The first-order approach to moral hazard problems with hidden saving

This paper proposes a general method to validate the first-order approach for moral hazard problems with hidden saving. I show that strong convexity assumptions both on the agent’s marginal utility of consumption and the distribution function of output arise naturally in this context. The first-order approach is valid given nonincreasing absolute risk aversion (NIARA) utility and log-convex distribution functions (LCDF) with monotone likelihood ratios (MLR). In a second step, I relax the LCDF condition by restricting the class of preferences and by imposing more structure on optimal wage schemes

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

Energy Harvesting Networks with General Utility Functions: Near Optimal Online Policies

We consider online scheduling policies for single-user energy harvesting communication systems, where the goal is to characterize online policies that maximize the long term average utility, for some general concave and monotonically increasing utility function. In our setting, the transmitter relies on energy harvested from nature to send its messages to the receiver, and is equipped with a finite-sized battery to store its energy. Energy packets are independent and identically distributed (i.i.d.) over time slots, and are revealed causally to the transmitter. Only the average arrival rate is known a priori. We first characterize the optimal solution for the case of Bernoulli arrivals. Then, for general i.i.d. arrivals, we first show that fixed fraction policies [Shaviv-Ozgur] are within a constant multiplicative gap from the optimal solution for all energy arrivals and battery sizes. We then derive a set of sufficient conditions on the utility function to guarantee that fixed fraction policies are within a constant additive gap as well from the optimal solution.Comment: To appear in the 2017 IEEE International Symposium on Information Theory. arXiv admin note: text overlap with arXiv:1705.1030

Efficiently Learning from Revealed Preference

In this paper, we consider the revealed preferences problem from a learning perspective. Every day, a price vector and a budget is drawn from an unknown distribution, and a rational agent buys his most preferred bundle according to some unknown utility function, subject to the given prices and budget constraint. We wish not only to find a utility function which rationalizes a finite set of observations, but to produce a hypothesis valuation function which accurately predicts the behavior of the agent in the future. We give efficient algorithms with polynomial sample-complexity for agents with linear valuation functions, as well as for agents with linearly separable, concave valuation functions with bounded second derivative.Comment: Extended abstract appears in WINE 201