Scaling up the sample average approximation method for stochastic optimization with applications to trading agents

Authors:
Amy Greenwald;Bryan Guillemette;Victor Naroditskiy;Michael Tschantz
Affiliations:
Department of Computer Science, Brown University, Providence, RI;Department of Computer Science, Brown University, Providence, RI;Department of Computer Science, Brown University, Providence, RI;Department of Computer Science, Brown University, Providence, RI
Venue:
AMEC'05 Proceedings of the 2005 international conference on Agent-Mediated Electronic Commerce: designing Trading Agents and Mechanisms
Year:
2005

Citing 6
Cited 2

Computationally Manageable Combinational Auctions

Management Science
Bidding algorithms for simultaneous auctions

Proceedings of the 3rd ACM conference on Electronic Commerce
The Sample Average Approximation Method for Stochastic Discrete Optimization

SIAM Journal on Optimization
A stochastic programming approach to scheduling in TAC SCM

EC '04 Proceedings of the 5th ACM conference on Electronic commerce
Botticelli: A Supply Chain Management Agent

AAMAS '04 Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems - Volume 3
Walverine: a Walrasian trading agent

Decision Support Systems - Special issue: Decision theory and game theory in agent design

A two-stage stochastic programming model for the parallel machine scheduling problem with machine capacity

Computers and Operations Research
Evaluating variance reduction techniques within a sample average approximation method for a constrained inventory policy optimization problem

Proceedings of the Winter Simulation Conference

Quantified Score

Hi-index	0.00

Visualization

Abstract

The Sample Average Approximation (SAA) method is a technique for approximating solutions to stochastic programs. Here, we attempt to scale up the SAA method to harder problems than those previously studied. We argue that to apply the SAA method effectively, there are three parameters to optimize: the number of evaluations, the number of scenarios, and the number of candidate solutions. We propose an experimental methodology for finding the optimal settings of these parameters given fixed time and space constraints. We apply our methodology to two large-scale stochastic optimization problems that arise in the context of the annual Trading Agent Competition. Both problems are expressed as integer linear programs and solved using CPLEX. Runtime increases linearly with the number of scenarios in one of the problems, and exponentially in the other. We find that, in the former problem, maximizing the number of scenarios yields the best solution, while in the latter problem, it is necessary to evaluate multiple candidate solutions to find the best solution, since increasing the number of scenarios becomes expensive very quickly.