Single-Sample Prophet Inequalities via Greedy-Ordered Selection

11/04/2021
by   Constantine Caramanis, et al.
0

We study single-sample prophet inequalities (SSPIs), i.e., prophet inequalities where only a single sample from each prior distribution is available. Besides a direct, and optimal, SSPI for the basic single choice problem [Rubinstein et al., 2020], most existing SSPI results were obtained via an elegant, but inherently lossy, reduction to order-oblivious secretary (OOS) policies [Azar et al., 2014]. Motivated by this discrepancy, we develop an intuitive and versatile greedy-based technique that yields SSPIs directly rather than through the reduction to OOSs. Our results can be seen as generalizing and unifying a number of existing results in the area of prophet and secretary problems. Our algorithms significantly improve on the competitive guarantees for a number of interesting scenarios (including general matching with edge arrivals, bipartite matching with vertex arrivals, and certain matroids), and capture new settings (such as budget additive combinatorial auctions). Complementing our algorithmic results, we also consider mechanism design variants. Finally, we analyze the power and limitations of different SSPI approaches by providing a partial converse to the reduction from SSPI to OOS given by Azar et al.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

03/24/2021

Single-Sample Prophet Inequalities Revisited

The study of the prophet inequality problem in the limited information r...
04/05/2021

Prophet Inequalities for Matching with a Single Sample

We consider the prophet inequality problem for (not necessarily bipartit...
10/30/2017

Prophet Secretary for Combinatorial Auctions and Matroids

The secretary and the prophet inequality problems are central to the fie...
12/14/2021

Secretary Matching With Vertex Arrivals and No Rejections

Most prior work on online matching problems has been with the flexibilit...
11/18/2019

Optimal Single-Choice Prophet Inequalities from Samples

We study the single-choice Prophet Inequality problem when the gambler i...
02/12/2020

A Matching Mechanism with Anticipatory Tolls for Congestion Pricing

This paper presents a matching mechanism for assigning drivers to routes...
04/03/2021

Optimal multiple testing and design in clinical trials

A central goal in designing clinical trials is to find the test that max...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.