this repo has no description
0
fork

Configure Feed

Select the types of activity you want to include in your feed.

Continue rapport

+12 -11
rapport/main.pdf

This is a binary file and will not be displayed.

+12 -11
rapport/proofs.typ
··· 11 11 $ forall s in S, Q'(s, 2) = 1/2 Q(s, 2) $ <dkl-zero-a2> 12 12 $ forall s in S, forall a in A - {1, 2}, Q'(s, a) = Q(s, a) $ <dkl-zero-else> 13 13 14 - #let kl = (a, b) => $#a log #a / #b$ 15 - 16 - #let crossout = (content, why) => $underbracket(cancel(#content), "d'après " #why)$ 14 + #let why = (content, reference) => $underbracket(#content, "d'après " #ref(reference))$ 15 + #let crossout = (content, reference) => $why(cancel(#content), reference)$ 17 16 18 17 On a 19 18 20 19 $ 21 20 22 21 D_"KL" ( Q || Q' ) 23 - &= sum_((s, a) in S times A) kl(Q(s, a), Q'(s, a)) \ 22 + &= sum_((s, a) in S times A) Q(s, a) log Q(s, a) / (Q'(s, a)) \ 24 23 &"On découpe la somme selon les valeurs de " A ":" \ 25 24 &= sum_(s in S) 26 - crossout( 27 - sum_(a in A - {1, 2}) kl(Q(s, a), Q(s, a)) , 28 - #[@dkl-zero-else] 29 - ) 30 - + kl(Q(s, 1), 2Q(s, 1)) + kl(Q(s, 2), 1/2 Q(s, 2)) \ 25 + sum_(a in A - {1, 2}) [ Q(s, a) log Q(s, a) / (Q'(s, a)) ] 26 + + Q(s, 1) log Q(s, 1) / (Q'(s, 1)) 27 + + Q(s, 2) log Q(s, 2) / (Q'(s, 2)) \ 28 + &= sum_(s in S) 29 + crossout(sum_(a in A - {1, 2}) Q(s, a) log Q(s, a) / (Q(s, a)), #<dkl-zero-else>) 30 + + Q(s, 1) log Q(s, 1) / why( 2 Q(s, 1), #<dkl-zero-a1>) 31 + + Q(s, 2) log Q(s, 2) / why( 1/2 Q(s, 2), #<dkl-zero-a2>) \ 31 32 &= sum_(s in S) 32 33 Q(s, 1) lr([ log Q(s, 1) - log Q(s, 1) - log 2 ], size: #200%) + 33 34 Q(s, 2) [ log Q(s, 2) - log Q(s, 2) - log 1/2 ] \ 34 - &= sum_(s in S) - Q(s, 1) log 2 + Q(s, 2) log 2 wide "d'après" #[@dkl-zero-a1 et @dkl-zero-a2] \ 35 - &= sum_(s in S) log 2 thin (cancel(Q(s, 2) - Q(s, 1))) wide wide thin "d'après" #[@dkl-zero-qeq] \ 35 + &= sum_(s in S) - Q(s, 1) log 2 + Q(s, 2) log 2 \ 36 + &= sum_(s in S) log 2 thin crossout((Q(s, 2) - Q(s, 1)), #<dkl-zero-qeq>) \ 36 37 &= sum_(s in S) 0 = 0 37 38 38 39 $