# Correlation robust stochastic optimization

@inproceedings{Agrawal2010CorrelationRS, title={Correlation robust stochastic optimization}, author={Shipra Agrawal and Yichuan Ding and Amin Saberi and Yinyu Ye}, booktitle={SODA '10}, year={2010} }

We consider a robust model proposed by Scarf, 1958, for stochastic optimization when only the marginal probabilities of (binary) random variables are given, and the correlation between the random variables is unknown. In the robust model, the objective is to minimize expected cost against worst possible joint distribution with those marginals. We introduce the concept of correlation gap to compare this model to the stochastic optimization model that ignores correlations and minimizes expected…

## 43 Citations

### Price of Correlations in Stochastic Optimization

- Computer Science, MathematicsOper. Res.
- 2012

This paper studies possible loss incurred on ignoring correlations through a distributionally robust stochastic programming model, and quantifies that loss as price of correlations (POC) using techniques of cost sharing from game theory.

### Mechanism design via correlation gap

- Computer ScienceSODA '11
- 2011

A theoretical explanation of how certain SPMs can approximate the optimal mechanism by a good constant factor is given, and tight analysis of a greedy-based SPM of Chawla et al. for several environments is given.

### Equilibrium Computation and Robust Optimization in Zero Sum Games With Submodular Structure

- Computer ScienceAAAI
- 2018

A pseudopolynomial-time algorithm which obtains a guaranteed (1 - 1/e)^2-approximate mixed strategy for the maximizing player and only requires access to a weakened version of a best response oracle for the minimizing player which runs in polynomial time.

### Incentives in dynamic markets

- Computer Science
- 2017

This thesis studies extensions of the so-called smoothness framework for mechanisms, a very useful technique for bounding the inefficiency of equilibria, to the cases of varying mechanism availability and participation of risk-averse players, and designs new algorithms that obtain constant competitive ratios for a variety of combinatorial problems.

### Equilibrium computation for zero sum games with submodular structure

- Computer ScienceArXiv
- 2017

A pseudopolynomial-time algorithm which obtains a guaranteed $(1 - 1/e)^2$-approximate mixed strategy for the maximizing player and only requires access to a weakened version of a best response oracle for the minimizing player which runs in polynomial time.

### OPTIMIZATION UNDER UNCERTAINTY: BOUNDING THE CORRELATION GAP A DISSERTATION SUBMITTED TO THE DEPARTMENT OF COMPUTER SCIENCE AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

- Computer Science
- 2011

It is shown that the upper bounds on correlation gap are also useful for solving many deterministic optimization problems like welfare maximization, k-dimensional matching and transportation problems, where it characterizes the performance of algorithmic strategies like random selection and independent randomized rounding.

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

- EconomicsArXiv
- 2018

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.

### Algorithms and Adaptivity Gaps for Stochastic Probing

- Computer ScienceSODA
- 2016

The first approximation algorithms for a number of stochastic probing problems, which have applications, e.g., to path-planning and precedence-constrained scheduling, are obtained.

### Smoothness for Simultaneous Composition of Mechanisms with Admission

- EconomicsWINE
- 2016

The main results are general composition theorems for smooth mechanisms when valuation functions of bidders are lattice-submodular and they rely on an interesting connection to the notion of correlation gap of submodular functions over product lattices.

### Constrained Non-monotone Submodular Maximization: Offline and Secretary Algorithms

- Mathematics, Computer ScienceWINE
- 2010

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.

## References

SHOWING 1-10 OF 24 REFERENCES

### Sampling-based approximation algorithms for multi-stage stochastic optimization

- Computer Science, Mathematics46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)
- 2005

This work obtains the first fully polynomial approximation scheme for a broad class of multi-stage stochastic linear programming problems with any constant number of stages, and analyzes the sample average approximation method, which is the one most commonly used in practice.

### Optimal approximation for the submodular welfare problem in the value oracle model

- MathematicsSTOC
- 2008

A randomized continuous greedy algorithm is developed which achieves a (1-1/e)-approximation for the Submodular Welfare Problem in the value oracle model and is shown to have a potential of wider applicability on the examples of the Generalized Assignment Problem and the AdWords Assignment Problem.

### Approximation in stochastic scheduling: the power of LP-based priority policies

- BusinessJACM
- 1999

A polyhedral relaxation of the performance space of stochastic parallel machine scheduling is presented, which generalizes previous results from deterministic scheduling and shows that all employed LPs can be solved in polynomial time by purely combinatorial algorithms.

### Sampling-Based Approximation Algorithms for Multistage Stochastic Optimization

- Computer ScienceSIAM J. Comput.
- 2012

The main result is to give the first fully polynomial approximation scheme for a broad class of multistage stochastic linear programming problems with any constant number of stages.

### Optimal Efficiency Guarantees for Network Design Mechanisms

- EconomicsIPCO
- 2007

This work proves for the first time that approximate budget-balance and efficiency are simultaneously possible in a cost-sharing problem and proves a new, optimal lower bound on the approximate efficiency achievable by the wide and natural class of "Moulin mechanisms".

### Boosted sampling: approximation algorithms for stochastic optimization

- MathematicsSTOC '04
- 2004

This framework is used to derive constant factor approximations for stochastic versions of Vertex Cover, Steiner Tree and Uncapacitated Facility Location for arbitrary distributions π in one fell swoop.

### Inapproximability Results for Combinatorial Auctions with Submodular Utility Functions

- Mathematics, EconomicsAlgorithmica
- 2007

It is proved that there is no polynomial time approximation algorithm which approximates the maximum social welfare by a factor better than 1–1/e ≃ 0.632, unless P = NP.

### Stochastic analyses for online combinatorial optimization problems

- Computer ScienceSODA '08
- 2008

For the online Steiner tree problem, it is shown that if each demand vertex is an independent draw from some probability distribution π: <i>V</i> → [0, 1], a variant of the natural greedy algorithm achieves <b>E</b><sub>ω</sub>[<b><i>A</i></b>(ω], and preliminary results on extending this result to the related "expected ratio" measure are given.

### New trade-offs in cost-sharing mechanisms

- EconomicsSTOC '06
- 2006

It is shown that incentive-compatibility, budget-balance, and approximate efficiency are simultaneously achievable for a wide range of cost functions, where efficiency is measured using the social cost---the sum of the incurred service cost and the excluded valuations.

### Approximation algorithms for combinatorial auctions with complement-free bidders

- Computer ScienceSTOC '05
- 2005

Three approximation algorithms for the allocation problem in combinatorial auctions with complement free bidders are exhibited and lower bounds on the possible approximations achievable for these classes of bidder are proved.