An expected win rate-based real-time bidding strategy for branding campaigns on display advertising

Abstract

For branding campaigns, the demand-side platforms (DSPs) in real-time bidding (RTB) usually need to win as many impressions as possible to inform most audiences about the product messages under constraints on budgets, campaign lifetimes and budget spending plans. In this paper, we propose a novel bidding strategy by introducing the concept of expected win rate. With the proposed expected win rate-based bidding strategy, the DSP can dynamically adjust the expected win rate for each incoming bid request based on factors such as the predicted number of bid requests in the near future, the remaining budget and the remaining lifetime of the campaign. The experimental results show that the proposed bidding strategy has a lower cost per thousand impressions and cost per clicks than existing pacing model-based bidding strategies for branding campaigns with the same budgets and budget spending plans.

Appendices

Appendix A: EWR algorithm

Algorithm 1 shows the details of the proposed bidding strategy. In the off-line initialization, the DSPs can averagely allocate the total budget to each time slot, or based on some phenomena, such as request flow of each time slot, to assign different budgets to different time slots. As mentioned in Sect. 4.1, the pacing rate for each time slot, $p\_r_t$, is set to the highest of the possible values to obtain the most opportunities to win impressions. In line 7, the request flow of the first time slot is predicted, and the flow prediction will continue updating to make a more precise prediction for the remaining time slots. Then, the bid function is established according to the historical bidding records (line 8), and the details of the bid function establishment are shown in Algorithm 3, where R represents the historical bidding records. In Algorithm 3, the optimized $\beta$ can be obtained by stochastic gradient descent (SGD) or other online learning methods. From lines 12 to 15, the approximation models, $\delta _3(\cdot , \cdot )$ and $\delta '_4(\cdot )$, are also trained based on the historical winning bids.

In the online bidding, when a new bid request arrives, the algorithm checks whether the current time slot has expired (line 20). If the current time slot has not expired, the steps described in the next paragraph are performed to determine the bid price of the incoming bid request. Otherwise, a new time slot begins, and the following steps are executed before the bid price determination. First, the models of the request flow prediction and the bid function of the new time slot are updated by the bidding records of the previous time slot (lines 21 and 22). Then, from lines 24 to 30, the remaining budget and the difference between the bid price and the winning price are updated. Additionally, the request flow in the new time slot is predicted. Finally, the buffers to store the bidding records, such as the bidding results in the new time slot, are also reinitialized (lines 33 and 35) for collecting new bidding records.

In bid price determination, based on the features of the incoming bid request and the current remaining resources, the expected win rate for this bid request is calculated in line 36. The details of the expected win rate calculation are shown in Algorithm 2. To raise the expected win rate (Eq. 22), the CTR can be estimated according to the methods proposed in prior studies on performance prediction [5, 13, 17, 21, 28], and $\alpha$ can be tuned based on historical data. With the expected win rate, the bid price is determined from lines 37 to 39, where $\tau$ is a bid price threshold to prevent overspending the budget, as shown in Eq. (1). If the remaining budget is less than the bid price, the request will be directly dropped or bid with the lowest price allowed by the ad exchange. (An ad exchange may ask all DSPs to submit their bid prices with no less than a minimal bid price for all bid requests.) Lines 41 to 51 address the returned bidding result. If the bid strategy wins the bid request, the remaining budget should be updated by the returned winning price of bid request $x_j$, $WP_j$.

Appendix B: Validation results

See Tables 5, 6, 7, 8 and 9.

Table 5 Parameter tuning for EWR

Table 6 Layer tuning for smart pacing on iPinYou campaign 3386

Table 7 Layer tuning for smart pacing on iPinYou campaign 1458

Table 8 Layer tuning for smart pacing on Tenmax campaign 215

Table 9 Budget spending rate by different layers on Tenmax campaign 215