TL;DR,

# 摘要

Real-Time Bidding (RTB) is an important paradigm in display advertising, where advertisers utilize extended information and algorithms served by Demand Side Platforms (DSPs) to improve advertising performance. A common problem for DSPs is to help advertisers gain as much value as possible with budget constraints. However, advertisers would routinely add certain key performance indicator (KPI) constraints that the advertising campaign must meet due to practical reasons. In this paper, we study the common case where advertisers aim to maximize the quantity of conversions, and set cost-per-click (CPC) as a KPI constraint. We convert such a problem into a linear programming problem and leverage the primal-dual method to derive the optimal bidding strategy. To address the applicability issue, we propose a feedback control-based solution and devise the multivariable control system. The empirical study based on real-world data from Taobao.com verifies the effectiveness and superiority of our approach compared with the state of the art in the industry practices.

DSP的一个常见问题是帮助广告主在预算约束下获得尽可能多的价值。现实情况中，广告主也会为广告计划增加一些KPI约束。

# 解决方法

1. 点击的出价，线性正比于转化率
2. 点击出价的线会过两点，如下图所示，$(p\cdot C, C)$$(-q\cdot C, 0)$
3. 并不过原点，也好理解，在单位点击成本约束下，如果我们想对高转化的商品出更高的价格，必然需要用较少的出价来竞得一些“垃圾”流量