Introduction Snippets Conclusion References. Beamer snippets. October 21, Decock Beamer snippets

Transcription

1 Jérémie DECOCK October 21, 2014

2 Introduction 2

3 Introduction TODO TODO TODO 3

4 4

5 Basic frame Subtitle... 5

6 Citations and references cite, label and ref commands Eq. (1) define the Bellman equation [Bel57] V (x) = max {F (x, a) + βv (T (x, a))} (1) a Γ(x) 6

7 Lists itemize, enumerate and description commands item 1 item item 1 2. item First item 1 Second item 2 Last... 7

8 Colors color environment small footnotesize scriptsize tiny 8

9 Fonts color color environment Red Green Blue 9

10 Centered image includegraphics command 10

11 Subfigures figure, subfigure and includegraphics commands 11

12 Blocks block command Block 1 Blablabla Block 2 Blablabla 12

13 Equations V (x) = max {F (x, a) + βv (T (x, a))} a Γ(x) V (x) = max {F (x, a) + βv (T (x, a))} a Γ(x) V (x) = max {F (x, a) + βv (T (x, a))} (2) a Γ(x) 13

14 Equation array eqnarray command Expectation of N = n E(Z i ) i=1 n β γ c(d) = d i=1 β/2 i αβ γ n 1 = c(d)β dβ/2 i i=1 αβ = z Variance of N = n V (Z i ) (3) i=1 n E(Z i ) (as V (Z i ) E(Z i )) (4) i=1 z 14

15 Matrices a 1,1 a 1,2 a 1,n a 2,1 a 2,2 a 2,n A m,n = a m,1 a m,2 a m,n M = ( x y ) A 1 0 M = B

16 Systems of equation array { n/2 if n is even f (n) = (n + 1)/2 if n is odd 16

17 Mathematical programming with align max z = 4x 1 + 7x 2 s.t. 3x 1 + 5x 2 6 (5) x 1 + 2x 2 8 (6) x 1, x

18 Mathematical programming with alignat Max z = x x 2 s.t. 13x 1 + x x 3 5 x 1 + x x 1 + x 2 = 14 x j 0, j = 1, 2, 3. Max z = x x 2 s.t. 13x 1 + x x 3 5 (7) x 1 + x 3 16 (8) 15x 1 + x 2 = 14 (9) x j 0, j = 1, 2, 3. 18

19 Animations Slide

20 Animations Slide

21 Animations Slide

22 Algorithms algorithmic command Require: S, A, T, R, an MDP γ, the discount factor ɛ, 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 zero δ, the maximum change in the utility of any state in an iteration repeat U U δ 0 for all s S do U [s] R[s] + γ max a s T (s, a, s )U[s ] if U [s] U[s] > δ then δ U [s] U[s] end if end for until δ < ɛ(1 γ)/γ return U 20

23 Verbatim To insert a verbatim paragraph, the frame have to be declared fragile. The title has to be written in frametitle command, not as argument of frame (I don t know why... )..--. o_o :_/ // \ \ ( ) / \ / \ \ )=( / # gcc -o hello hello.c 21

24 Listings I 1 #!/ usr / bin / env python 2 # -*- coding : utf -8 -*- 3 4 # Author : Jéré mie 5 6 def main (): 7 """ Main function """ print " Hello world!" 11 if name == main : 12 main () listings/test.py 22

25 Table tabular command γ = 1 (small noise) γ < 1 (large noise) 1 Proved rate for R-EDA β α 1 2β α Former lower bounds α 1 α 1 R-EDA experimental rates α = 1 β α = 1 2β Rate by active learning α = 1 2 α =

26 Multi-columns columns and column commands Blablabla 24

27 URL JDHP 25

28 Conclusion 26

29 Conclusion TODO TODO TODO 27

30 References I Richard Ernest Bellman, Dynamic programming, Princeton University Press, Princeton, New Jersey, USA,