The emergence of real-time auction in online advertising has drawn huge attention of modeling the market competition, i.e., bid landscape forecasting. The problem is formulated as to forecast the probability distribution of market price for each ad auction. With the consideration of the censorship issue which is caused by the second-price auction mechanism, many researchers have devoted their efforts on bid landscape forecasting by incorporating survival analysis from medical research field. However, most existing solutions mainly focus on either counting-based statistics of the segmented sample clusters, or learning a parameterized model based on some heuristic assumptions of distribution forms. Moreover, they neither consider the sequential patterns of the feature over the price space. In order to capture more sophisticated yet flexible patterns at fine-grained level of the data, we propose a Deep Landscape Forecasting (DLF) model which combines deep learning for probability distribution forecasting and survival analysis for censorship handling. Specifically, we utilize a recurrent neural network to flexibly model the conditional winning probability w.r.t. each bid price. Then we conduct the bid landscape forecasting through probability chain rule with strict mathematical derivations. And, in an end-to-end manner, we optimize the model by minimizing two negative likelihood losses with comprehensive motivations. Without any specific assumption for the distribution form of bid landscape, our model shows great advantages over previous works on fitting various sophisticated market price distributions. In the experiments over two large-scale real-world datasets, our model significantly outperforms the state-of-the-art solutions under various metrics.
In the view of distribution modeling methods, there are two phases. In the early phase, researchers proposed several heuristic forms of functions to model the market price distribution. In @cite_7 @cite_32 @cite_1 , the authors provided some analytic forms of winning probability w.r.t. the bid price applied on the campaign level, which is based on the observation of the winning logs. Later in the recent researches, some well-studied distributions are applied in market price modeling. presented a log-normal distribution to model the market price ground truth. proposed a regression model based on Gaussian distribution to fit the market price. Recently, Gamma distribution for market price modeling has also been studied in the work @cite_18 . The main drawback of these distributional methods is that these restricted empirical preassumptions may lose the effectiveness of handling various dynamic data and they even ignore the sophisticated real data divergence as we show in Figure .
@cite_18 @cite_1 @cite_32 @cite_7
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In Real-Time Bidding (RTB) advertising, estimating the winning price is an important task in evaluating the bid cost of bid requests in Demand-Side Platforms (DSPs). The prior works utilize censored linear regression for winning price estimation by considering both winning and losing bid records. In the traditional regression models, the winning price of each bid request is based on Gaussian distribution. However, the property of Gaussian distribution is not suitable for the winning price of each bid request, and it is hard to link the physical meaning of Gaussian distribution and the winning price. Therefore, in this paper, based on our observation and analysis, the winning price of each bid request is modeled by a unique gamma distribution with respect to its features. Then we propose a gamma-based censored linear regression with regularization for winning price estimation. To derive the parameters of our proposed complicated model based on bid records, our approach is to divide this hard problem into two sub-problems, which are easier to solve. In practice, we also provide four heuristic initial parameter settings that are able to greatly reduce the computation cost when deriving the parameters. The experimental results demonstrate that our approach is highly effective for estimating the winning price compared with the state-of-the-art approaches in three real datasets. Abstract This paper proposes a stochastic and dynamic mixed-integer linear program (SD-MILP) for optimal coordinated bidding of a risk-averse profit-maximizing hydropower producer. The day-ahead, intra-day, and real-time markets are considered. To model and predict day-ahead, intra-day, and real-time prices, the Holt–Winter (HW) and the Generalized Autoregressive Conditional Heteroscedastic (GARCH) predictors are combined using a proposed Markov switch. The discrete behavior of intra-day and real-time prices is modeled as different Markov states. The proposed Markov-based HW–GARCH model with a standard scenario generation-reduction technique is used to capture the uncertainty in day-ahead, intra-day, and real-time prices. The time-dependent conditional value at risk (T-CVaR) is proposed to model the risk of trading in different considered markets. The convex combination of the expected profit and T-CVaR is used as the objective of SD-MILP. The Markov-based HW–GARCH is modeled in Matlab and the SD-MILP is coded in GAMS. The Markov-based HW–GARCH predictor and the SD-MILP are used to develop the bidding curve of a three-reservoir hydropower producer using the electricity prices from the Nordic power market. To further examine the developed models a seven-reservoir hydropower producer is also studied. For these two cases, the coordinated bidding curves are derived and discussed. We consider a dynamic auction model, where bidders sequentially arrive to the market. The values of the bidders for the item for sale are independently drawn from a distribution, but this distribution is unknown to the seller. The seller offers a personalized take-it-or-leave-it price for each arriving bidder and aims to maximize revenue. We study how well can such sequential posted-price mechanisms approximate the optimal revenue that would be achieved if the distribution was known to the seller. On the negative side, we show that sequential posted-price mechanisms cannot guarantee a constant fraction of this revenue when the class of candidate distributions is unrestricted. We show that this impossibility holds even for randomized mechanisms and even if the set of possible distributions is very small or when the seller has a prior distribution over the candidate distributions. On the positive side, we devise a simple posted-price mechanism that guarantees a constant fraction of the known-distribution revenue when all candidate distributions exhibit the monotone hazard rate property. Real-time auction has become an important online advertising trading mechanism. A crucial issue for advertisers is to model the market competition, i.e., bid landscape forecasting. It is formulated as predicting the market price distribution for each ad auction provided by its side information. Existing solutions mainly focus on parameterized heuristic forms of the market price distribution and learn the parameters to fit the data. In this paper, we present a functional bid landscape forecasting method to automatically learn the function mapping from each ad auction features to the market price distribution without any assumption about the functional form. Specifically, to deal with the categorical feature input, we propose a novel decision tree model with a node splitting scheme by attribute value clustering. Furthermore, to deal with the problem of right-censored market price observations, we propose to incorporate a survival model into tree learning and prediction, which largely reduces the model bias. The experiments on real-world data demonstrate that our models achieve substantial performance gains over previous work in various metrics. The software related to this paper is available at https: github.com zeromike bid-lands.