Introduction to the Scenario Approach
The scenario approach studies how experience can be used to optimize decisions in relation to intended goals. It turns out that deep results can be established that provide performance guarantees under minimal assumptions on the environment to which the decision is applied. In the course, I shall try to give an introductory view of the main theoretical aspects underpinning scenario optimization, and will present applications to control, identification and machine learning.
Tuesdays and Thursdays, 4-6pm in the Fishbowl, Wisenbaker Engineering Building, from Oct 20-Nov 5. First lecture on Oct 20.
His office will be in Room 333B, WEB.
Foundational theoretical papers:
- M.C. Campi and S. Garatti. The Exact Feasibility of Randomized Solutions of Uncertain Convex Programs. SIAM Journal on Optimization, 19, no.3: 1211-1230, 2008.
- M.C. Campi and S. Garatti. A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality. J. of Optimization Theory and Applications, 148: 257–280, 2011.
Scenario Approach in Control
- G. Calafiore and M.C. Campi. The Scenario Approach to Robust Control Design. IEEE Trans. on Automatic Control, AC-51:742-753, 2006.
- S. Garatti and M.C. Campi. Modulating Robustness in Control Design: Principles and Algorithms. IEEE Control Systems Magazine, 33: 36–51, 2013.
Scenario approach for machine learning:
- M.C. Campi. Classification with Guaranteed Probability of Error. Machine Learning, 80:63-84, 2010.
Scenario approach for identification:
- M.C. Campi, G. Calafiore and S. Garatti. Interval Predictor Models: Identification and Reliability. Automatica, 45:382-392, 2009.
Scenario approach and sparsity:
- M.C. Campi and A. Carè. Random convex programs with L1-regularization: sparsity and generalization. SIAM Journal on Control and Optimization, 51, no.5: 3532-3557, 2013.
First paper on the scenario approach:
- G. Calafiore and M.C. Campi. Uncertain convex programs: randomized solutions and confidence levels. Mathematical Programming, 102, no.1: 25-46, 2005.