观看并学习：根据显示的偏好反馈进行优化
Watch and Learn: Optimizing from Revealed Preferences Feedback
摘要：
Stackelberg博弈是领导者和追随者之间的博弈。领导者首先选择一个行动，然后跟随者采取他的最佳对策。领导者的目标是在追随者给出最佳对策的情况下，选择能使他的收益最大化的行动。在本文中，我们提出了一种方法来解决领导者的最优策略，在某些Stackelberg游戏的追随者的效用函数（从而随后的最佳反应的追随者）是未知的。例如，Stackelberg博弈捕捉了生产者和消费者之间的以下互动。生产者选择他生产的商品的价格，然后消费者选择购买效用最大化的一捆商品。在这里，卖方的目标是设定价格，使他的利润最大化-他的收入，减去购买捆绑产品的生产成本。很自然，在这个例子中，卖方不应该知道买方的效用函数。然而，他确实可以获得显示的偏好反馈-他可以设定价格，然后观察购买的捆绑包和他自己的利润。我们给出了算法有效地解决，在计算和查询的复杂性，广泛的一类Stackelberg游戏中，追随者的效用函数是未知的，只使用“显示偏好”访问它。这类包括特别是利润最大化问题，以及最佳收费问题在非原子拥塞游戏，当延迟函数是未知的。令人惊讶的是，我们能够解决这些问题，即使优化问题是非凸的领导者的行动。
英文摘要：
A Stackelberg game is played between a leader and a follower. The leader first chooses an action, then the follower plays his best response. The goal of the leader is to pick the action that will maximize his payoff given the follower's best response. In this paper we present an approach to solving for the leader's optimal strategy in certain Stackelberg games where the follower's utility function (and thus the subsequent best response of the follower) is unknown. Stackelberg games capture, for example, the following interaction between a producer and a consumer. The producer chooses the prices of the goods he produces, and then a consumer chooses to buy a utility maximizing bundle of goods. The goal of the seller here is to set prices to maximize his profit---his revenue, minus the production cost of the purchased bundle. It is quite natural that the seller in this example should not know the buyer's utility function. However, he does have access to revealed preference feedback---he can set prices, and then observe the purchased bundle and his own profit. We give algorithms for efficiently solving, in terms of both computational and query complexity, a broad class of Stackelberg games in which the follower's utility function is unknown, using only "revealed preference" access to it. This class includes in particular the profit maximization problem, as well as the optimal tolling problem in nonatomic congestion games, when the latency functions are unknown. Surprisingly, we are able to solve these problems even though the optimization problems are non-convex in the leader's actions.
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。
