Learning from rational behavior: Predicting solutions to unknown linear programs

Shahin Jabbari, Ryan Rogers, Aaron Roth, Steven Wu

Research output: Contribution to journalConference articlepeer-review

5 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1578-1586
Number of pages9
JournalAdvances in Neural Information Processing Systems
StatePublished - Jan 1 2016
Externally publishedYes
Event30th Annual Conference on Neural Information Processing Systems, NIPS 2016 - Barcelona, Spain
Duration: Dec 5 2016Dec 10 2016

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