Fairness in Learning:
Classic and Contextual
Bandits
Jamie Morgenstern
joint w. Mathew Joseph, Michael Kearns, Aaron Roth
University of Pennsylvania
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Automated decisions of
consequence
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Hiring Lending Policing/
sentencing/
parole
[Miller, 2015],[Byrnes, 2016]
[Rudin, 2013], [Barry-Jester et al., 2015]

No content

Each individual has inherent ‘quality’

Each individual has inherent ‘quality’
(expected revenue for giving a loan)

Each individual has inherent ‘quality’
(expected revenue for giving a loan)

Each individual has inherent ‘quality’
(expected revenue for giving a loan)
entitling them to access to a resource

Each individual has inherent ‘quality’
(expected revenue for giving a loan)
entitling them to access to a resource
(high-revenue individuals deserve loans)

Each individual has inherent ‘quality’
(expected revenue for giving a loan)
entitling them to access to a resource
(high-revenue individuals deserve loans)

Each individual has inherent ‘quality’
(expected revenue for giving a loan)
entitling them to access to a resource
(high-revenue individuals deserve loans)
Observe features, not qualities directly,

Each individual has inherent ‘quality’
(expected revenue for giving a loan)
entitling them to access to a resource
(high-revenue individuals deserve loans)
Observe features, not qualities directly,
must learn relationship

Each individual has inherent ‘quality’
(expected revenue for giving a loan)
entitling them to access to a resource
(high-revenue individuals deserve loans)
Observe features, not qualities directly,
must learn relationship
(observe loan application)

Each individual has inherent ‘quality’
(expected revenue for giving a loan)
entitling them to access to a resource
(high-revenue individuals deserve loans)
Observe features, not qualities directly,
must learn relationship
(observe loan application)
(assume different for different groups!)

A source of bias in ML
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A source of bias in ML
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• Data feedback loops: only observe/update estimates
for individuals current model believes are high-
qualilty

A source of bias in ML
4
• Data feedback loops: only observe/update estimates
for individuals current model believes are high-
qualilty

We study
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We study
5
A new notion of fairness:
high-quality individuals must be
treated as well as lower-quality
individuals

We study
5
A new notion of fairness:
high-quality individuals must be
treated as well as lower-quality
individuals
And the “cost” of this constraint
wrt learning rate R(T)
(regret minimization)

We study
5
A new notion of fairness:
high-quality individuals must be
treated as well as lower-quality
individuals
And the “cost” of this constraint
wrt learning rate R(T)
(regret minimization)
Fair learning
rather than
finding a
fair model

Assumptions
k groups
each group has
a function mapping features to ’qualities’
(initially unknown, belonging to C)
(can be different for different groups)

Information/decision model
Each day t [T]
Observe feature vector from each group
Choose one individual based on features
Observe noisy estimate of quality of chosen
Goal: maximize expected average quality

Fairness Definition
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Fairness Definition
8
An algorithm A( ) is fair if, for all (0, 1]

Fairness Definition
8
with probability 1
An algorithm A( ) is fair if, for all (0, 1]

Fairness Definition
8
with probability 1
An algorithm A( ) is fair if, for all (0, 1]
For any sequence x1, . . . , xT

Fairness Definition
8
for all rounds
with probability 1
An algorithm A( ) is fair if, for all (0, 1]
For any sequence x1, . . . , xT

Fairness Definition
8
for all rounds
with probability 1
An algorithm A( ) is fair if, for all (0, 1]
and all pairs of groups i, j
For any sequence x1, . . . , xT

Fairness Definition
8
for all rounds
with probability 1
An algorithm A( ) is fair if, for all (0, 1]
and all pairs of groups i, j
For any sequence x1, . . . , xT
If E[quality of i at t] ≥ E[quality of j at t] then

Fairness Definition
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for all rounds
with probability 1
An algorithm A( ) is fair if, for all (0, 1]
and all pairs of groups i, j
For any sequence x1, . . . , xT
If E[quality of i at t] ≥ E[quality of j at t] then
A favors i over j in round t

Fairness Definition
8
for all rounds
with probability 1
An algorithm A( ) is fair if, for all (0, 1]
and all pairs of groups i, j
For any sequence x1, . . . , xT
If E[quality of i at t] ≥ E[quality of j at t] then
P A chooses i at t |
x1, . . . , xt
P A chooses j at t |
x1, . . . , xt

Separation between
fair and unfair learning
without features
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Separation between
fair and unfair learning
without features
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Theorem 1

Separation between
fair and unfair learning
without features
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For any fair algo, R(T) = ˜ k3T .
Theorem 1

Separation between
fair and unfair learning
without features
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Without fairness one can achieve regret
For any fair algo, R(T) = ˜ k3T .
Theorem 1

Separation between
fair and unfair learning
without features
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Without fairness one can achieve regret
˜
O( kT)
For any fair algo, R(T) = ˜ k3T .
Theorem 1

Feature-based fair learning
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[Strehl and Littman, 2008]
[ Li et al., 2011]

Feature-based fair learning
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[Strehl and Littman, 2008]
[ Li et al., 2011]
Theorem 2 implications:

Feature-based fair learning
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[Strehl and Littman, 2008]
[ Li et al., 2011]
Theorem 2 implications:
There is a fair algorithm for d-dimensional linear
mappings from features to qualities w. regret
R(T) = O T1 c · poly(k, d, ln 1 )

Feature-based fair learning
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[Strehl and Littman, 2008]
[ Li et al., 2011]
Theorem 2 implications:
There is a fair algorithm for d-dimensional linear
mappings from features to qualities w. regret
R(T) = O T1 c · poly(k, d, ln 1 )
Any fair algorithm for d-dimensional conjunction
mappings must have regret R(T) = Ω 2d

Fairness through Datamining
- Pedreshi et al, ’08
- HDF ’13, HDFMB ’11, ZKC ’11, ….
“Group” Fairness
- CV ’10, FKL ’16, JL’15, KC ’11,
KKZ ’12, KAAS ’12…
“Individual” Fairness
- Dwork et al, 2012
- Johnson, Foster, Stine ’16
- Hardt, Price, Srebro ’16
- Kleinberg, Mullainathan, Raghavan ’16
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Related Work

Fairness through Datamining
- Pedreshi et al, ’08
- HDF ’13, HDFMB ’11, ZKC ’11, ….
“Group” Fairness
- CV ’10, FKL ’16, JL’15, KC ’11,
KKZ ’12, KAAS ’12…
“Individual” Fairness
- Dwork et al, 2012
- Johnson, Foster, Stine ’16
- Hardt, Price, Srebro ’16
- Kleinberg, Mullainathan, Raghavan ’16
11
Related Work
Our work
focuses on fair
learning rather
than finding a
fair model

Conclusions
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Conclusions
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New notion of fairness:
higher-quality ⇒ better treatment

Conclusions
12
Must be *confident* about relative qualities
before preferential treatment ensues
New notion of fairness:
higher-quality ⇒ better treatment

Conclusions
12
There’s a cost to fairness
Must be *confident* about relative qualities
before preferential treatment ensues
New notion of fairness:
higher-quality ⇒ better treatment

Conclusions
12
There’s a cost to fairness
in some cases, this cost is mild, in others, great
Must be *confident* about relative qualities
before preferential treatment ensues
New notion of fairness:
higher-quality ⇒ better treatment

Conclusions
12
There’s a cost to fairness
in some cases, this cost is mild, in others, great
Must be *confident* about relative qualities
before preferential treatment ensues
New notion of fairness:
higher-quality ⇒ better treatment
Thanks!