Real-time bidding (RTB) has achieved great success and significantly improved the efficiency and transparency of online advertising. It allows advertisers to purchase ad impressions via auctions. Advertisers who adopt RTB always seek an optimal strategy of budget spending to reach as a wider range of audiences with a more sustainable impact as possible. Traditional bidding strategies, such as fixed bid and performance-based bid, easily lead to being either too aggressive (budgets wiped out too fast) or conservative (budget surplus exists at the end with low clicks), due to lack of optimal budget management. In this paper, we study the optimization of budget efficiency under the smooth delivery constraint for display advertising. We model the problem as a multi-constrained budget allocation optimization and use a heuristic algorithm to solve an approximate optimal budget allocation. The key to the solution is to determine the bidding function for each time slot. Here, we propose a piecewise bidding strategy to filter out the lowquality impressions, where each time slot has its own predicted click-through rate (pCTR) threshold-only when the pCTR of an impression is not lower than the threshold, will the campaign participate in the bidding. However, determining the pCTR threshold is challenging due to market uncertainty, we tackle this problem by modeling the distributions of pCTRs and market prices in each time slot. On this basis, we derive an optimal bidding function for each time slot to make the bid price more adaptable to its available budget. We conduct our experiments on a public real-world dataset and the results show that our proposed method performs the best in terms of various standard metrics (e.g., the number of clicks, cost-per-click) under a given budget comparing to the state-of-the-art baselines.
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