Related papers: Extreme Points in Multi-Dimensional Screening
We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of the process, which is related to the entrance in certain…
We efficiently solve the optimal multi-dimensional mechanism design problem for independent bidders with arbitrary demand constraints when either the number of bidders is a constant or the number of items is a constant. In the first…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
In this paper we consider multidimensional mechanism design problem for selling discrete substitutable items to a group of buyers. Previous work on this problem mostly focus on stochastic description of valuations used by the seller.…
Our work explores fusions, the multidimensional counterparts of mean-preserving contractions and their extreme and exposed points. We reveal an elegant geometric/combinatorial structure for these objects. Of particular note is the…
We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…
We consider markets consisting of a set of indivisible items, and buyers that have {\em sharp} multi-unit demand. This means that each buyer $i$ wants a specific number $d_i$ of items; a bundle of size less than $d_i$ has no value, while a…
The Performance Estimation Problem (PEP) approach consists in computing worst-case performance bounds on optimization algorithms by solving an optimization problem: one maximizes an error criterion over all initial conditions allowed and…
In environmental applications of extreme value statistics, the underlying stochastic process is often modeled either as a max-stable process in continuous time/space or as a process in the domain of attraction of such a max-stable process.…
In structured prediction problems where we have indirect supervision of the output, maximum marginal likelihood faces two computational obstacles: non-convexity of the objective and intractability of even a single gradient computation. In…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
In mechanism design it is typical to impose incentive compatibility and then derive an optimal mechanism subject to this constraint. By replacing the incentive compatibility requirement with the goal of minimizing expected ex post regret,…
We study a model of delegation in which a principal takes a multidimensional action and an agent has private information about a multidimensional state of the world. The principal can design any direct mechanism, including stochastic ones.…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
Many offline unsupervised change point detection algorithms rely on minimizing a penalized sum of segment-wise costs. We extend this framework by proposing to minimize a sum of discrepancies between segments. In particular, we propose to…
Input-affine dynamical systems often arise in control and modeling scenarios, such as the data-driven case when state-derivative observations are recorded under bounded noise. Common tasks in system analysis and control include optimal…
We provide sufficient conditions for revenue maximization in a two-good monopoly where the buyer's values for the items come from independent (but not necessarily identical) distributions over bounded intervals. Under certain distributional…
This paper considers the problem of maximizing multiple linear functions over the probability simplex. A classification of feasible points is indicated. A necessary and sufficient condition for a member of each class to be an efficient…
We study multi-product monopoly pricing where the seller jointly designs the selling mechanism and the information structure for the buyer to learn his values. Unlike the case with exogenous information, we show that when the seller…
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…