扩散，然后目标，再宣传：在波浪中优化广告渠道预算分配
Spread, then Target, and Advertise in Waves: Optimal Budget Allocation Across Advertising Channels
AI总结：
本文研究了在有限预算下如何优化广告渠道分配，通过波浪式投放最大努力，随后停止以让影响传播，同时强调在选举前夕应投资于能精准定位个体的渠道。
摘要：
我们分析了在有限预算下如何在不同广告渠道上分配资源，以影响网络中个体的社会意见。我们考虑了外生影响机制（如广告活动）和内生影响机制（如口碑和同伴压力），并使用扩散动力学建模。我们证明，对于广泛的目标函数家族，最优影响策略在每个时间点使用所有渠道的最大速率或完全不使用，即bang-bang策略。此外，我们证明在这些极端之间切换的次数上限通常远小于个体数量。这意味着最优影响策略是每个渠道在波浪中施加最大努力，然后停止以让影响传播。我们还表明，在活动开始时，外生广告渠道的总成本调整覆盖量决定了其相对价值。相反，随着接近投资期限（如选举日），最优策略是投资于能精准定位个体的渠道而非广泛覆盖的渠道。我们证明在多个实际案例中，最优影响策略易于计算，并明确刻画了线性目标函数的最优控制。最后，我们看到在选举活动的典型例子中，识别后期决定者是优化设计的关键组成部分。
英文摘要：
We analyze optimal strategies for the allocation of a finite budget that can be invested in different advertising channels over time with the objective of influencing social opinions in a network of individuals. In our analysis, we consider both exogenous influence mechanisms, such as advertising campaigns, as well as endogenous mechanisms of social influence, such as word-of-mouth and peer-pressure, which are modeled using diffusion dynamics. We show that for a broad family of objective functions, the optimal influence strategy at every time uses all channels at either their maximum rate or not at all, i.e., a bang-bang strategy. Furthermore, we prove that the number of switches between these extremes is bounded above by a term that is typically much smaller than the number of agents. This means that the optimal influence strategy is to exert maximum effort in waves for every channel, and then cease effort and let the effects propagate. We also show that, at the beginning of the campaign, the total cost-adjusted reach of an exogenous advertising channel determines its relative value. In contrast, as we approach our investment horizon (e.g., election day), the optimal strategy is to invest in channels able to target individuals instead of broad-reaching channels. We demonstrate that the optimal influence strategies are easily computable in several practical cases, and explicitly characterize the optimal controls for the case of linear objective functions in closed form. Finally, we see that, in the canonical example of designing an election campaign, identifying late-deciders is a critical component in the optimal design.
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。
