the scenario approach stochastic …j. of optimization theory and applications, 148: 257-280, 2011....
TRANSCRIPT
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THE SCENARIO APPROACHto
STOCHASTIC OPTIMIZATION
Marco C. CampiUniversity of Brescia
Italy
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“What I like about experience is that it is such an honest thing. … You may have deceived yourself, but experience is not trying to deceive you.”
C.S. Lewis
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thanks to:
AlgoCare’
Giuseppe Calafiore
Maria Prandini
BernardoPagnoncelli
Federico Ramponi
Simone Garatti
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classificationcontroller synthesis
portfolio selectionoptimization program
optimization
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uncertain environment
exercise caution
classificationcontroller synthesis
portfolio selectionoptimization program
optimization
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uncertain optimization:
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uncertain optimization:
not a valid mathematical formulation
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uncertain optimization:
not a valid mathematical formulation
often, a description of uncertainty is not available, or it is only partially available
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scenario-based knowledge:
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scenario-based knowledge:
knowledge about uncertainty can be acquiredthrough experience,
that is, we look at previous cases, or scenarios, of the same problem
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example: portfolio optimization
[with B. Pagnoncelli & D. Reich]
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example: portfolio optimization
[with B. Pagnoncelli & D. Reich]
1$
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example: portfolio optimization
[with B. Pagnoncelli & D. Reich]
1$
assets
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= percentage of capital invested on asset
example: portfolio optimization
[with B. Pagnoncelli & D. Reich]
1$
assets
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= percentage of capital invested on asset
example: portfolio optimization
[with B. Pagnoncelli & D. Reich]
1$
assets
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= percentage of capital invested on asset
example: portfolio optimization
[with B. Pagnoncelli & D. Reich]
1$
assets
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example: portfolio optimization
[with B. Pagnoncelli & D. Reich]
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record of past rate of returns:
= return of asset over period
example: portfolio optimization
[with B. Pagnoncelli & D. Reich]
(scenarios)
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example: portfolio optimization
[with B. Pagnoncelli & D. Reich]
(scenarios)
record of past rate of returns:
= return of asset over period
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example: classification - defibrillation
[with A. Caré]
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example: classification - defibrillation
[with A. Caré]
decide whether a defibrillator has to be applied
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example: classification - defibrillation
[with A. Caré]
(scenarios)
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example: classification - defibrillation
[with A. Caré]
(scenarios)
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“scenario” optimization(convex case)
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min-max “scenario” optimization
[with G. Calafiore]
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min-max “scenario” optimization
[with G. Calafiore]
convex in
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[with G. Calafiore]
convex in
min-max “scenario” optimization
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[with G. Calafiore]
convex in
min-max “scenario” optimization
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[with G. Calafiore]
convex in
min-max “scenario” optimization
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[with G. Calafiore]
convex in
min-max “scenario” optimization
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[with G. Calafiore]
convex in
min-max “scenario” optimization
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what are the guarantees for unseen situations?
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how guaranteed is for another ?
what are the guarantees for unseen situations?
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from the “visible” to the “invisible”
how guaranteed is for another ?
what are the guarantees for unseen situations?
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about uncertainty
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about uncertainty
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about uncertainty
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about uncertainty
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about uncertainty
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about uncertainty
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comments
generalization need for structure
good news: the structure we needis only convexity
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… more comments
N depends on how complex the decision is via
N does not depend on how complex the “real world” is
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… more comments
don’t try to reconstruct the real world to answer easy
questions!
N depends on how complex the decision is via
N does not depend on how complex the “real world” is
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… more comments (IPM = Interval Prediction Model)
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… more comments (IPM = Interval Prediction Model)
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… more comments (IPM = Interval Prediction Model)
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… more comments (IPM = Interval Prediction Model)
risk = prob. that next point is outside IPM
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… more comments (IPM = Interval Prediction Model)
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… more comments
N is independent of Pr (distribution-free result)
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… more comments
N is independent of Pr (distribution-free result)
“What I like about experience is that it is such an honest thing. … You may have deceived yourself, but experience is not trying to deceive you.”
C.S. Lewis
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a more general theoretical result
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risk0 0.2 0.4 0.6 0.8 1
0
5
10
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risk0 0.2 0.4 0.6 0.8 1
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risk0 0.2 0.4 0.6 0.8 1
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application: classification - defibrillation
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application: classification - defibrillation
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application: classification - defibrillation
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application: classification - defibrillation
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generalizations and beyond
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generalizations: risk-return tradeoff
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generalizations: risk-return tradeoff
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generalizations: risk-return tradeoff
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generalizations: risk-return tradeoff
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generalizations: risk-return tradeoff
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generalizations: risk-return tradeoff
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generalizations: risk-return tradeoff
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performance - risk plot
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performance - risk plot
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generalizations
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generalizations
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generalizations
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generalizations
relevanto to: quantitative finance (minimum return)control with constraints (MPC)
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Many have given a contribution:
T. Álamo, G. Andersson, F. Borrelli, G. Calafiore, A. Carè, F. Dabbene, L. Fagiano, S. Garatti, P. Goulart, O. Granichin, J. Hespanha, H. Hjalmarsson, G. Iyengar, T. Kanamori, D. Kuhn, C. Lagoa, J. Luedtke, A. Luque, J. Lygeros, K. Margellos, M. Morari, J. Matuško, B. Pagnoncelli, M. Prandini, F. Ramponi, D, Reich, C. Rojas, B. Rustem, G. Schildbach, M. Sznaier, A. Takeda, R. Tempo, B. Van Parys, P. Vayanos, M. Vrakopoulou, J. Welsh, W. Wiesemann
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the theory is still in its infancy
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non-convex
the theory is still in its infancy
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margin
the theory is still in its infancy
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the problem of extracting knowledge from observations is perhaps the most central issue of all science
… concluding
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the scenario approach is one way, and a lot of work remains to be done
the problem of extracting knowledge from observations is perhaps the most central issue of all science
… concluding
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certainly: it is a wonderful world to explore!
the scenario approach is one way, and a lot of work remains to be done
the problem of extracting knowledge from observations is perhaps the most central issue of all science
… concluding
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certainly: it is a wonderful world to explore!
THANK YOU!
the scenario approach is one way, and a lot of work remains to be done
the problem of extracting knowledge from observations is perhaps the most central issue of all science
… concluding
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REFERENCES
M.C. Campi and S. Garatti. The Exact Feasibility of Randomized Solutions of Uncertain Convex Programs. SIAM J. 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.
B.K. Pagnoncelli, D. Reich and M.C. CampiRisk-Return Trade-off with the Scenario Approach: A Case study in Portfolio Selection.J. Of Optimization Theory and Applications, 155: 707-722, 2012.
G. Calafiore and M.C. Campi. Uncertain Convex Programs: randomized Solutions and Confidence Levels. Mathematical Programming, 102: 25-46, 2005.
G. Calafiore and M.C. Campi. The Scenario Approach to Robust Control Design.IEEE Trans. on Automatic Control, AC-51: 742-753, 2006.
M.C. Campi, G. Calafiore and S. Garatti.Interval Predictor Models: Identification and Reliability. Automatica, 45: 382-392, 2009.
M.C. Campi. Classification with guaranteed probability of error. Machine Learning, 80: 63-84, 2010.