge of other operators is limited due to the distribu…
Optimal Boost Design for Auto-bidding Mechanism with Publisher Quality Constraints
本文提出q-Boost算法，在考虑发布者质量约束下优化在线竞价中的提升因子，实验显示在福利提升方面优于传统方法。
Optimal Strategies in Sequential Bidding
我们对最大限度地提高社会福利的机制感兴趣。在文献[1]中，研究了具有单位需求投标人的多单位拍卖和公共项目问题，并且在每种情况下，在可行的和激励相容的机制类中确定了社会福利非支配机制。改进这些最优结果的一种方法是允许参与者顺序移动。考虑到这一点，我们在这里研究连续版本的两个可行的格罗夫斯机制用于单一项目拍卖：维克里拍卖和贝利卡瓦洛机制。由于在这个序列设置中没有优势策略，我们专注于一个较弱的最优策略的概念。对于每种机制，我们引入自然的最优策略，并观察到，在每种机制中，这些策略表现出不同的行为。然而，我们发现，在所有的最优策略中，我们为每个机制引入的策略在每个参与者都遵循它的情况下使社会福利最大化，由此产生的社会福利可以大于同时设置中获得的社会福利。最后，我们表明，当解释这两种机制作为同时的，向量的建议的战略形成一个帕累托最优的纳什均衡类的最优策略。
We study a class of manipulations in combinatorial auctions where bidders fundamentally misrepresent what goods they are interested in. Prior work has largely assumed that bidders only submit bids on their bundles of interest, which we call simple bidding: strategizing over the bid amounts, but not the bundle identities. However, we show that there exists an entire class of auction instances for which simple bids are never optimal in Bayes-Nash equilibrium, always being strictly dominated by complex bids (where bidders bid on goods they are not interested in). We show this result for the two m…
In this paper, we consider the problem of optimizing the revenue a web publisher gets through real-time bidding (i.e. from ads sold in real-time auctions) and direct (i.e. from ads sold through contracts agreed in advance). We consider a setting where the publisher is able to bid in the real-time bidding auction for each impression. If it wins the auction, it chooses a direct campaign to deliver and displays the corresponding ad. This paper presents an algorithm to build an optimal strategy for the publisher to deliver its direct campaigns while maximizing its real-time bidding revenue. The op…
We study the online learning problem of a bidder who participates in repeated auctions. With the goal of maximizing his T-period payoff, the bidder determines the optimal allocation of his budget among his bids for $K$ goods at each period. As a bidding strategy, we propose a polynomial-time algorithm, inspired by the dynamic programming approach to the knapsack problem. The proposed algorithm, referred to as dynamic programming on discrete set (DPDS), achieves a regret order of $O(\sqrt{T\log{T}})$. By showing that the regret is lower bounded by $Ω(\sqrt{T})$ for any strategy, we conclude tha…
In many online advertisement (ad) exchanges, ad slots are each sold via a separate second-price auction. This paper considers the bidder's problem of maximizing the value of ads they purchase in these auctions, subject to budget constraints. This 'second-price knapsack' problem presents challenges when devising a bidding strategy because of the uncertain resource consumption: bidders win if they bid the highest amount, but pay the second-highest bid, unknown a priori. This is in contrast to the traditional online knapsack problem, where posted prices are revealed when ads arrive, and for which…
Multi-Platform Autobidding with and without Predictions
本文研究多平台自动出价问题，提出无需预测的算法（查询复杂度O(m log(mn) log n)）及利用预测的学习增强算法，实现预测正确时O(m)查询、错误时仍保持原复杂度的两全其美效果。
Analyzing the Interaction of Optimal Strategies in Mean-Payoff Bidding Games
本文针对多智能体系统中智能体互动分析的挑战，聚焦两智能体图上的平均收益竞标博弈，分析对抗优化策略的互动，证明特定条件下博弈最终周期性并开发效用计算算法。
Convergence (virtual) bidding is an important part of two-settlement electric power markets as it can effectively reduce discrepancies between the day-ahead and real-time markets. Consequently, there is extensive research into the bidding strategies of virtual participants aiming to obtain optimal bids to submit to the day-ahead market. In this paper, we introduce a price-based general stochastic optimization framework to obtain optimal convergence bid curves. Within this framework, we develop a computationally tractable linear programming-based optimization model, which produces bid prices an…
Real-Time Bid Optimization for Group-Buying Ads
团购广告在交易到期前寻求最低数量的客户越来越多地被日常交易提供商使用。与传统的网络广告不同，团购广告的广告主的利润取决于到期时间和满足最小群体规模所需的额外客户。由于这两个数量都是时间依赖的，最佳出价金额，以最大限度地提高利润的变化与每一个印象。因此，传统的静态投标策略远非最优。相反，投标价值需要实时的优化，以最大化预期的投标人利润。这种交易利润的在线优化是由于提供实时的（现货）竞价的广告交易所的出现而成为可能。为此，我们提出了一种基于在线优化出价值的团购交易实时的出价策略。我们得到的预期投标人的利润的交易作为一个功能的出价金额，并动态地改变出价，以最大限度地提高利润。此外，为了满足时间约束的在线投标，我们提出的方法，最大限度地减少计算时间。随后，我们推导出传统广告的实时的广告选择，可接受性和实时的出价作为所提出的方法的特殊情况。我们评估建议的投标，选择和入场策略上的数百万点击流的935个广告。所提出的实时的投标，选择和受理显示显着的利润增加了现有的战略。进一步的实验说明了投标和可接受的计算时间的鲁棒性。
We consider the problem of optimal bidding for virtual trading in two-settlement electricity markets. A virtual trader aims to arbitrage on the differences between day-ahead and real-time market prices; both prices, however, are random and unknown to market participants. An online learning algorithm is proposed to maximize the cumulative payoff over a finite number of trading sessions by allocating the trader's budget among his bids for K options in each session. It is shown that the proposed algorithm converges, with an almost optimal convergence rate, to the global optimal corresponding to t…
Welfare and Rationality Guarantees for the Simultaneous Multiple-Round Ascending Auction
同步多轮拍卖（SMRA）和组合时钟拍卖（CCA）是用于出售带宽的两种主要机制。在真实投标下，SMRA输出瓦尔拉斯均衡，最大化社会福利提供投标人的估价函数满足总替代品属性。最近，它表明，组合时钟拍卖（CCA）提供了良好的福利保证一般类的估值函数。这引发了一个问题，即在一般估值职能的情况下，类似的福利保障是否适用于SMRA。我们的答案是否定的，但我们证明，良好的福利保障仍然会出现，如果在投标人的估值互补的程度是有界的。特别地，如果投标人估价函数是$α$ -近次模化的，则在真实投标下，SMRA具有至多为$(1+α)$的福利比率（最优分配的社会福利与拍卖分配的社会福利之间的最坏情况比率）。子模赋值的特殊情况，即$α=1$，并产生单独的合理的解决方案。然而，对于$α>1$来说，这是一个双准则保证，在真实投标下获得良好的福利需要放松个体理性。最后，我们研究需要什么策略，以确保个人的理性，在一般的评价功能的SMRA。首先，我们提供了一个弱的表征，即\emph{secure bidding}，为个人的理性。然后，我们表明，如果投标人使用利润最大化的安全投标策略的福利比是最多$1+α$。因此，通过安全投标，可以获得与真实投标相同的福利保障，而不会丧失个人理性。
C2:Cross learning module enhanced decision transformer with Constraint-aware loss for auto-bidding
C2通过交叉学习模块和约束感知损失改进决策变压器，以提升自动拍卖中的决策性能。
A dynamic pricing model for unifying programmatic guarantee and real-time bidding in display advertising
在展示广告中，有两种主要的展示方式。它们或者通过拍卖机制现货出售，或者通过担保合同提前出售。前者通过实时的【形】竞价（RTB）实现了显著的自动化;然而，后者仍然主要通过直接销售在柜台上完成。本文提出了一个数学模型，分配和价格之间的实时的【形】拍卖和保证合同的未来印象。在传统的经济假设下，我们的模型表明，这两种方式可以无缝结合编程和出版商的收入可以通过价格歧视和最优分配最大化。我们认为广告主是风险厌恶的，如果总成本低于他们的私人价值，他们会愿意购买有保证的印象。我们还认为，广告客户的购买行为可以同时受到保证价格和购买时间与印象交付日期之间的时间间隔的影响。我们的解决方案建议提前出售未来展示的最佳百分比，并提供一个明确的公式来计算以什么价格出售。我们发现最优保证价格是动态的，并且不随时间而减少。我们使用RTB数据集对我们的方法进行了评估，发现该模型根据竞争水平在分配和定价方面采取了不同的策略。从实验中我们发现，在一个竞争较少的市场，较低的价格的保证合同将鼓励提前购买，收入的增加主要是由未来RTB的竞争加剧。在竞争激烈的市场中，广告客户更愿意购买有保证的合同，因此预计价格会更高。收入增长主要来自保证销售。
The majority of online display ads are served through real-time bidding (RTB) --- each ad display impression is auctioned off in real-time when it is just being generated from a user visit. To place an ad automatically and optimally, it is critical for advertisers to devise a learning algorithm to cleverly bid an ad impression in real-time. Most previous works consider the bid decision as a static optimization problem of either treating the value of each impression independently or setting a bid price to each segment of ad volume. However, the bidding for a given ad campaign would repeatedly h…
Real-time bidding (RTB) based display advertising has become one of the key technological advances in computational advertising. RTB enables advertisers to buy individual ad impressions via an auction in real-time and facilitates the evaluation and the bidding of individual impressions across multiple advertisers. In RTB, the advertisers face three main challenges when optimizing their bidding strategies, namely (i) estimating the utility (e.g., conversions, clicks) of the ad impression, (ii) forecasting the market value (thus the cost) of the given ad impression, and (iii) deciding the optima…
This paper considers an electric vehicle charging scheduling setting where vehicle users can reserve charging time in advance at a charging station. In this setting, users are allowed to explicitly express their preferences over different start times and the length of charging periods for charging their vehicles. The goal is to compute optimal charging schedules which maximize the social welfare of all users given their time preferences and the state of charge of their vehicles. Assuming that users are self-interested agents who may behave strategically to advance their own benefits rather tha…
We introduce a new numerical framework to learn optimal bidding strategies in repeated auctions when the seller uses past bids to optimize her mechanism. Crucially, we do not assume that the bidders know what optimization mechanism is used by the seller. We recover essentially all state-of-the-art analytical results for the single-item framework derived previously in the setup where the bidder knows the optimization mechanism used by the seller and extend our approach to multi-item settings, in which no optimal shading strategies were previously known. Our approach yields substantial increases…
With the advent and increasing consolidation of e-commerce, digital advertising has very recently replaced traditional advertising as the main marketing force in the economy. In the past four years, a particularly important development in the digital advertising industry is the shift from second-price auctions to first-price auctions for online display ads. This shift immediately motivated the intellectually challenging question of how to bid in first-price auctions, because unlike in second-price auctions, bidding one's private value truthfully is no longer optimal. Following a series of rece…
Online Causal Inference for Advertising in Real-Time Bidding Auctions
本文针对实时竞价拍卖中的广告效果评估问题，提出基于最优出价识别的因果推断方法，并设计自适应汤普森采样算法在最小化实验成本的同时恢复广告效果，理论和实验均验证了其优越性。
In programmatic advertising, ad slots are usually sold using second-price (SP) auctions in real-time. The highest bidding advertiser wins but pays only the second-highest bid (known as the winning price). In SP, for a single item, the dominant strategy of each bidder is to bid the true value from the bidder's perspective. However, in a practical setting, with budget constraints, bidding the true value is a sub-optimal strategy. Hence, to devise an optimal bidding strategy, it is of utmost importance to learn the winning price distribution accurately. Moreover, a demand-side platform (DSP), whi…
In recent years, RTB(Real Time Bidding) becomes a popular online advertisement trading method. During the auction, each DSP(Demand Side Platform) is supposed to evaluate current opportunity and respond with an ad and corresponding bid price. It's essential for DSP to find an optimal ad selection and bid price determination strategy which maximizes revenue or performance under budget and ROI(Return On Investment) constraints in P4P(Pay For Performance) or P4U(Pay For Usage) mode. We solve this problem by 1) formalizing the DSP problem as a constrained optimization problem, 2) proposing the augm…
Vulnerabilities of Single-Round Incentive Compatibility in Auto-bidding: Theory and Evidence from ROI-Constrained Online Advertising Markets
本文研究 ROI 约束在线广告自动出价市场，证明第二价格拍卖的单轮 IC 存在计算困难、非单调、效用不稳和干扰 A/B 测试等缺陷。
Learning to Bid Optimally and Efficiently in Adversarial First-price Auctions
针对首价拍卖中投标人面临的最优出价问题，提出首个极小极大最优在线出价算法，实现$\widetilde{O}(\sqrt{T})$遗憾，并通过层次化专家链结构改进为计算高效版本，在真实数据集上验证了优越性能。
In this paper, we analyze a natural learning algorithm for uniform pacing of advertising budgets, equipped to adapt to varying ad sale platform conditions. On the demand side, advertisers face a fundamental technical challenge in automating bidding in a way that spreads their allotted budget across a given campaign subject to hidden, and potentially dynamic, cost functions. This automation and calculation must be done in runtime, implying a necessarily low computational cost for the high frequency auction rate. Advertisers are additionally expected to exhaust nearly all of their sub-interval (…
This research focuses on the bid optimization problem in the real-time bidding setting for online display advertisements, where an advertiser, or the advertiser's agent, has access to the features of the website visitor and the type of ad slots, to decide the optimal bid prices given a predetermined total advertisement budget. We propose a risk-aware data-driven bid optimization model that maximizes the expected profit for the advertiser by exploiting historical data to design upfront a bidding policy, mapping the type of advertisement opportunity to a bid price, and accounting for the risk of…
Bidding in real-time auctions can be a difficult stochastic control task; especially if underdelivery incurs strong penalties and the market is very uncertain. Most current works and implementations focus on optimally delivering a campaign given a reasonable forecast of the market. Practical implementations have a feedback loop to adjust and be robust to forecasting errors, but no implementation, to the best of our knowledge, uses a model of market risk and actively anticipates market shifts. Solving such stochastic control problems in practice is actually very challenging. This paper proposes…
Bid optimization for online advertising from single advertiser's perspective has been thoroughly investigated in both academic research and industrial practice. However, existing work typically assume competitors do not change their bids, i.e., the wining price is fixed, leading to poor performance of the derived solution. Although a few studies use multi-agent reinforcement learning to set up a cooperative game, they still suffer the following drawbacks: (1) They fail to avoid collusion solutions where all the advertisers involved in an auction collude to bid an extremely low price on purpose…
Real-time Bidding for Online Advertising: Measurement and Analysis
实时的【形】竞价（RTB），也就是程序化购买，最近已经成为在线广告中增长最快的领域。RTB不是批量购买和以库存为中心的购买，而是模仿证券交易所，利用计算机算法自动实时的【形】买卖广告;它使用每个印象上下文，并根据有关他们的数据将广告定位于特定人群，从而大大提高了显示广告的有效性。在本文中，我们提供了一个生产广告交易的实证分析和测量。利用从需求和供应两方面采样的数据，我们旨在提供对新兴的印象销售基础设施及其竞标行为的第一手见解，并帮助识别此类系统中的研究和设计问题。从我们的研究中，我们观察到周期性模式出现在各种统计数据中，包括展示，点击，出价和转化率（查看后和点击后），这表明时间依赖模型适用于捕捉RTB中的重复模式。我们还发现，尽管声称的第二价格拍卖，第一价格支付实际上是占总成本的55.4%，由于软地板价格的安排。因此，我们认为，在目前的RTB系统中设置软底价使广告客户处于不利地位。此外，我们对会话率的分析表明，目前的出价策略远不如最佳，这表明对优化算法的重大需求，这些算法将诸如广告显示的时间行为、频率和新近度等事实结合起来，这些事实在过去没有得到很好的考虑。
Learning against Non-credible Auctions
本文研究非可信重复第二价格拍卖中的在线竞价问题，竞价者需同时学习竞争对手出价分布与卖家可信度，作者在多种信息模型下建立遗憾下界并提供近最优的在线竞价算法。
Online Bidding Algorithms with Strict Return on Spend (ROS) Constraint
本文研究严格ROSC约束下的自动竞价问题，证明即使i.i.d.环境下在线算法也无法实现次线性遗憾，并给出价值恒定时对数最优遗憾的算法。
Cost-Control in Display Advertising: Theory vs Practice
针对展示广告对偶出价中成本约束仅渐近收敛导致成本控制失效的问题，本文修改最优出价公式，并通过真实数据大规模评估证明其可将成本违规降低50%。
A Negotiator's Backup Plan: Optimal Concessions with a Reservation Value
本文针对具有私有保留值的双边自动谈判，提出名为 MIA-RVelous 的最优出价策略，通过贪心算法在 O(n²D) 时间内求解最优出价序列，并指出该结果有助于利用并发谈判作为概率性后备计划。
Guiding the Recommender: Information-Aware Auto-Bidding for Content Promotion
本文提出了一种信息感知的自动出价方法，通过双目标优化平衡短期价值与长期模型改进，提升内容推广效果和长期推荐质量。
Displaying banner advertisements (in short, ads) on webpages has usually been discussed as an Internet economics topic where a publisher uses auction models to sell an online user's page view to advertisers and the one with the highest bid can have her ad displayed to the user. This is also called \emph{real-time bidding} (RTB) and the ad displaying process ensures that the publisher's benefit is maximized or there is an equilibrium in ad auctions. However, the benefits of the other two stakeholders -- the advertiser and the user -- have been rarely discussed. In this paper, we propose a two-s…
High-dimensional Bid Learning for Energy Storage Bidding in Energy Markets
针对现有方法无法充分利用能源市场高维报价的问题，提出神经网络嵌入报价的强化学习方法，通过策略网络训练、单调离散调整及等价转换实现高维报价学习，在真实数据集上收益较基线提升18%。
While it is relatively easy to start an online advertising campaign, obtaining a high Key Performance Indicator (KPI) can be challenging. A large body of work on this subject has already been performed and platforms known as DSPs are available on the market that deal with such an optimization. From the advertiser's point of view, each DSP is a different black box, with its pros and cons, that needs to be configured. In order to take advantage of the pros of every DSP, advertisers are well-advised to use a combination of them when setting up their campaigns. In this paper, we propose an algorit…
In online display advertising, guaranteed contracts and real-time bidding (RTB) are two major ways to sell impressions for a publisher. For large publishers, simultaneously selling impressions through both guaranteed contracts and in-house RTB has become a popular choice. Generally speaking, a publisher needs to derive an impression allocation strategy between guaranteed contracts and RTB to maximize its overall outcome (e.g., revenue and/or impression quality). However, deriving the optimal strategy is not a trivial task, e.g., the strategy should encourage incentive compatibility in RTB and …
In online display advertising, guaranteed contracts and real-time bidding (RTB) are two major ways to sell impressions for a publisher. Despite the increasing popularity of RTB, there is still half of online display advertising revenue generated from guaranteed contracts. Therefore, simultaneously selling impressions through both guaranteed contracts and RTB is a straightforward choice for a publisher to maximize its yield. However, deriving the optimal strategy to allocate impressions is not a trivial task, especially when the environment is unstable in real-world applications. In this paper,…
Learning Safe Strategies for Value Maximizing Buyers in Uniform Price Auctions
针对重复统一价格多单位拍卖中价值最大化买家的RoI约束出价问题，提出安全出价策略概念及多项式时间学习算法，实现次线性遗憾且可推广至更复杂模型。
Dynamic Resource Allocation with Karma: An Experimental Study
通过行为实验验证Karma机制在重复资源分配中的公平与效率，发现尽管人类行为偏离理论最优，Karma仍实现帕累托改进，为实际应用提供稳健性能下界。
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