Online Learning and Profit Maximization from Revealed Preferences

Abstract

We consider the problem of learning from revealed preferences in an online setting. In our framework, each period a consumer buys an optimal bundle of goods from a merchant according to her (linear) utility function and current prices, subject to a budget constraint. The merchant observes only the purchased goods, and seeks to adapt prices to optimize his profits. We give an efficient algorithm for the merchant's problem that consists of a learning phase in which the consumer's utility function is (perhaps partially) inferred, followed by a price optimization step. We also give an alternative online learning algorithm for the setting where prices are set exogenously, but the merchant would still like to predict the bundle that will be bought by the consumer, for purposes of inventory or supply chain management. In contrast with most prior work on the revealed preferences problem, we demonstrate that by making stronger assumptions on the form of utility functions, efficient algorithms for both learning and profit maximization are possible, even in adaptive, online settings.

How Can a Cognitive Radar Mask its Cognition?

“…Several works in literature [17], [18], [19] highlight how an adversary benefits from learning the radar's utility function. In [17], the adversary optimize its probes to increase the power of its statistical hypothesis test for utility maximization.…”

“…In [17], the adversary optimize its probes to increase the power of its statistical hypothesis test for utility maximization. [18], [19] show how revealed preference-based IRL techniques can be used to manipulate consumer behavior.…”

Learning Market Parameters Using Aggregate Demand Queries

“…Recently, Balcan et al (2014) gave efficient learning algorithms for a general class of utility functions including linear, separable piecewise linear concave, and Leontief. Amin et al (2015) propose efficient algorithms for a profit maximization problem of a merchant that queries a single buyer with a linear utility function. In another related work, Roth, Ullman, and Wu (2015) study profit maximization of a leader in a Stackelberg game when the follower's utility function is unknown.…”

“…Clearly, once these are determined, a variety of different objectives can be considered for optimization. For example, one can construct online learning scenarios using our algorithms for linear utilities similar as in (Amin et al 2015).…”

“…The goal is to explain the observed behavior using a suitable model for their utility function and to predict future agent behavior. More recent work has also studied different goals of the learner, such as revenue maximization (see, e.g., (Amin et al 2015;Roth, Ullman, and Wu 2015) and our discussion of related…”