Learning Economic Parameters from Revealed Preferences

A recent line of work, starting with Beigman and Vohra (2006) and Zadimoghaddam and Roth (2012), has addressed the problem of {\em learning} a utility function from revealed preference data. The goal here is to make use of past data describing the purchases of a utility maximizing agent when faced with certain prices and budget constraints in order to produce a hypothesis function that can accurately forecast the {\em future} behavior of the agent. In this work we advance this line of work by providing sample complexity guarantees and efficient algorithms for a number of important classes. By drawing a connection to recent advances in multi-class learning, we provide a computationally efficient algorithm with tight sample complexity guarantees ($\Theta(d/\epsilon)$ for the case of $d$ goods) for learning linear utility functions under a linear price model. This solves an open question in Zadimoghaddam and Roth (2012). Our technique yields numerous generalizations including the ability to learn other well-studied classes of utility functions, to deal with a misspecified model, and with non-linear prices

Social welfare and profit maximization from revealed preferences

Consider the seller's problem of finding optimal prices for her $n$ (divisible) goods when faced with a set of $m$ consumers, given that she can only observe their purchased bundles at posted prices, i.e., revealed preferences. We study both social welfare and profit maximization with revealed preferences. Although social welfare maximization is a seemingly non-convex optimization problem in prices, we show that (i) it can be reduced to a dual convex optimization problem in prices, and (ii) the revealed preferences can be interpreted as supergradients of the concave conjugate of valuation, with which subgradients of the dual function can be computed. We thereby obtain a simple subgradient-based algorithm for strongly concave valuations and convex cost, with query complexity $O(m^2/\epsilon^2)$, where $\epsilon$ is the additive difference between the social welfare induced by our algorithm and the optimum social welfare. We also study social welfare maximization under the online setting, specifically the random permutation model, where consumers arrive one-by-one in a random order. For the case where consumer valuations can be arbitrary continuous functions, we propose a price posting mechanism that achieves an expected social welfare up to an additive factor of $O(\sqrt{mn})$ from the maximum social welfare. Finally, for profit maximization (which may be non-convex in simple cases), we give nearly matching upper and lower bounds on the query complexity for separable valuations and cost (i.e., each good can be treated independently)

Cooperative weakest link games

We introduce Weakest Link Games (WLGs), a cooperative game modeling domains where a team's value is determined by its weakest member. The game is represented as an edge-weighted graph with designated source and target vertices, where agents are the edges. The quality of a path between the source vertex and target vertex is the minimal edge weight along the path; the value of a coalition of edges is the quality of the best path contained in the coalition, and zero if the coalition contains no such path. WLGs model joint projects where the overall achievement depends on the weakest component, such as multiple-option package deals, or transport domains where each road has a different allowable maximum load. We provide methods for computing revenue sharing solutions in WLGs, including polynomial algorithms for calculating the value of a coalition, the core, and the least-core. We also examine optimal team formation in WLGs. Though we show that finding the optimal coalition structure is NP-hard, we provide an O(log n)-approximation. Finally, we examine the agents' resistance to cooperation through the Cost of Stability

Optimal-time adaptive strong renaming, with applications to counting

10.1145/1993806.1993850Proceedings of the Annual ACM Symposium on Principles of Distributed Computing239-24885LR