安全在线竞价优化与投资回报及预算约束
Safe Online Bid Optimization with Return on Investment and Budget Constraints
AI总结：
本文提出GCB_safe算法，在保证投资回报和预算约束安全的同时，通过容忍度ψ和ϕ实现子线性遗憾和线性约束违反。
摘要：
在在线营销中，广告商旨在平衡实现高成交量和高盈利能力。公司的业务单元通过在保证最低投资回报率（ROI）水平的同时最大化成交量来解决这一权衡问题。此类任务可以自然地建模为一个带有ROI和预算约束的组合优化问题，该问题可以在线解决。在这种情况下，学习者对约束参数的不确定性起着关键作用，因为算法的探索选择可能导致在学习过程中违反这些约束。此类违反行为是采用在线技术在现实应用中面临的主要障碍。因此，在学习过程中控制算法的探索至关重要，以使人类信任在线学习工具。本文研究了优化和学习问题的本质。特别是，我们证明了学习问题在任何因子下都是近似不可行的（除非P=NP），并提供了一个伪多项式时间算法来解决其离散化版本。随后，我们证明了没有任何在线学习算法可以在学习过程中保证子线性遗憾的同时，仅违反（ROI或预算）约束的子线性次数。我们提供了GCB算法，该算法以线性数量的约束违反为代价保证子线性遗憾，并提供了GCB_safe算法，该算法以线性遗憾为代价保证以高概率保证约束违反次数的常数上界。此外，我们设计了GCB_safe(ψ,ϕ)，该算法以接受ROI和预算约束满足的容忍度ψ和ϕ为代价，保证了子线性遗憾和安全性。最后，我们提供了实验结果，以比较GCB、GCB_safe和GCB_safe(ψ,ϕ)的遗憾和约束违反情况。
英文摘要：
In online marketing, the advertisers aim to balance achieving high volumes and high profitability. The companies' business units address this tradeoff by maximizing the volumes while guaranteeing a minimum Return On Investment (ROI) level. Such a task can be naturally modeled as a combinatorial optimization problem subject to ROI and budget constraints that can be solved online. In this picture, the learner's uncertainty over the constraints' parameters plays a crucial role since the algorithms' exploration choices might lead to their violation during the entire learning process. Such violations represent a major obstacle to adopting online techniques in real-world applications. Thus, controlling the algorithms' exploration during learning is paramount to making humans trust online learning tools. This paper studies the nature of both optimization and learning problems. In particular, we show that the learning problem is inapproximable within any factor (unless P = NP) and provide a pseudo-polynomial-time algorithm to solve its discretized version. Subsequently, we prove that no online learning algorithm can violate the (ROI or budget) constraints a sublinear number of times during the learning process while guaranteeing a sublinear regret. We provide the $GCB$ algorithm that guarantees sublinear regret at the cost of a linear number of constraint violations and $GCB_{safe}$ that guarantees w.h.p. a constant upper bound on the number of constraint violations at the cost of a linear regret. Moreover, we designed $GCB_{safe}(ψ,ϕ)$, which guarantees both sublinear regret and safety w.h.p. at the cost of accepting tolerances $ψ$ and $ϕ$ in the satisfaction of the ROI and budget constraints, respectively. Finally, we provide experimental results to compare the regret and constraint violations of $GCB$, $GCB_{safe}$, and $GCB_{safe}(ψ,ϕ)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
