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Poster
Learning from Rational Behavior: Predicting Solutions to Unknown Linear Programs
Shahin Jabbari · Ryan Rogers · Aaron Roth · Steven Wu

Mon Dec 05 09:00 AM -- 12:30 PM (PST) @ Area 5+6+7+8 #24
in Monday Posters »

We define and study the problem of predicting the solution to a linear program (LP) given only partial information about its objective and constraints. This generalizes the problem of learning to predict the purchasing behavior of a rational agent who has an unknown objective function, that has been studied under the name “Learning from Revealed Preferences". We give mistake bound learning algorithms in two settings: in the first, the objective of the LP is known to the learner but there is an arbitrary, fixed set of constraints which are unknown. Each example is defined by an additional known constraint and the goal of the learner is to predict the optimal solution of the LP given the union of the known and unknown constraints. This models the problem of predicting the behavior of a rational agent whose goals are known, but whose resources are unknown. In the second setting, the objective of the LP is unknown, and changing in a controlled way. The constraints of the LP may also change every day, but are known. An example is given by a set of constraints and partial information about the objective, and the task of the learner is again to predict the optimal solution of the partially known LP.

Keywords: Learning Theory · Online Learning · (Other) Machine Learning Topics · Model Selection and Structure Learning · Game Theory and Econometrics
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Author Information

Shahin Jabbari (University of Pennsylvania)
Ryan Rogers (University of Pennsylvania)
Aaron Roth (University of Pennsylvania)
Steven Wu (University of Pennsylvania)

zstevenwu.com

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