Introduction Snippets Conclusion References

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Jeremie DECOCK

October 21, 2014

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Introduction

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Introduction

TODOTODO

TODO

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Basic frameSubtitle

. . .

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Citations and referencescite, label and ref commands

Eq. (1) define the Bellman equation [Bel57]

V (x) = maxa∈Γ(x)

{F (x , a) + βV (T (x , a))} (1)

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Listsitemize, enumerate and description commands

I item 1

I item 2

I . . .

1. item 1

2. item 2

3. . . .

First item 1

Second item 2

Last . . .

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Colorscolor environment

small

footnotesize

scriptsize

tiny

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Fonts colorcolor environment

Red Green Blue

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Centered imageincludegraphics command

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Subfiguresfigure, subfigure and includegraphics commands

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Blocksblock command

Block 1Blablabla

Block 2Blablabla

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Equations

V (x) = maxa∈Γ(x)

{F (x , a) + βV (T (x , a))}

V (x) = maxa∈Γ(x)

{F (x , a) + βV (T (x , a))}

V (x) = maxa∈Γ(x)

{F (x , a) + βV (T (x , a))} (2)

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Equation arrayeqnarray command

Expectation of N =n∑

i=1

E(Zi )

=n∑

i=1

γ

dβ/2

c(d)β

iαβ

=γ

dβ/2c(d)β

n∑i=1

1

iαβ

= z

Variance of N =n∑

i=1

V (Zi ) (3)

≤n∑

i=1

E(Zi ) (as V (Zi ) ≤ E(Zi )) (4)

≤ z

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Matrices

Am,n =

a1,1 a1,2 · · · a1,n

a2,1 a2,2 · · · a2,n

......

. . ....

am,1 am,2 · · · am,n

M =

56

16 0

56 0 1

6

0 56

16

M =

( x y

A 1 0B 0 1

)

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Systems of equation array

f (n) =

{n/2 if n is even−(n + 1)/2 if n is odd

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Mathematical programmingwith align

max z = 4x1 + 7x2

s.t. 3x1 + 5x2 ≤ 6 (5)

x1 + 2x2 ≤ 8 (6)

x1, x2 ≥ 0

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Mathematical programmingwith alignat

Max z = x1 + 12x2

s.t. 13x1 + x2 + 12x3 ≤ 5

x1 + x3 ≤ 16

15x1 + x2 = 14

xj ≥ 0, j = 1, 2, 3.

Max z = x1 + 12x2

s.t. 13x1 + x2 + 12x3 ≤ 5 (7)

x1 + x3 ≤ 16 (8)

15x1 + x2 = 14 (9)

xj ≥ 0, j = 1, 2, 3.

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Animations

Slide 1

I . . .

I . . .

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Animations

Slide 2

I . . .

I . . .

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Animations

Slide 3

I . . .

I . . .

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Algorithmsalgorithmic command

Require:〈S,A,T ,R〉, an MDPγ, the discount factorε, the maximum error allowed in the utility of any state in an iteration

Local variables:U,U′, vector of utilities for states in S, initially zeroδ, the maximum change in the utility of any state in an iteration

repeatU ← U′

δ ← 0for all s ∈ S do

U′[s]← R[s] + γmaxa∑

s′ T (s, a, s′)U[s′]if |U′[s]− U[s]| > δ thenδ ← |U′[s]− U[s]|

end ifend for

until δ < ε(1− γ)/γreturn U

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Verbatim

To insert a verbatim paragraph, the frame have to be declared”fragile”. The title has to be written in frametitle command, notas argument of frame (I don’t know why. . . ).

.--.

|o_o |

|:_/ |

// \ \

(| | )

/’\_ _/‘\

\___)=(___/

# gcc -o hello hello.c

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Listings I

1 #!/usr/bin/env python

2 # -*- coding: utf -8 -*-

3

4 # Author: Jeremie Decock

5

6 def main():

7 """ Main function """

8

9 print "Hello world!"

10

11 if __name__ == ’__main__ ’:

12 main()

listings/test.py

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Tabletabular command

γ = 1 (small noise) γ < 1 (large noise)Proved rate for R-EDA 1

β ≤ α1

2β ≤ αFormer lower bounds α ≤ 1 α ≤ 1R-EDA experimental rates α = 1

β α = 12β

Rate by active learning α = 12 α = 1

2

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Multi-columnscolumns and column commands

Blablabla

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URL

http://www.jdhp.org/

JDHP

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Conclusion

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Conclusion

TODOTODO

TODO

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References I

Richard Ernest Bellman, Dynamic programming, PrincetonUniversity Press, Princeton, New Jersey, USA, 1957.

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