Robust Optimization and Applications in Machine Learning

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Robust Optimization andApplications in Machine
Learning

• Laurent El Ghaoui
• SAC Capital and UC Berkeley
• elghaoui_at_eecs.berkeley.edu
• IMS Tutorial, N.U. Singapore,
• January 9, 2006

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Thanks
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Outline
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Part 1 Overview of robust optimization
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Optimization models
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Pitfalls
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Robust Optimization Paradigm
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Approximating a robust solution
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LP as a conic problem
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Second-order cone programming
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Semidefinite programming
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Dual form of conic program
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Robust conic programming
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Polytopic uncertainty
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Robust LP
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Robust LP with ellipsoidal uncertainty
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Robust LP as SOCP
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Example robust portfolio design
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Solution of robust portfolio problem
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Robust SOCP
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Example robust least-squares
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Robust SDP
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Example robust control
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Analysis of robust conic problems
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Relaxations
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Quality estimates
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Quality estimates some results
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Restriction
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Sampling
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Robust Optimization challenges
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Robust optimization in machine learning
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Part 1 summary