Prediction and sequential decision problems in adversarial environments

141 Pages·2015·2.41 MB·English

by  Peter Bartlett

Prediction and sequential decision problems in
adversarial environments
Peter Bartlett
ComputerScienceandStatistics
UniversityofCaliforniaatBerkeley
CDAR Symposium
October 16, 2015
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Decision problems: regression, classification, order allocation,
dynamic pricing, portfolio optimization, option pricing.
Rather than model the process generating the data probabilistically,
we view it as an adversary.
Decision-making = hedging against the future choices of the
process generating the data.
Game-Theoretic Statistics
Formulating decision problems as sequential games
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Rather than model the process generating the data probabilistically,
we view it as an adversary.
Decision-making = hedging against the future choices of the
process generating the data.
Game-Theoretic Statistics
Formulating decision problems as sequential games
Decision problems: regression, classification, order allocation,
dynamic pricing, portfolio optimization, option pricing.
2/47
Decision-making = hedging against the future choices of the
process generating the data.
Game-Theoretic Statistics
Formulating decision problems as sequential games
Decision problems: regression, classification, order allocation,
dynamic pricing, portfolio optimization, option pricing.
Rather than model the process generating the data probabilistically,
we view it as an adversary.
2/47
Game-Theoretic Statistics
Formulating decision problems as sequential games
Decision problems: regression, classification, order allocation,
dynamic pricing, portfolio optimization, option pricing.
Rather than model the process generating the data probabilistically,
we view it as an adversary.
Decision-making = hedging against the future choices of the
process generating the data.
2/47
Outline
Decision problems as sequential games
•
1 Allocation to dark pools
2 Pricing options
3 Linear regression
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Outline
Decision problems as sequential games
•
1 Allocation to dark pools
2 Pricing options
3 Linear regression
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2 Adversary chooses outcome yt .
∈Y
3 Player incurs loss (cid:96)(at,yt).
Minimize regret:
1 Player chooses prediction at .
∈A
1
2
Player’s aim: 3∗1
3
2
T T
(cid:88) (cid:88) (cid:96)(a ,y ) = a y 2.
(cid:96)(at,yt) min (cid:96)(a,yt). t t (cid:107) t − t(cid:107)
−a∈A
t=1 t=1
Prediction as a game
A repeated game:
At round t:
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3 Player incurs loss (cid:96)(at,yt).
Minimize regret:
2 Adversary chooses outcome yt .
∈Y
1
2
Player’s aim: 3∗
3
2
T T
(cid:88) (cid:88) (cid:96)(a ,y ) = a y 2.
(cid:96)(at,yt) min (cid:96)(a,yt). t t (cid:107) t − t(cid:107)
−a∈A
t=1 t=1
Prediction as a game
A repeated game:
At round t:
1 Player chooses prediction at .
∈A
1
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Minimize regret:
3 Player incurs loss (cid:96)(at,yt).
2
Player’s aim: 3∗
3
2
T T
(cid:88) (cid:88) (cid:96)(a ,y ) = a y 2.
(cid:96)(at,yt) min (cid:96)(a,yt). t t (cid:107) t − t(cid:107)
−a∈A
t=1 t=1
Prediction as a game
A repeated game:
At round t:
1 Player chooses prediction at .
∈A
2 Adversary chooses outcome yt .
∈Y
1
1
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