1.

2.
ACM FAT*

3.
f

4.
f( )=A

5.
f( )=A
f

6.
f( )=A
f

7.
f( )=A
f
f

8.
f( )=A
f
f

9.
X Y ̂YX
S = S =
X
Y
S
̂Y

10.
ℙ{ ̂Y ∈ 𝒜|S = s} = ℙ{ ̂Y ∈ 𝒜|S = s′}
𝒜, s, s′
=
̂Y|S = ̂Y|S =

11.
ℙ{ ̂Y ∈ 𝒜|Y = y, S = s} = ℙ{ ̂Y ∈ 𝒜|Y = y, S = s′}
𝒜, y, s, s′
Y ̂Y

12.
Y = 1 ̂p
Y = 1 ̂p
ℙ{Y = 1| ̂p = p, S = s} = p
p, s
p
̂p = p|S =

13.
x, x′
D( f(x), f(x′)) ≤ d(x, x′)
≈ ⟹
f : 𝒳 → Δ(𝒴)

14.
f( )=A
f

15.
minf Err(f ) + ηUnfair(f )
minf Err(f ) Unfair(f ) ≤ η

16.
Q
Q f
minQ 𝔼f∼Qℙ{f(X) ≠ Y} M𝔼f∼Q[μ(f )] ≤ c
𝔼{f(X)|S = 0} = 𝔼{f(X)}
𝔼{f(X)|S = 1} = 𝔼{f(X)}

17.
minQ 𝔼f∼Qℙ{f(X) ≠ Y} M𝔼f∼Q[μ(f )] ≤ c
maxλ∈ℝK
+,∥λ∥≤B minQ 𝔼f∼Qℙ{f(X) ≠ Y} + λ⊤
(M𝔼f∼Q[μ(f )] − c)

18.
minf ∑
n
i=1 (h(Xi)C1
i + (1 − h(Xi))C0
i )

19.
λ Q
μ

20.
Q
λ

21.

22.
g( )= z
f( )=A
zz

23.
g( )
g( )
z

24.
g( )
g( )
z

25.
g( )
g( )
z
f( )=A
z

26.
g( )
g( )
z

27.
g( )=
f( )=A
d( )=z
z
z

28.

29.
minf Likelihood(f(X), Y) + ηI(f(X), S)

30.
f( )=A

31.
f( )=A

32.
f( )=A

33.
f( )=A

34.
̂Y = 1

35.
maxy,s (VC(ℱ) + ln(1/δ))/(nPy,s)
maxy,s ln(1/δ)/(nPy,s)

36.
maxy,s (VC(ℱ) + ln(1/δ))/(nPy,s)
maxy,s ln(1/δ)/(nPy,s)
(y, s)

37.
minθ 𝔼[ℓ0(X, θ)] 𝔼[ℓi(X, θ)] ≤ 0

38.
ϵ
m
Rn(ℱ)
ϵ + Rn(ℱ) + ln(1/δ)/n
(m ln(1/ϵ) + ln(m/δ))/n

39.
ϵ + Rn(ℱ) + ln(1/δ)/n
(m ln(1/ϵ) + ln(m/δ))/n
ϵ
m
Rn(ℱ)

40.
̂Y = 1 h : 𝒳 → [0,1]
h ℓ0
ℙx,x′{|h(x) − h(x′)| > d(x, x′) + γ} ≤ α
(γ, α)

41.
maxi,j max(0,|h(x) − h(x′)| − d(xi, xj)) ≤ γ
m = O(poly(1/ϵα,1/ϵγ,1/ϵ)) ϵ
(α + ϵα, γ + ϵγ) h

42.

43.
∑
T
t=1
r(t)
x(t)
1 , . . . , x(t)
K i
r(t)
= fi(x(t)
i )
x(t)
i(t)
r(t)

44.
πi(t) > πj(t) fi(x(t)
i ) > fj(x(t)
j )
fi(x(t)
i )

45.
K3
T ln(Tk/δ)
T4/5
K6/5
d3/5
∨ k3
ln(k/δ)
Ω( T) Ω( K3
ln(1/δ))
TKd ln(T)

46.
πi(t) ≠ ℙ{i = arg maxj rj}
D(π(t)
i , π(t)
j ) ≤ ϵ1D(ri, rj) + ϵ2

47.

48.
(KT)2/3
1 − δ D(π(t)
i , π(t)
j ) ≤ 2D(ri, rj) + ϵ2

49.
|πi(t) − πj(t)| ≤ d(x(t)
i , x(t)
j )
x(t)
i
π(t)
r(t)
O(t)
ϵ

50.
r(t)
maxπ∈ΔK
∑
K
i=1
riπi |πi − πj | ≤ dij

51.
K, d T
d T ln(T/δ)
K2
d2
ln(TKd)
K2
d2
ln(kdT/ϵ) + K3
ϵT + d T ln(T/δ)
K2
d2
ln(d/ϵ)
ϵ = 1/K3
T T

52.
∑
∞
t=τ
γt−τ
r(t)
s(t)
a(t)
r(t)

53.
ϵ
1/(1 − γ)
πi(t) > πj(t) fi(s(t)
i ) > fj(s(t)
j )

54.

55.
f

56.
f

57.
• [Hardt+16] Moritz Hardt, Eric Price, and Nathan Srebro.
Equality of Opportunity in Supervised Learning. In: NeurIPS,
pp. 3315-3323, 2016. https://arxiv.org/abs/1610.02413
• [Pleiss+17] Geoff Pleiss, Manish Raghavan, Felix Wu, Jon
Kleinberg, and Kilian Q. Weinberger. On Fairness and
Calibration. In: NeurIPS, pp. 5680-5689, 2017. https://arxiv.org/
abs/1709.02012
• [Dwork+12] Cynthia Dwork, Moritz Hardt, Toniann
Pitassi, Omer Reingold, Rich Zemel. Fairness Through
Awareness. In: the 3rd innovations in theoretical computer
science conference, pp. 214-226, 2012. https://arxiv.org/abs/
1104.3913

58.
• [Agarwal+18] Alekh Agarwal, Alina Beygelzimer, Miroslav
Dudík, John Langford, and Hanna Wallach. A Reductions
Approach to Fair Classification. In: ICML, PMLR 80, pp.
60-69, 2018. https://arxiv.org/abs/1803.02453
• [Agarwal+19] Alekh Agarwal, Miroslav Dudík, and Zhiwei
Steven Wu. Fair Regression: Quantitative Definitions and
Reduction-based Algorithms. In: ICML, PMLR 97, pp. 120-129,
2019. https://arxiv.org/abs/1905.12843
• [Zafar+13] Rich Zemel, Yu Wu, Kevin Swersky, Toni Pitassi,
and Cynthia Dwork. Learning Fair Representations. In: ICML,
PMLR 28, pp. 325-333, 2013.

59.
• [Zhao+19] Han Zhao, Geoffrey J. Gordon. Inherent Tradeoffs in
Learning Fair Representations. In: NeurIPS, 2019, to appear.
https://arxiv.org/abs/1906.08386
• [Xie+16] Qizhe Xie, Zihang Dai, Yulun Du, Eduard
Hovy, Graham Neubig. Controllable Invariance through
Adversarial Feature Learning. In: NeurIPS, pp. 585-596, 2016.
https://arxiv.org/abs/1705.11122
• [Moyer+18] Daniel Moyer, Shuyang Gao, Rob
Brekelmans, Greg Ver Steeg, and Aram Galstyan. Invariant
Representations without Adversarial Training. In: NeurIPS, pp.
9084-9893, 2018. https://arxiv.org/abs/1805.09458

60.
• [Woodworth+18] Blake Woodworth, Suriya Gunasekar, Mesrob
I. Ohannessian, Nathan Srebro. Learning Non-Discriminatory
Predictors. In: COLT, pp. 1920-1953, 2017. https://arxiv.org/abs/
1702.06081
• [Cotter+19] Andrew Cotter, Maya Gupta, Heinrich
Jiang, Nathan Srebro, Karthik Sridharan, Serena Wang, Blake
Woodworth, Seungil You. Training Well-Generalizing
Classifiers for Fairness Metrics and Other Data-Dependent
Constraints. In: ICML, PMLR 97, pp. 1397-1405, 2019. https://
arxiv.org/abs/1807.00028
• [Rothblum+18] Guy N. Rothblum, Gal Yona. Probably
Approximately Metric-Fair Learning. In: ICML, PMLR 80, pp.
5680-5688, 2018. https://arxiv.org/abs/1803.03242

61.
• [Joseph+16] Matthew Joseph, Michael Kearns, Jamie
Morgenstern, Aaron Roth. Fairness in Learning: Classic and
Contextual Bandits. In: NeurIPS, pp. 325-333, 2016.
• [Liu+17] Yang Liu, Goran Radanovic, Christos
Dimitrakakis, Debmalya Mandal, David C. Parkes. Calibrated
Fairness in Bandits. In: 4th Workshop on Fairness,
Accountability, and Transparency in Machine Learning
(FATML), 2017. https://arxiv.org/abs/1707.01875
• [Gillen+18] Stephen Gillen, Christopher Jung, Michael
Kearns, Aaron Roth. Online Learning with an Unknown
Fairness Metric. In: NeurIPS, pp. 2600-2609, 2018. https://
arxiv.org/abs/1802.06936

62.
• [Jabbari+17] Shahin Jabbari, Matthew Joseph, Michael Kearns, Jamie
Morgenstern, Aaron Roth. Fairness in Reinforcement Learning. In:
ICML, PMLR 70, pp. 1617-1626, 2017. https://arxiv.org/abs/1611.03071
• [Liu+18] Lydia T. Liu, Sarah Dean, Esther Rolf, Max
Simchowitz, Moritz Hardt. Delayed Impact of Fair Machine Learning.
In: ICML, PMLR 80, pp. 3150-3158, 2018. https://arxiv.org/abs/
1803.04383
• [Aivodji+19] Ulrich Aïvodji, Hiromi Arai, Olivier Fortineau, Sébastien
Gambs, Satoshi Hara, Alain Tapp. Fairwashing: the risk of
rationalization. In: ICML, 2019. https://arxiv.org/abs/1901.09749
• [Fukuchi+20] Kazuto Fukuchi, Satoshi Hara, Takanori Maehara. Faking
Fairness via Stealthily Biased Sampling. In: AAAI, Special Track on AI
for Social Impact (AISI), 2020, to appear. https://arxiv.org/abs/
1901.08291