Nonlinear Kalman Filtering with Reparametrization Gradients

We introduce a novel nonlinear Kalman filter that utilizes reparametrization gradients. The widely used parametric approximation is based on a jointly Gaussian assumption of the state-space model, which is in turn equivalent to minimizing an approximation to the Kullback-Leibler divergence. It is possible to obtain better approximations using the alpha divergence, but the resulting problem is substantially more complex. In this paper, we introduce an alternate formulation based on an energy function, which can be optimized instead of the alpha divergence. The optimization can be carried out using reparametrization gradients, a technique that has recently been utilized in a number of deep learning models.

An Efficient Deep Distribution Network for Bid Shading in First-Price Auctions

Since 2019, most ad exchanges and sell-side platforms (SSPs), in the online advertising industry, shifted from second to first price auctions. Due to the fundamental difference between these auctions, demand-side platforms (DSPs) have had to update their bidding strategies to avoid bidding unnecessarily high and hence overpaying. Bid shading was proposed to adjust the bid price intended for second-price auctions, in order to balance cost and winning probability in a first-price auction setup. In this study, we introduce a novel deep distribution network for optimal bidding in both open (non-censored) and closed (censored) online first-price auctions. Offline and online A/B testing results show that our algorithm outperforms previous state-of-art algorithms in terms of both surplus and effective cost per action (eCPX) metrics. Furthermore, the algorithm is optimized in run-time and has been deployed into VerizonMedia DSP as production algorithm, serving hundreds of billions of bid requests per day. Online A/B test shows that advertiser's ROI are improved by +2.4%, +2.4%, and +8.6% for impression based (CPM), click based (CPC), and conversion based (CPA) campaigns respectively.

Bid Shading by Win-Rate Estimation and Surplus Maximization

This paper describes a new win-rate based bid shading algorithm (WR) that does not rely on the minimum-bid-to-win feedback from a Sell-Side Platform (SSP). The method uses a modified logistic regression to predict the profit from each possible shaded bid price. The function form allows fast maximization at run-time, a key requirement for Real-Time Bidding (RTB) systems. We report production results from this method along with several other algorithms. We found that bid shading, in general, can deliver significant value to advertisers, reducing price per impression to about 55% of the unshaded cost. Further, the particular approach described in this paper captures 7% more profit for advertisers, than do benchmark methods of just bidding the most probable winning price. We also report 4.3% higher surplus than an industry Sell-Side Platform shading service. Furthermore, we observed 3% - 7% lower eCPM, eCPC and eCPA when the algorithm was integrated with budget controllers. We attribute the gains above as being mainly due to the explicit maximization of the surplus function, and note that other algorithms can take advantage of this same approach.

Bid Shading in The Brave New World of First-Price Auctions

Online auctions play a central role in online advertising, and are one of the main reasons for the industry's scalability and growth. With great changes in how auctions are being organized, such as changing the second- to first-price auction type, advertisers and demand platforms are compelled to adapt to a new volatile environment. Bid shading is a known technique for preventing overpaying in auction systems that can help maintain the strategy equilibrium in first-price auctions, tackling one of its greatest drawbacks. In this study, we propose a machine learning approach of modeling optimal bid shading for non-censored online first-price ad auctions. We clearly motivate the approach and extensively evaluate it in both offline and online settings on a major demand side platform. The results demonstrate the superiority and robustness of the new approach as compared to the existing approaches across a range of performance metrics.