Prophet Secretary for Combinatorial Auctions and Matroids

  title={Prophet Secretary for Combinatorial Auctions and Matroids},
  author={Soheil Ehsani and Mohammad Taghi Hajiaghayi and Thomas Kesselheim and Sahil Singla},
  booktitle={ACM-SIAM Symposium on Discrete Algorithms},
The secretary and the prophet inequality problems are central to the field of Stopping Theory. Recently, there has been a lot of work in generalizing these models to multiple items because of their applications in mechanism design. The most important of these generalizations are to matroids and to combinatorial auctions (extends bipartite matching). Kleinberg-Weinberg \cite{KW-STOC12} and Feldman et al. \cite{feldman2015combinatorial} show that for adversarial arrival order of random variables… 

Single-Sample Prophet Inequalities via Greedy-Ordered Selection

This work develops an intuitive and versatile greedy-based technique that yields SSPIs directly rather than through the reduction to OOSs, and analyzes the power and limitations of different SSPI approaches by providing a partial converse to the reduction from S SPI to O OS given by Azar et al.

Single-Sample Prophet Inequalities Revisited

A framework for analyzing policies against a greedy-like prophet solution is developed, and the first SSPI for general (non-bipartite) matching environments is obtained, as well as improved competitive ratios for transversal and truncated partition matroids.

An O(log log m) Prophet Inequality for Subadditive Combinatorial Auctions

A simple and incentive compatible mechanism based on posted prices that achieves an O(log log m) approximation to the optimal revenue for subadditive valuations under an item-independence assumption is constructed.

Improved Approximations for Free-Order Prophets and Second-Price Auctions

It is shown that for every value of the number of buyers $n$, the eager second price (ESP) auction and sequential posted price mechanisms respectively earn at least $0.6620 and 0.6543 fractions of the optimal revenue, which implies an improved bound for free-order prophet inequalities.

Optimal Online Contention Resolution Schemes via Ex-Ante Prophet Inequalities

The first optimal $1/2$-OCRS for matroids is designed by reducing the problem to designing a matroid prophet inequality where it is compared to the stronger benchmark of an ex-ante relaxation.

An Improved Lower Bound for Matroid Intersection Prophet Inequalities

We consider prophet inequalities subject to feasibility constraints that are the intersection of q matroids. The best-known algorithms achieve a Θ( q )-approximation, even when restricted to

On Submodular Prophet Inequalities and Correlation Gap

Improved constant factor combinatorial prophet inequalities for both monotone and non-monotone submodular functions over any constraint that admits an Online Contention Resolution Scheme are obtained and efficient polynomial-time algorithms are described that achieve these bounds.

Improved Truthful Mechanisms for Combinatorial Auctions with Submodular Bidders

This work presents a computationally-efficient truthful mechanism with approximation ratio that improves upon the state-of-the-art by an exponential factor and achieves an O((log logm)^3) -approximation in expectation, uses only O(n) demand queries, and has universal truthfulness guarantee.

Prophet secretary through blind strategies

A new type of multi-threshold strategy, called blind strategy, that sets a nonincreasing sequence of thresholds that depends only on the distribution of the maximum of the random variables, and the gambler stops the first time a sample surpasses the threshold of the stage is introduced.

Query Efficient Prophet Inequality with Unknown I.I.D. Distributions

A new model is proposed in which the algorithm has access to an oracle that answers quantile queries about the distribution and the extent to which it can use a small number of queries to achieve good competitive ratios is studied.



Matroids, secretary problems, and online mechanisms

An O(log k)-competitive algorithm for general matroids (where k is the rank of the matroid), and constant-competitive algorithms for several special cases including graphicMatroids, truncated partition matroIDS, and bounded degree transversal matroid algorithms are presented.

Matroid prophet inequalities

The results imply the first efficiently computable constant-factor approximations to the Bayesian optimal revenue in certain multi-parameter settings and imply improved bounds on the ability of sequential posted-price mechanisms to approximate optimal mechanisms in both single-parameters and multi- parameter Bayesian settings.

Prophet Secretary

Interestingly, it is shown that, even for a simple case in which the input elements are drawn from identical and independent distributions, there is no constant competitive online algorithm for the minimization variant of the prophet secretary problem.

Online Matroid Intersection: Beating Half for Random Arrival

This work presents the first randomized online algorithm that has a $\frac12 + \delta$ competitive ratio in expectation, where $\delta >0$ is a constant.

Constrained Non-monotone Submodular Maximization: Offline and Secretary Algorithms

These ideas are extended to give a simple greedy-based constant factor algorithms for non-monotone submodular maximization subject to a knapsack constraint, and for (online) secretary setting subject to uniform matroid or a partition matroid constraint.

Online budgeted matching in random input models with applications to Adwords

An online assignment problem, motivated by Adwords Allocation, in which queries are to be assigned to bidders with budget constraints is studied, with a tight analysis of Greedy in this model showing that it has a competitive ratio of 1 - 1/e for maximizing the value of the assignment.

Price of anarchy for greedy auctions

A simple deterministic mechanism for general combinatorial auctions that obtains an O(√m) approximation at every Bayes-Nash equilibrium (BNE) is exhibited.

Online prophet-inequality matching with applications to ad allocation

We study the problem of online prophet-inequality matching in bipartite graphs. There is a static set of bidders and an online stream of items. We represent the interest of bidders in items by a

Combinatorial Prophet Inequalities

A novel framework of Prophet Inequalities for combinatorial valuation functions is introduced and a variant of the Correlation Gap Lemma for non-monotone submodular functions is shown.

Automated Online Mechanism Design and Prophet Inequalities

By combining dynamic programming with prophet inequalities (a technique from optimal stopping theory), this work is able to design and analyze online mechanisms which are temporally strategyproof and approximately efficiency-maximizing and prove new prophet inequalities motivated by the auction setting.