Adaptive optimization problems under uncertainty with limited feedback
Name
1006889672-MIT.pdf
Description
Full printable version
Size
1.59 MB
Format
Adobe PDF
Checksum (MD5)
825e6294febf81c3e525c0ce534905f7
Author(s)
Flajolet, Arthur
Advisor(s)
Patrick Jaillet.
Date Issued
2017
Publisher
Massachusetts Institute of Technology
Abstract
This thesis is concerned with the design and analysis of new algorithms for sequential optimization problems with limited feedback on the outcomes of alternatives when the environment is not perfectly known in advance and may react to past decisions. Depending on the setting, we take either a worst-case approach, which protects against a fully adversarial environment, or a hindsight approach, which adapts to the level of adversariality by measuring performance in terms of a quantity known as regret. First, we study stochastic shortest path problems with a deadline imposed at the destination when the objective is to minimize a risk function of the lateness. To capture distributional ambiguity, we assume that the arc travel times are only known through confidence intervals on some statistics and we design efficient algorithms minimizing the worst-case risk function. Second, we study the minimax achievable regret in the online convex optimization framework when the loss function is piecewise linear. We show that the curvature of the decision maker's decision set has a major impact on the growth rate of the minimax regret with respect to the time horizon. Specifically, the rate is always square root when the set is a polyhedron while it can be logarithmic when the set is strongly curved. Third, we study the Bandits with Knapsacks framework, a recent extension to the standard Multi-Armed Bandit framework capturing resource consumption. We extend the methodology developed for the original problem and design algorithms with regret bounds that are logarithmic in the initial endowments of resources in several important cases that cover many practical applications such as bid optimization in online advertising auctions. Fourth, we study more specifically the problem of repeated bidding in online advertising auctions when some side information (e.g. browser cookies) is available ahead of submitting a bid. Optimizing the bids is modeled as a contextual Bandits with Knapsacks problem with a continuum of arms. We design efficient algorithms with regret bounds that scale as square root of the initial budget.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2017.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 159-166).
Subjects
Operations Research Center.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
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