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Methods to compute generalization error bounds using Scenario Theory

#Scenario-Theory-Py-Generalization-Assessment-Methods

Methods to compute generalization error bounds using Scenario Theory

Types of bounds ε on the violation probability

non-convex Scenario programs (a-posteriori)

Bounds derived and applied in:

• [] M. C. Campi, S. Garatti and F. A. Ramponi, "A General Scenario Theory for Nonconvex Optimization and Decision Making," in IEEE Transactions on Automatic Control, vol. 63, no. 12, pp. 4067-4078, Dec. 2018, https://ieeexplore.ieee.org/document/8299432

• [] Roberto Rocchetta, Luis G. Crespo, Sean P. Kenny, A scenario optimization approach to reliability-based design, Reliability Engineering & System Safety, Volume 196, 2020, 106755, ISSN 0951-8320, https://doi.org/10.1016/j.ress.2019.106755.

convex scenario program with relaxed constraints (a-posteriori)

Bounds derived and applied in:

• [] Garatti, Simone & Campi, Marco. (2019). Risk and complexity in scenario optimization. Mathematical Programming. https://doi.org/10.1007/s10107-019-01446-4
• []

Wait and Judge convex programs (a-posteriori)

Bounds derived and applied in:

• [] Campi, Marco & Garatti, Simone. (2016). Wait-and-judge scenario optimization. Mathematical Programming. https://doi.org/10.1007/s10107-016-1056-9
• [] Carè, A., Garatti, S. & Campi, M.C. The wait-and-judge scenario approach applied to antenna array design. Comput Manag Sci 16, 481–499 (2019). https://doi.org/10.1007/s10287-019-00345-5

Sample-and-discard convex programs (a-priori)

• [] Campi, M.C., Garatti, S. A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality. J Optim Theory Appl 148, 257–280 (2011). https://doi.org/10.1007/s10957-010-9754-6