A MATHEMATICAL ANALYSIS OF ACTOR-CRITIC

!"
#
$
"%&'( )*&
+ ,*
- $(
$%+. #&/0 12 ,3+$4#+65
798#:<;>=@?BADCFEGH=I=IGJ;>K*LM;N:O?PRQSQ"K08#:TUCOV9;NGIWX?RYOZ[Z\Z
TM8#g=H=I8QS]W[b[Q^hi8>QN_9;#LjTMb[QS8W\K0:`DkUaD:Db\QSGIlWQSceWXdfLmGIGHQSbmn:OdfQ
Vo8pLmb[8:qYOrst#uev#vSw
xzy|{F}D~iR}
NÞ ß[fàfá fâ£Ìfjqfq>N>*fDfNm9jNÑqjjf NNÈ¥ "«mS§ £°H§JjªÀ´[U¶¨pU± ¤¥§@ªOj·>«¬¹X ®
Rf9NUNNNR^qjjHmjfS>9jOMNNN^f>Njf ¡HfDNSSNJUNOUj>S º«j± ¯oÕq¯ND§÷¨"mºÀHNÁDNNqjNm"Njof£N j¼ ¡jfNmjoN¡NO¯ i±fª¬°²¹X«j®
N9£¨>N°²±³µq´Xj¶¢¨p±of§Jª¸¢·Nf«jN¹>º«¬f± £|§©¤¥¨"º¼¦S½qNjR¾NfRq¢jf Nm^NU§©¨pª¬N«¬¬® fª£«mN§©°HN§@ªÀ ¿mÑfU> S>N^> mSj¼ jÑU>mÌOqSNN£N¥jÌffjN mUo>Ñ¸@R±ª£°£¹[f«mÌNS ¸
¯ NNjj U0m"fUf#¢N¯ NSNjfUONNf¯»¥f¯ UfUNjNqf mf"ODjeN¿"j|0jN£ NjUm"eNOjNjSO#fjÀNNDfqjNFÀ N¿
¿Â"±fFª¬°²À¹X«jN®ÃNª¬N«j§©j°I§Jªf mNfN>N >¥NÁSmfjNUNm¼3 ÄF mÅN ffNMNjU9Mf>ÃN Nª£«mo§©°H¿SÃ§@>ª£N¼RfjÕqjUNSM0ãmÁNjË¢f(NN¾j¢¿SUNNjSmÖN9N"^ÌqNqNNjU£*äjoM¢q>jfUSjmj*Á>NNj
f"> jÉÊU^NNf£¦ÇjUÆÈfN9fNfj>IÉÊ^9fjffNN>(^£ÌONm¤*Ã¦jËj NÉÊ9ffj>mfÌN½q ¿Í £¥ÅNjjNNfmjSjR¢ff0 ÌMjNNUNUËjMN Ë¢9£ÅNN#jUjfmB(ff>>f@Nj
jÏSÎ¡f NmÌOjÌSÆSfNN9 NÌeqff>N¥NÐÑN¿NqmNjN ¼| ÒFqfj jNqffmUNNN ff¿fNmjU#Nf¥0j>¥mU"ËN#f¿f9jBN¢Nfjj>*f¦mjjN9qmfN
N¢9NNm#NËf 9 >|*Á>^>9£Ó fjjj^ffµNmËfU>>» mj¢f9"f>jÃ>ffMS0NNÔ j¾¿fmS@N@9Ã>#fjN >Ñ¾j#ffjj0^f»fNUNjÑ»NfjMmNfm(¼^#ÕqUNmjf¢N È
¿SNUNNefmÌOfqjNMf»qjS¿f£j@ffjjNfm|ËN^ffm>¼ÑÕqUNoi#Uj²H fUjfN>j jm|MN¿qÞ NON mNfDHÖÌXNm >NNNÁNj
M NNfMffN>qfUSqj>j )£¢¥>fÃjÖNjmffSI¿fÌDmNfmmN¢jMfq9f^SNN9j ¼ m Þ |ß[¿fàfÆSÀá j9fâ#SNNNjI£fÉÊ¦fmjemß[NÌNà f NâDfNjDNfN f>Nffo NÃN> ^¿j£qÌ£¦f¤*NjjÀNNj fÉÊj mÞjÌß[½qà ffâ#ff>f> fÉÊ S
Þ ß[àf>á eß\ àÎOáfáfâ¡f>>ÌÈÆÈjNqf 9ÌfNMoÐÑNNNmDN Þß[àfÑá â£9¼ijÆÈfN f@
× ØDÙ }i~DÚUÛÖÜUR}iÝjÚ Ù
jSÕq N¢oU9o jf">Ujf o¾NNRNHjfqjN(jSM^fNf9j>NUjo¼ N¬
Õq0NoNNÖNNjo0ÁoN§©¨pÑª¬N«¬ m¬¨N°±À³U´[¶>¨p± jj§JSª¸·N«jf¹º«¬M± jN§©¨"º jSjUNmÑmfNjmNRNq¬ÓpjmÁpSN£NNf>OfNS
Þ¤¥9fe¦S>N"m>Ìfß\Uàáfàfqâ¬NÌfqfN£f»¯ mUf9ÔNNÑNqjFojIj¯ jUfmN"jDq NNN¯»q¯fNN£Í ffm¥ ÞfÑ9Nf£j@ffjMfN(¥>jfm ÌÁfUoSfN>NNjNMfN\â£N¼)¿S Õq>NNff
">HjfqÀfS@N >^m"j¿SNNNU9m^"m¼NoÐÀf0N£jÅNNjjjojSÁ9N±jN·N«j§@¹[f«j § Nj#Ì NÁfojf¥¦ ãf¤ 9NSfËÀNffN#9jNËNÍO¢NNf»jjNÑN^Njm »¤
¤¥>¦S oNf>Þ Nß[àfáffà£â£(ÌÑqo>N¥¿S NSj)f"N(Î¡NfU>ÌãUÆSN¥ ÌÁ^N£ NN£N N£of">qNUmj"#fjSjfjDmÌNNffRNjff ¡^ffRjSÑj>DjHjj j)@f
fN>j¥j¥Sf¿fMm¢Nfjj¢MqNj*NSNË¾qjfNNNN¿äj»jjSN(I#¼UfÐÑjSS NNfm^jËÁNËj9SjNo¢)">f9N>jjÀ^Á*fm|SRqff¦#NÌÑNN jNNfNFN@
fÑiNSNU£@Nff99N[@Nfj»fmfjq NNNUjjUS9j¼Á½q»mNjMR >¥Uq N0oNfN¦SNNqÑ*>fqSf£N ff¾>m"¿SfÔ
ëúÊ÷òöëHúÍç²øDéJæMå ç@çû"øHç ëó¬è£úÊéJòãé@ë#êjë÷üëIöfé@ç@çó£ìÍíøIýjç îÊúÍÍõmï çífêmõqçðIøIñ\ùë©òfïÑúÍó¬ó£òfþ ô#øfòfîÍçê£õõòfïÀèmõDç"ÿ ô#ë÷ê£öföfé@ç#ójëHóøIø©çíôðùf#ó£øIöfòëHóÀê¬ë©úÊòXò[ø©ë÷üfífúÍê£ê£çîÃéIõFñ\ðç@ó£çòfòõÑðë©ó£ó¬éIúÊííùéDéJífêjó£ë©èmúÍéHçó¬úÍÑè¬òXúÊøòfçIëIòê£ó ëî N£ÅNfNjf>Ë Hj. NSMm£ÅNf#mjjf)j»q jR¥fN>¢imfNM#O N¢jNjN¦SNNqj
ê£mòfüSõRçð@úÊúÍòfê¬ø÷îeúÍè£ë©öföë©ê£ìÔòíñîjøRðó ê£îÍøHÑóç²ëHòXó ëIøfê£úÍòfðIö õqð²méHífúÍë÷ëHúÍëIð@ó£úÍòø ÑNôø#öföfê£óoýjç#öföfêjø¡ç²îÊü"úÊò çõDífífç@øòfðè¬çéJõoçêjó£ë©îÍíï é jfS ¿S UfqNNmj|Sj¼D ÕqNDN >j NNNqjRf>fUOmÁ#jjNfÀ#fjfÑNmNjÑU SS
üfë÷[öð²ê£úÊúÍé@òç@ë÷òfñ\úÍê£ðúÊòfîÊç Íèïó£ó£ø©ííò¢üòfüSë©õöó£êjúÍéJë÷øqëIúÍó£çø÷òõÀíù ùHï çðFëDé@úÊê£òòò\ë í Ñç²éJó£ífø¡ôê£<ï[øìÍé@ó #öë©úÍöføÑç ô#eó£êjéIñUë÷úÍó£ôòfêjê£ø î ÌN9NÀjNjÀUMN£HjÀoUfNÁNfR> q
)(
+*
-, /. 0
1
32
+4+*
+5
8:9
+*6*
;(
+7
=<
?>
(
'&
!"# B1
A@
@DC
%$
ÒFff9ß
NN¢MjfNÁN^ÑÁjo>Uf9¦fMmf¢Nj>¼ »NÐÑN>mfM>fjNÑ N^ÔH£
SNjj>fjjfo9q^fNfNmjf²Jmf^UÁjSjmU ¥oqN £@Nf>fM¬Jj@@f@¥UH
N"jÖN¼jjf»|#9¿SjËS^>9 mf> >
} }DÝjq ~ mÝ Ý Ù M~DÝ À{
@N½ÏS>j#j^¢)fÁÑNËNNfffN¿fNËjf >¥fN>U Nf>j Njjf NfM )jN(NOI9>ffN9>m f9>fffNO0)j S»S¿fjNS
NNjf¼Ë¤¥f9jffj¢FHNfUfNOäjo>jfUMoNNfSNNNU)ejNffNNf¸
¿ ">q»N9NNMjNjjj#UMmf">Nf #ffNSSÁjjOU¿"jjS ffNoNmjN¢qNmj£¼
TVU³Ù
E
N¨N§©°O NNÇ±X«fj¹ q´fp£ª¬§N£§JO¹[¨oN°± j\RÌ[Rqq#NO N[À@ >N£°²±XÞ °H§J¹X¨p±[«m¶ D® pâ
jff>N f>U»fON N$NMjRfoMHNjN j¾fÌ >S ÌSMfmf>f¢fomS Ì
eNNf¼ fÐÑN^Nf>N> 9jN N)j9HNfNjfÁj fj mNÌRÌqËNf0N>NNf>¢jfNNN¥S9jNof>fUfNU)Nm £ÅSj
jmjfjj f(jRqf(N9>jfU0jS#¿S¢Nfj>UmjUSjN¼^m(Õq>£ ÅNofmNj¥NHNmf»»S
#fj j¢fqmNf¢¢jRNf¢HNNNjf¥f q»>j(NNj¢jNN Ë¼ HNN¬

<
F
IHBJLK
G
NMPO
QJRM SK
J
(
TVUXW
(
3nporqSsP>+jutvlxw

B
B A
ml

TVU³â
QorNq ` w
TVUT
TVUê
±
Ls
N<
0 S.
·
{ ¯ Qo©p´r¶ ·³µ ¸?¹ «
¹
/ ?»SS¹ ¼ ¼S¼
E

o
¾V¿ ¬
V{ÁÀ
Å $
ps
².
X
!
× Ø
(
·
s
·

R
·³½
¹
o
³.
Ã.
²
ÇÈÉÊ²ËSÌÇÈÎÍÊ%ÏÐAÑ6ÌÒVÍÊ3Ó ÔÉ²ÕÔ²ÌÒVÒ%ÍÎÑÕLÖ
l
L<
0

~j
ø ¯ {

{
«?{
(
sn
ï ð ` s
{
ø ¯ { oúù

û{

nzéyztÚnréy
ø
0
÷á ÷,

`
Rø ¯ >yzt[y

s
(
®qò A ?ó®«?{ w
`óô« ¶
{ ¼

+õö
o
º
XÆ
~j
B{ky
ï'ð ` ño

NÄ.
<
Nqf¿fm 9Ì ËÌ#fN MÌ#N N
Þ â
Þ â Þ Þ ââ
Þ â
Þ Sâ
Õqf^N N"¥>£fÅNS#j@j¢mj>mjÁjSoÇ>¹[f¨^£R® £f°@N·(³¹\¹ ¥± Èj£j±fj´ ¿¿jfNÔÌÌ
ff NU9j>U ÁfjRfÌNfm f Þ Áâ£ÌSjfjNjj NÌ jf¿SNNMNSMjj
jUÕqNNj jÌSqHfqOmf£f¢f>NzffNNjRfÌSÖN #NÞ NÞ f#âjâ£²¼
ff
S
Þ "â Þ "Þ â Þ ââ Ô Njq¼
ÕqjN>f ¡j mNÌ Þ âR DS9NÑN¿ >ND£H@NNmm^f"9¦fNNm f>9jM¿fINfÀ fMfS>
D¼(ÐÑNÌOIfojf£ S ËÌRN N¢N¢f#jf
Þ Sâ Þ Sâ
¤¥¹£·N9£«j±[£°I¹[j« »£¼ ¢f#jf»ÑjNmHf6U³ ¹[ª£±³ Ã±ª ·
·
·
<
o s
E
/Â
1
®{¯°uy
k{ ¹ ¹
s {
ë^ `Zkì®ZQ ]¦Rîí£Nf\:Zh^3\:¥

3« ¬§
(

ãª ?h^3\Áä6å\ÁdhÁd ©ãª\ æçdhf ?h¦R\f
<
^QhZ'aRNf' ?hf¡£¢¤d¥ `^I¦RcIh§f'¡©¨ªfh§¦;\c
%(
ÝÞ
j l «
xl

ÕqfNUÀ j>ÅÈNm|q>N jjfm>""j^NMNNmÑfÀjfmN Nj¢Þ f9ß[â£ÌSNqÑN>ÃÑ
NUj(If¢qNj ¼ N>9f¢USjf#Nfoj qDmÌ@HN #UN NjofËoÌ m Nm
H°N¹[° ±DS³qÌeN f£¢·NSÃ# ª¬@°» Ã´¥N´Xf§ \ª£¿¹ fSN¨N°ÃH´ÖN>«j£j° Sf«jÖ¨ fÞ f¬NNNoN¢Ö«¬¬f° S «j¨Sâ
Þâ
Þ Þ ââ
qNmNmj UNj0S ¥fN NNf ">jÞ Nj¥Þ µââHj
j£ ¤¥Àj ¼ Nj>fNo§J´f£±³e f±³ ±X°H§J¹X¨ S¨pª£°I§J¹X¨NÌ
NMmN¢HfSfN fN#fj¼
é@ífçøIø÷çíõÀîÍeëHúÊøçò»jôýj#ç@ë÷öfé@çOë©çOöfêjë÷ç²õ[öfîÍöfççøIç@ó£øé@é@ôçeïq#ë÷ó£úÍöë©ì é@öqó£ífë©öfè£ç#öfó£úÊòífëIëSç@òëIóÁë"ó¬ë÷öfì"çFçýmüç@éJòó£ë©ùfífê¬ê£ùîÊÍúÊïî úÍøHç ë÷\úÍëIðNç@ìòfó£õ[é ÁúÊòfíè îÍeë÷êjöfë÷ójúÍçøIó£øIø òç
~Ü0
ks
xyzorq{D>+jut}|~w
(
A
R4
Lj ?(
k
s { Pènèéªy
=(

(
S0á
¤¥jmMNmf¥ff^U>U»NS¥jfN0fFNfjojRNff¢ fÞ jfS²Jâ j»£NoÔ ¼
¤*qN Rjj¿jNÁNjjjN^N9fUfSNÔHNMNONm Uj DfÌNNq>N O>jÑffS¬
NSMjUNNÑjfäjÑj9 j9RU>Ñ¿SNmRNHNeNmff >Þ ¼Á¤*â£9ÌNNN
""jjm>fq#O9jfRN>f"Oäm >jN>¡fH#j$jfRNNeS>NÑÑ>fjjjÁNf¢ ¬
N@¾f>Àf mfj>N >fUmÌpfRMfoNjfNÞ mI¼j¼ NÌ m¥ SqNj N^j> ÁSNjmfffËÃâ£¼
qfNNjUNfjM¼N9Sj6qDj¿fm"Nf¢jf¾U#j@H
oL+q6 ` Bow
x?

l
D(
0

` kj
á SÂ
p
Y[Z\:]3^`_bac3_d\^IcRegfcIh
kj
²ßà
«
N jf Njf¼Áf¤¥Ì[N¢OfÈjJ #fNNNUUäjj¢ÀN jm¢ mÀfjNÌNqj N q NÁNjOfpj
N)mNRf >>j»NfNMÑjqqje¿NN >R @H9NNSj fNm¼ ¼ >fRfS NÀj
jf Ñ¤¥iÞ fâo >NUmNMqfN |m¿|j¢N^j ¢f NfN¦fUq¿Ã^j>SfN¿"mm fj¼ÁNUÕqNjNSjj0Ìj>>Nj¢¿"jjÁ²
Nã^NfNfN>ff06N>£fÅNN@@N o mH>Nj¾NjÞ j â >j¾S
Hj^qUjÃf¢> £N mMM¼ÁD¤¥fj 9ffqNjÃÑ¢>ffÑ "qmÍ
fÞNNUâ NjjÞ >â j9NUjNUmNNofDqj£ÁÅN#jj m¾Þ ¿ â£>Ìq¼
i
YÚZQ\]3^_u¢Ûf ?d¥6d^3cbZ¥Á]

üj
s { 3o
(
Bø

s ø ¯ { ¼

ý áS.
ÒFff
Nþ
>
TVU²ÿ
Áe
ë^ `Z' B^d h^3\:¥
>ffq j £ ËÌ S MÌN oÌ#N NNf#j
Ôf N Þ â Þ Þ ââ
Þ "â Þ "â fNjq¼
ÐÀ NÌ#Hqjf£ "N MÌ N NoNMmff
Þ Sâ Þ Sâ
j@fffN > f ÌHf¡jfS£ fN oÌNN NN
Ô N Þ â *Å Þ â
Þ Sâ Þ SâNjqÌ
q£NNSmf9fU NN>Njj¿jSSe¥ SNN jff>NNUfjjRNHSf^¡f¿S> >jM¥N
ÅNË9ÌN>& NNM£@Nj0f# jS¦fNj ¥¿fN¼ËÐÑ>ÌOH$MjS Ã
Þ "â Þ "â
§#¯ f·N¤¥j«j¢¹ ff ¯À£H¬m¨N° U¹£·N£"«jS¢±[¢°¹[j«Áf£¼ÑNÕqNmf>9M f>f#»#jjNfMS f f¦fo >³ j¹[fª£ ±¢³#j¿·ÈfÀ¹³ÊN§JNª¬m¶
HjeMfNÁFmNjNSiM#fjjNfj>¼ÐÑHf RMjN j>qNm Ì j NjfS
#^m¿SfjfÁ9mf>99j >jjj SjN(f¥9>jS jjN )>jm¼ã0Õq>>q|j¿fN
RN^j(fj¥Nqj j*S¢¥f)mfjN¿fm >jUNmN@@f Njf0#jNjmUUjSN @ Ì
@)">ÁfjS9HfNU> NjÀof>jNÌDÀNf¿fjfjNNfN¾OqNemNONjNN|f£ ¼
fffqNSfN9¢# ÈjeHjfpNj9N¢jÌSjfiNf»qNO Uj> D> 9imjfU>NSj ¼
ÏjUjffjf#mfS9¥N9UmNÁDN<DmjNNqjN#UNffmf N¿NÑ > @jjfN>ffqDËfq>ÁqfSN9jij>oNNHMFUHfU ¼
£NNmfNMÏff¿j¡| >jNef9È@#R fjq*fN f> jf» i»jmffNUN j>¼ f@ffMmfDpfNÁNUSUff¦>¦f
D >U ¼ qNfDjURRj¢q qOS">NNUj^ONNfNFjf¿f>m9fqNf#ejDf#f@
qNmNfo£¥¿fN¢NjNF MNSDNÁ9ÀjNfNDNfN >jUfo@RS|¿ffM¿iUmfUM>Sff¦N
9Sf¦Njf¿fNÀq ¢NjNjSÀ¿fNÀHfR9f¼
j
>nptÚn

ð
Ã
B{y

ð s
Ã
%o
s

Ã
C

ð s
Vo
s
(
l
ð s { ¼
Ã
j
{ky
<
i
/(
õ
(

SÂ
>nré~yztÚn

s { Io

ï ð `

N{
TVU
!
"
#
ÕqjNRm>N¿"N¡NjNojSIfjqM >9NfDjNNmfjD<Hf ^Nj¼»N¤¥qoMfNNfS
>
<
{ xo-{À
s
v
~j lxw
å^3egR¦çhZhÁd^3c ^A@®hæRf-¨
C hZ'hÁd^3cRZQ\!DB^d ¯ 3orï ðE s
w
Rq+ø
3¿
µ
Ã
{ ¯
B@^3\zZ
fh¦R\c
`ó
s
£ï ð
Äq+ø

÷ý
,
S.Á0
S0 t
?^

~s
<
« ¶
+õö

å ^Ic3_Vf'\ Vf'cR `fmh^ûí çhÁde Z'dh

ÛcR¡Rf'\
ãª¥ RcR :æR\^3c;^3¦R¥ví£Nf\Z'h^3\bãªRçd `Z'ä
hÁd^3c
S.Á0
NC
{ ¯ 3op ` s

<
Á(
x j£
QC
i
nréyztÚnréy
S^Æ Njf NÞ fâ ¾#fjÞ Ì Þ jfââ¡)Hqfjf NfNmj ¾Sq¥Nmf ¿S¥ >
NSj& Njq SNf N
Þ â Þ Þ ââ
F G Þ "â
ÕqUNÑR "SjjzjjNf¸ÖHM&f¿fNmM^#f^S9qSNO9¿S mmBÑ<ORNmSjjÌ>jNS
qi¥>"f>¥fUNNfff¾f¿UNMNIMNNjo j£N¾N SNN¥jS¿fNf¿ÑM#jfj²
fNf ¿j9NNË#jNfÃ) >S^ ÑNE ¢Þ ¿fÞ Njâ â£¼(ÕqÞ >â UIfq >UÖ"mËN¬j Ì
qNNf jffNUfNNj"0ijR¿j*fUÔMmÌfNNNqq>fNfNq¥Njfj²HjfmÑUj¬
jfNjm 9SN£NfNNUjÀjm¼
H:IJKLJ*MONQPRNQJTSVUXW
ª± «¬; ¹X¨p[¹ Z]j³Ê¶Ë\ °²¹¥±X¨N¶(±[« ¬§©°I«¬±[«m¶ Þ â M§ Ç° È±£¬·¨ ·³ §J£4 ´*± £¶(¨NY ®
C
Ã
Ã
TVU
Ã
®(
E
/0
?>
é~y
Ã

¹
» S¼ ¼S¼

{ nméy ¹ ¹
<
s { s { s » { » ¼SS¼ ¼
E E
{
¬ V
%o
s
E
E
÷0
,
ÄÜ ³,
0RÄ
ß
Â
q+ø
ð s { ¼
0
<
C
<
~j
{
s
/(
o
ï ð ` Qo

s
s { 3o
ð >nªtÚn

¹
o
ï ð I¿pï ð s
j
>nréyztÚnréy
Ã

l
ffN¿f9mUR9qfm>N$0»Df "#>jjNjf&q% U%NNN Njf#jfo Ì
N¥f NÞ jmj â ÌqmfNoN¼ONÕq¢> q¡f¥¿fj¡¥ >q MfOM#f ">jjJN¿jN
Þ ' m(f'@â¿f)N%*R' NÞ * ',+ Þ (',+ â¡â [HÞ qf. â-0[/Þ ¼ >âfqfSÌfqNNj£
±£j·1 ·$q³Ê§@ªÃÌN±XR°H§@¹[¨B9¹ N²°NÁ¢o¹£·Nm£«jN±[°Ñ¹[>« f£N«jR¹ NN2N$j»Ô± £¶M¨p>ª f«¬N¹X¨p¹ Hf
ffSfMf SNN#jjNj pNjmf ¢fH¡jH f¼ 3 @¾$¥¯ Noq NmN£9fjjÌ fR£9»fR#fjS²
ËNÀNSjSjÔH
Ë ¡f>Nf NfMIÌqqNNj0£9ÁNUÏHfU9NNfRfmN¡H¿S Mq
ª££ÅN¹[j¨ÀfN£: q«@9'º" 9>°¹¾ÃNÖ¹¬q·NN°I§ N¯ q£^±j³Ê¿f§©9°Ij¶» ÔqSN4 j5Nq47m6 »fN<8U#4 ff>jqN@¿jf< NN; ¾Ñ=>N9fj¼
¿ÁfS @(NMqj>jff9> H>fÑ¥ff#qSj(Á¢jf¢9>NfMNNNjm0>»jjN ¢>NNjNmff#fjfË(HS»Ë¢fNÔ
UjBNo¥qm^N9RHfN£ jffm¼ >f¢S£ÅN¼ UNÌ
;\^`_%fegfcIh£í£Nf'\Z'ä
¯ { ¯ ¼

<
®{
qò{

©jw
¹ jw ¹ 0
s { Ý ², ®{
t
S0
{ ¯
D+hf\Z'hÁd^3c
TVU
B^d ÕqNq m·N^¹S³Ê§@^ª£¶M§÷°²f¬«¬±XN°H§J¢¹X¨q> ¾SjjSN^>NNjfjF >jj Ofoff>NËU¬
mqfmNNË >U(_IffN¢q >N|j^Nj NNM m m ' *'ÌRojfN@NI
E _ Þ ' Þ ââ U Å E _ Þ â
H(f' FjfÞ £ â¡H¼DÁÕqN RN¼ SjmOj >fmefD"» (' Þ â
¹
{ ¯
ï ð
½
{
E

½
>
/(
E
3o
Bs
ï ð
®½ s
s
E
`
{
o
ÒFff
N7
jãj¤¥SjÖ fj f0fojN¢¥ m#ÒD|9ffN#N9f> >j Ë¾#¢fß^j¾(0NNjN ËÞ f00SâµNmjNNjf Ì
NjÑoR9qf! >Ujm ¿fm"ÑNUfj¡f ¡ ¡ffNNNM[ÅNN mjjf »U¢M>jU#fNNj
Hmj fqfDff¢N¡NfR SfjÞ NmN>N jâFffNo¿fjj FezNqfONÑNj">> jNÁNjq S¼ Np@j#qNfmNjj
¿ >>fqNfRjfS¿jjÑ9fN f@f¼
¹
(
{ ¯
¹
{
s
.`
a
TVUXW
Nj
¹
l
s
;(
<
<
{
¹ <
Â
.
RZQ\frYÚ¦çhdçfgã
` s
ï ð
ks
ï ð
3o
. L.
D0
Ü Xßqø
Üý²ßNq+ø
Ü ²ßNq+ø
Ü Xßq
Ü ²ßNq

{ÁÀ

{À
; j£
{ À 3o

õ
?óP« ¶
+õö
<
<

{ À
N{
~jw
Ä
0q+ø
:Â
qò{ R
ï ð
0

J
G
w
,
S.Á0
¹
ý
s
BM
<
<
C
{
¹ Ä ³, 0
S0
S0
ý
®0 .
Ä
¹ ¹
3, /,
,
0
s {
, PjPÝ ³,
0
Â
0
q+ø
/,
:Â
÷.0
²0 Ä
0
w q w

w q+ø
w

w
Ã
ø w

ø w
Ã
Ä
Ä ², Ä
<
¼
<
S0 ³,
w q
w

Ã
Ä
0
{ ± 0 ²0VÄ
Â Ã.
µ Ä
0
Þ
', Ý Ä
0.
0 /.
b+hf'\Z'hdÎc
N{ À
.
03Ä
Z'¦;f
(
?hÁd^3c;¥
ÕqNH qNqo¦fjjNj¼
q:rAs!JTIs!tuUbv ·f·N¹ \Ç° N±[°|±[¨±[« £§©°I«¬±X«j¶ \w ¬¨pª£(¹
¹£±£·N··È£«j£±[±[°« ¹[^« §©¨ £D«j¹¨>¯ §©°²m³Ê¶B¹ £°²x¬¨, § Ç ±£Â··§©¨z³ §J£y ´¥f°§J¹ª Â\£¹ ±ª ¾ ¹£Þ ·N¬«¬±[°¹[âR« \
¯ q° N«¬¬®
{ È¬¨ q§ q 476 4 Þ â9 [§ £° \¹[«9Ã±ª
°H§È¯ ³ °H±§÷¨"³Ê§©º °I¶m\ w £¨pª£¹ ¡·È¹³Ê§Jª¬¶® f±³ ¡·N±[§©« Ñª£¹[¨ f¬«JºS q°¹»¹¬·N®
jN¤¥mM¼ ¢N¿fMNoH qN9j mjfÖqNjf¿f
q:rAs!JTIs!t|k~}Á¹[¨ ¬«JºS£¨ ªÃµ°¹|¹¬·N°I§ ¯ ±³Ê§÷°H¶9¨p££´¸¨p¹[°Ñ¹[ª£®
³ ª ¹ SyO« §©£S¨"± º¨p´f\¬£«»° µ± £¹ »¶x ¨p¹£8ª ·Nf £«j«j¹[!±[¨p°¹[¹ « R» ±¬·f·³ §Jª£±[°I§J¹[¨¾¹ ±[¨>¶|¹ q° È \¹³ ®
££ª´ 8 x ! # #
£ \
¢¿fÎ¡f>*NU9ÕqINN jN@ojjj -fNÖoßHÌf NFNN¥¢fSÃNj>jjN9RNË0q NNj£Ë m¼¾NjÕqoSN¿fm jf">fmjj NNjm
|>¦SjÌR¿f m>B Sf0D£ÅNN mNf@¿fN)NoNNf jjNÌOfN ¥¢ffN>¦ff¿0>Nfjm Uf¬
SÑNj#NfjmjqJe¿f#Nj»f>f¡oHjfS¡jqjNoÃj9NNNjÑjf¼ > @ËNMHj j"ÌO>jNNjj
ffNU @oR j¢ff>j¦fÌNq¿^Nm"£¿S¢jfN¢U#m">jÌDj¢jfI£f)qNf ¿So >j fÂjj¼ j
"NmfÕqDfNSNj#ff£¦SjNj ËJ¿fßUN Ë9>O#NNf£fHjN¢iRH N£»NUNNm¿"fjDUÔHjmS" ">q¿^jmjSNfNjmÀfNjMMj¢fNS
U @ qNffSmj ÌqU>HfqNjNj¼
q:rAs!JTIs!t|bW Y Þ Þ ââ
°Þ N£¨± âµ£¶¶¨p§Jjª ³f´ «jM¹[¨pªÃ¹X¹ ¨ f*£«@±£º"·¬·¨p³Ê§@ª£ªÃ±X°²°H§@¹¹[¨3¹£·>°H¹ § Þ ±³â §©°I[¶¹[\ «Ux ±³©8³ °¹
¯
Nf9>ÕqNNjNjqMj^fj N>NfoH>N»0 q SµNNHNjNNj.mBÕq>Þ jf¿â Uj IfÞ Ußâ mf£N[ Þm|â ¼ Mm¤¥f
NNÀ qNjNRjÖNÏÌ HfNoqjmNfÑNË@RMÁNq> j£R^f>S»¿SmNfjÑ ^SjRj²
jN9fj>j äjf¢i#fj9jf ¼
JIJ?QIU=W |±³©³D° È £·È£ª¬°²£´Ö«j yã±X«¬´ Þ âU±X«¬
¨p±£·¹[·¨>³Ê¨p§@ªÃI±Xº"°H±X§@°H¹[§ ¨¾fÑ¹ ±X¨p´ LÞ x â 8 \¹[°«ã¹ ±Þ³©³ #° NâÀ£Ü¶§J± m£³ ¶´ ¨pª ª£f¹X«j¨ ¹[¨p¬¹ «j®
º"¬¨pª£°¹U¹£·>°H§ ¯ ±³Ê§©°I¶ \ JIJ?QIlkW
ª°²£¹±[°I¹£§J¹[·>¨Ç°H§ ¹ ±³ §©°I¶\ x ,°Y¹ ÑÞ ° È¬¨ ±â£¶¶§@¨pjª ³´ µ«¬¹Xª£¨p¹X¹ ¨ ¾¬«J±£ºS·¬·¨p³Êª£§÷®
¯
3C
Õq#fN jf9±S³ > µ§©°£Ñ«j±[j°I§JU¹[öNN>SNjmNN¼OÐÀN"j9m#UfNjm qÖfUHfRNqN£f
c Þ Þ ââ U Å c Þ d â
q#fDjMNje)>j9jU¾NNjoSMfe£N#Sffj >¼»qHÕqNimMf£ jÌe¾NRNfj f
R¿S FNN9mN»»ÑNjÅNj»>3NON>£@Ájj¿¥N"f¦ fNmfN¢N¿RfN>jjqjNjf
fÕqjÀ>ÑHf Nj¼ j¿fNfHNNmf RNNN SNÀ
N U9NMSm& NN >jfR SNffN
Þ "#â e f
Þ â U Å Þ â
g
Õq NNM¿S >¿fÑ ¿jjÑf 9NN¢SjqmNËNfµËHffRN ¿SfNÖM¿NfjNM HSNNN£
fNSMNjjNofjjNfj ¿£j9Ñ"No#UNÅ N ÑNÞ O¿ â¬>¼ij¤¥ Þ ¦SâN
Þ ß\fàfMájàfqâoÀfN>jUf»N>jÁ9N¿fmNjOUjNRUff9ONjNNj9NM¿fffND">HfÃ R>jMf>NffN0 m9NjfjRNfSÔ
NfÁNj$NjqfNjiUhRj®³ £f±[«m¨N§©R¨"º 9¼e¤¥NqÀfHfeq>NÑqjIf9ÖNÌfq"Np£
qUÀfNNfNfÀHqfNq>N#fjj¼
H:IJKLJMjNQP8N?JSlkXm £¶¨pª «¬¹X¨p¹ |±£··³ §Jª£±[°I§J¹[¨¹ o° N \£°
¹ª£(¹[¨ ¹£·N¬£«JºS«j±[£°¨ ¹[ªÃ« °¹U¹¬·N °I§ ±°²³Ê§÷¹0°H¶ ±X\ ¨ ±[« £§©°I«¬±X«j¶ Þ âÇ¶§Jj³´
¯
MÝ pÙ o Ñ{¡Ü £}i{
n
ÕqmNf¿fMfNN¡ÁNSRRUjimNfSÑSN m>»j N#Áj9SN£¿NefIfNemNfÁ¿S >N
jNNÑ#f >jUj^j ">jfN¢jjfÀfDN SSOj9>ffN£>¦S NUjNfU#fOjjj99
NjN¿fjjUjSeNjfff@fm¼ÑÌfÕqfS>j9NNqN£ MmN f¿OSONmÀNjjjfoS¿fjmf@
# Ñ9SqjNjN9mNj¢fNf¡NjSHNÀjjNfMmjNfjSoHDfeUD» jjSf@@NjN
"NjNÖ¼Âf½Ï¢jqNÁfqmjSfH>fjNjj M¼ q@¢>fM>MN"N#jjmNoÑÍqON>Ãj)¿Sj@ Ì
RMf¿Ñf jNÑqNNRNS¼
"p¥ÁfÂ@^Qd zí£Nf'\Z'h§Î\¥PæRZ'hå^3eûä
ÙUW
þ

<
þ
<
®C

`4
³, ¹ ¹ S0
s {
/,
Ä;ï ð ` s
÷.0
S0
Â
¹
;¿©{ VÄ

jPÝ
ÄPqø w pq
w

Ã
¹
¹
Äq+ø
{
¹ ², ±
I{ Io ¬ Ä
Äq+ø w kq
w

Ã
Ä

ÄN{
w q
o°{ ¯
w
Ã
<
¹
<
Â
5

{
E

{ »
S¼ ¼S¼
÷0x A
S0
/,
÷.0
S0
Â
¹ Ý ³¹,
s {
Ý ², ¹ ¹ ÷0
s {

,
S0
S.Á0
Â
ÒFff
L8
Hj>NNjSÐÀ»Nf>(fNjMFUÁËjjqU #ÑefÌOf>q9fNjj£S¥fjDj(fjNm"fN¿jN^ jNNNjjMR (NSjN>OjU¿fNNN@
RSÁNfRjfS¿jjNjof>U @U#fNm ¼
q:rAs!JIst3m £¶¨pª «¬¹X¨p¹ ¾±£··³Ê§@ªÃ±X°H§@¹[¨B¹ ° È \¬° $
ºS¹ (£¨ ¹£ªÃ£·N± £5°«j¹U$±[°¹¬¹[·N« Ë°I§ ¯ °²¹ ±³Ê§÷±[°Hx ¨¶o§ R±X « ¬¾§©°H«j±[±[¨ «j´ ¶ Þ Rß !âËÁ¶¹[§J« m³ ´ ª£¹[¨ ¬«j®
&$
x ¾±X¨p´ zBRß \
NN¿S9ÆÈNf >ÀNj#Uj¿UMNM¥Oj#mf¢UNNfff^> jN¾jNfU¥R^N9>¬ßH ÌfNjIfN¼]>D"Ïojm¿fNNjOfNRmf jmNmj Ì
R^fqNÁjj^j>if¿9»Nj>Ñf9 ¥SqjNjj^ >R¥»jmffNN S>NjjNmNjo¢NH
<9Õq>> MÔJHj 9qNN£o¦">m|NmNfqfÑ#Njfj¼ NSj£ÅNfU> m
f¦fUÀNj>^N¼ j0¥jN 0ÕqNjfj ^¢Ìq
q:rAs!JIst|v X··È¹ \° N±[°± \ w >¬¨pª£9¹ o¹£·N£«j±[°¹[« §
¹´X§££°°H±[«j§©§ ¨ ÃS´ °I§J£¹[¶À¨Ç§©¨p¹ ´f¬²«·N£¨p´£¨>° x «¬,±[¨ ´f¹ ¯ \± ª ¯ ¢·#° ³ÊN§©¨"±[º °ã¬ «¬¹ ¬¯ «j¶|± ¹¬·Èf¬Ã«j´®
±\X°²w¹X« ¬È¨p± ª£Ñ¢¨p¹ ¹X9¨ ¹£·N££«j«j¹q±[·>°¹[«¬¹« MÃ± °£¹^§I³Ê§©±X°I¨N¶ ¶¢\: {§©¨NÈ§©¬°I¨¾§J±³#±£·f·N·#¹³Ê³ §J§Jª£ª£±X¶°H® §Jf¹X±¨Â³ ¹ Àq·È° f±X§©§ «
Þ¬§H³Ê§÷°H¶ â9\ ¶§Jm³ ´ |ª£¹[¨ f£«@º"¬¨pª£°¹¾¹¬·N°I§ ¯ ±³Ê§÷°H<¶ yO§©° ¢·N«¬¹ £±[®
;«
Ä
0
0
,
Ä
¹
S.Á0
÷ý
Ü Aß £oÛq+ø w q w

Üýß ôorq+ø w q
w

Ã
s
L«
;«
{
¹
6þ
Ä ², 0
÷0
:Â
? l
<
3«
þ
6ý
0
ý.
R, ÷0
0 ¹ . ¹
s {
ý
ý
:.
÷0
³,
0 /.
Ä
0 0
0
QÄ
'ÞQ±
÷Â Rq+ø w Bq
w0A. /, ³,
/Â

Ã
6ý 6ý
',
Ä ², 0
Ä
0
Â .
÷0
Â
²,
6ý
"Û¥frÂ@<B^Qd í£Nf'\Z'h§Î\¥®æ;Z'h
ZQeûdcRf C dc3fûãª ?hdÎcR¥
ÙUT
aä
jÏSffB¦fRNjMfjN¿N»f>NN¾jjFÀN f»mN NSjDN¿fÑ¢Uj#fU¦fDjN£UNfUN>¢f>j@DÁ¿fËÀm9Ñfjo#SfUOfjS ¼
Õq¿N m>9¥fff#Nj¢ffU¢9RmffN¦0NSN0j9fjNff¥Nq¥¥NËNSfj¦Nf>jjfS
¿ >>ÑfIfjRf£N M¾ Ì SNmÌO f¼ N 9ÌON N¢N
jff S
Þ "â
Þ SâÔ Njq¼N Þ â Þ â
ÐÀ NÌ#Hqjf£ "N MÌ N NoNMmff
Þ Sâ Þ "â
Þ
q:rAs!JIst|bW Y Þ Þ ââ
°Þ È¬¨ ± âÃ¶¶¨ §Jmª ³ ´ «¬¹[¨ ª£¹X¹ ¨ ¬«J±£ºS·¬·¨p³Ê§@ª£ªÃ±X°H°§@¹U¹[¨¹¬·N°I¹ § ±³Êâ §©°I\¶ ¹[\ «Ux ±(³÷³ °¹
¯
N¤¥SRNN£jN9OfjN9fNNND¿NNfjÀNqfDfj9 jNffÑfSM¢NNjND9fN N"N>N N»MNfÑNNNMÀNfjff»¸N
N f#jf9q)N¢N¢mjf0jfN> fN
<

ð
Ã
ð s
Ã
Ã
3ogù
~<

rj
>nptÚn
s

<
PjÝ
w
Ã
NfN£¦SN^ mffjÌ"q > £¢RMN*N N¼q¤¥ ÑN¬
UÞ "Åâ Þ â Þ â 2Ôf NjqÌ
Þ Sâ
fNN > Nm Ì"9oNfUjiNN" p>ff Ì"RqH>>j
Þ "â Þ Sâ
q:rAs!JTIs!tuXW Þ
±ª£¹[£¶¨ ¨pf£ª «@fº"«j¬¹[¨p¨pª£¹ Ñ°¹U±£·¹£··>³°H§J§ ª£±[â °I±§J³Ê¹[ §©°I¨U¶ \¹ Þ ( â \ ¹X«Â± ³©µ³ £°²°¹ ±[Þ° Ñâ¡° È¶§J¬m¨ ³ ´
¯
(
Ã
ù
{ Vo
Ã
/(
>ÁyztÚy
(
/,
Â
ï ð A w
ÄL{
÷.0
s { 3o

s { ¼
Ã
{ÁÀ RÄ
ÄQq
Ã
"p¥Áfz^A@YÚ¦hÁdä C
ÙU³Ù
ko
>nzéyztÚnréy
Ã
¹ Ã
S0
q{
{
;(
Ã
w
30
s
0 ¹ ¹Ý ²,
{
hfbì®ZQ ]¦;í
S0
f\Z'ä
h^3\¥
@¢f S¢j^S¿fNj(N>jS ^N *q>Þ feHâ¬fÌOqqNjU0*fNoN^¾>f mfÌDf
UNfjf^Ë>f»HfU qfm¼ NÞ ¿fjÞ ââ£¼M¤¥¸MÌ Nj¥£¾ÅNÌ mN¾Nµ Ì
fN¢#f ¿f"jfmDÌNN N
+
Þ Þ ââ Þ â
Þ eâ
qNfjm>jjUNj¢S DÑffNNN > ÁÞ SNjNÞmÑââ
HfNjqf£f >£J3jo Sefâ£¦¼Uf>ÕqjNfMM¿MNi #J Þj)efjâ >j äjÞ efâ¬ ¼
qO qN jNjm"OfNN[ÅNUfR Þ â
¾qN£ËN9fDqN9 > »jj jNfjm(S
Þ â¬¼
ÕqNj ÌfHOjÃ ËÌ ÌSfN$9S# f ¿fqSjj
DÌN NNf#jf
Þ "â
Þ S â Þ eâ Ô Nmq¼ ¼
Õq0N"f09mjÌNfj N )»Þ âN¢S0¿fNNz9I#NJNjj 0SffN¦ff>jNfj0 ¿HfN
ffF >G D¼^ÐÀNÌDIfjf£ S ËÌON >U>Uf#jf
F G Þ "â Þ "â
¤¥¹£·ND£«jj±[f°¹[f« £¼ mffeSjNmeIf³ ¹[ªÃ±³ ¯ N³Ê°I§©® £°²²· £±fª X·
ÕqNN£ÅNqjNÀ qofmNj ämf|iÕqNmfm >¼
q:rAs!JTIs!t|bm £¶¨pª f«j¹[¨p¹ Ö±¬·f·#³Ê§Jª£±[°I§J¹X¨ ¹ 9° È \¬° $
º"¹ (¬¨p¹¬ª£·È¬°«¬¹U±X°²¹£¹X·>« ¾°H§ ¯ °¹*±F ³Ê§©±XG°I¨3¶»§ R±[« ¬§©°I«¬±[«m¶ Þ â ¶§Jj³´ Çª£¹X¨ ¬«j®
£± &$ 3 ¡ x 8 ^±[¨p´ Rß !O¹[«
:$ F G x 8 ¾±X¨p´ Rß \
C
ï ð s
Bs
xï ð s
mj 3sÛ¤n
B
P{® y
(
·
·
·
E
¶
²
·
?
¸
¹
` s 3op ´
º
« s `®
ó « {
(
ï ð

¹
/
E
»
S¼ ¼S¼/
¬Á
®¾
ø ¯

ø ¯

z·²½ (

o
{
m{
Vï ð )E s 3oÛï ð s
{ ¯

pj
s { 3o
ø ¯

~s
>Ánré yzt[nré y
ø

(
s { ¼
.
0
Ä
E
·
< ·

or
s
~j sPn
Rø ¯
> yztÚy

ï ð s
Qo
{ o ù
{
/(
ø
¹
Á(
« `{
{

0
ý /áS.
8
L0
0
Ü Xß ®o
ø
Üý²ß £o
ø

/,
Ä
q
q
¹
÷.Á0
÷ý

w
Ã
{
s
w
«
¹
Ä ², 0
S0
Â
«
6þ
? l
ÒFff
N4
Ü 'M~¥¤
¤¥Ojf>S¿¿fjRNjNjjjqSqj9fNj > fO@NÁjqÁ>jN»fFNfON>jji SNNjjfN
¿SN¢NN#ONffjm( jÞ fUmÌiN¥jjf¾UoSjN£jNmÌÁfNfN£J¥jfm¥f9NfNN£â£Ô ¼
ÕqNN£ÀUUj" ¿jjjNNjÁÑÑNIffmIÌfÌXqNNjqNmqMÑSNq9j#jDjRqNmj
DfNfNN9"fjjNjm ¼Of¤ NN ¡NfjNRqUjqNNO£UNfN>£ ¢jfqS¿fjmffmNNjj
efNNRj 9NNjfRqNjjm ¿fNqfNÌfiN¡OSUmNjÔHSNNOoM>NUNÀ NN
qNNj£M RNfjR¡jfjÁNNDÑfSONmjjmNÑ9jNNfqjfNeD Ñf NjNUejD>@
«jjjS³± fH±[f°I§J¹[ Ü¦*·#³ N±X¨N9¨N§©j¨"fºµÌSfjjffËNHjÌfqqÑNÆSÃNfjf ÉÊNÞNß\»ààS£â
j£ÅN>N9qjNo9MfÑN">j¾Nejjejj0NNfÑ£@f mSNf)joNff fN ¼
#> NfMjNS#jjNfUO¿SfffNÌÁmÌf9Nfj>q»|fR"Oj>#>Ãj > 9mf¿f>NRfNN¿SMNijN >@D@jfjSD 9# NSNj^f>UNÔ
NjNMÁj>N NÁjmffNoRjM¿fqfNDmONNqN¬HfN#e mIffe>> j>¿SNfÀfHNNNjj ¼
o 1§ Ñ~ Ù À{
ÎOÞ>ß[àfÌÑá ÐMâ£¼ ¼ öq¼jÌÑNÆSNfN¦f 95Ì mµ m¼ãUÆ#j¼SÌ ©zÐÀNfNMNjmfËf fÌ»¿À9¼ãN¤ Ô© ¼
±fjª¬N°H§@¹[9¨ |j¹Xl¨ NvNN¶)£°j fSf¥ÀN±[¨»N±Xj¨pUi´ m}D¼ª¶ £W¬¬«L«j«L¨p«¬°H§@ª {>«j±[¨#®£®Ì
á [á È¼ ¯
Î¡fÞ Nß[Ì#àfáfÐMàT¼ â£öX¼ ¼°DÌÆS£±[>«j¨N§÷¨" º(*Ì µ±[¨ ¼´ Æ#¼\*Ì © w >¤¥¬¨Nf°I§J±¦S³N´fm£Ìª¬À§ £¼ §J¹[¯N¨ ¼pÀ¼ ± ½[®¼
§¢©¨"ºÐ (Þ ²ÏN±¿fÑjÆÂÕi@mÃ> N¢jfL qf£mSNjámà[Ì³Àà jâ£N¼qÐÑUNj¯ Sjej Ì
RfNNmÁN @SIff UÆSjjNm¼
½ÏffNN 8Ì @¯NÁ¼f½È¼ Þ jß[Nàfjá fâ£Ô@¼iNÄ<Nj#fNONÑjfNNNqj>fj fiÕqNNUR#Nf@S
N¯NL¼ jö9¼iRoN#£f@NNjIÌj¢©
SÕ¼jË¼ j¼ Â@ £Nµj¼È Æ#Þ ¼ ÄDÂNm £¼ âN¥¦S±XI® Ì
·NUª «j¹\§©¨pN±´ª ¼ °i£µp±[¹«m³ ¨N§©¯ ¨"º!L =W¬W£mÀ¼ ¨XDmÀÐÑ«j°I§Ájª¬§JÌ"±R³Ð W£¨>°²¢m³©f³Ê§º"f¬¨p ª£¶ÀfmÏS·N©®
qfjÌeÆ#¼Oß\àá â£¼ W¬¨N°H«j¹\´ ª£°I§J¹[¨Ë°
¸R«¬¹º«¬± ¯o¯ §©¨"º¹¼ Ïj=
ºRf¦ O¹ÐÀjv>f°²N¹[ªmNU± £°I§JÒD&ª ·µj¶m¨p¼ ± ¯ §Jª
ÆÈf9jNfjINÌNÐM»¼ >D¼NÞUß[àNMâ£¼ fUÆSÀUOË£NjN£¦fNmjËj:¼ W±» ½f¼£N¹ SN«j ®
¨p±³M¹ ¾Ñ \£±[«jª ±[¨pi´ ·o fm³ ¹£· ¯ ¬¨N° ®Ì Nß àS¼
qj>Sj <ÄR¼SÐM¼ >jfm">fNfN0¯N¼ >jNU
Þ ÄD>j¼Íâ Þ ß[à fâ£¼ }Á¹ ¯ · S°²¬« |±X¨p=´ { N¹ fº °H=¼ qm
ºÁf¦ ¢8 ¨R½qI¼
ÆSNf TÌ ¼Æ#¼ Þ ß\àfá "â¬5¼ { ¯ ·N¹[«j±³eª¬«¬£´[§©°q± £§ º¨ ¯ ¬¨N°R§©¨
¢
£
K
K
3<
¬
S±
<

J +J QJ
(
0
+764 85
0
0Ýà
Ý
®0 /.
2;C
BC

ý
+4
+5
,
Ä

2;C
8 ¬ þ
úi
òÝ
Và
8+8
,
¬
Ä
S0 .
;Ä
S0
6*
0
* þ ¬
C
>
0
6*+*
0

0Ý`à
ÃÝ
Ý
þ +5 þ 64
ý
/0AÝ
Ä
J
+7
N>
f¿ÕD«¬¬mj§©£¨ N[@N¹[^«¬jª£ ¯À¢q¬¨Nm°D³ £±[Ñ£«j"á¨>>§©¨" jºf¼<â¬jÒD¼ÌD ÐÑ¿¼ ³¼ N³ÀjjÞff¢ Ì ²q±ÑNÔÆ
ÆSNUfmÌNSN¼Á Æ#¼ ÈÞ jß[Uàfáf#áfâ£¼ fNmÔÓfj>m >N¥jjm(¼ Ç>±jª N§©j¨pS°i£±[«mN¨N ®
§©¨"º ®Ìpà[ >¼
ÆSNfm f,Ì µ¼XjÆ#¢¼ Þ ß[£àfNà â£j¼mFNeHfjRNjfiNqNN5 ÌSN³º5f>ÏNÐMNÌNfÌSfNS
¨Nm§©f¨Sjº¼ >N¼lv>°²±X¨ \¹[«j´<v·N«j§©¨Sºv>¶ ¯ ·N¹ £§ ¯ ¹X¨Á¸q³±[¨N®
¤¥f«¬¦"ÃyãNm±XÌ«¬´ À£T¼¼O¯>ÒD¼p À¼Ä³¼p¼½µ³À¼ Þ ß\àfmáàfâ¬Â¼ f°D £Ì±[R«j¨>f§©9¨"º N£ «¬>¹ f¯ ²Ï´jN³±[¿f¶"j£²´
@ÌRf9NNfÌNÄDNfN ¼
¤¥jf>fjNÌÁÒF ¿.¼ D¯>¼ SÞ ß\jàfUá f â¬e¼¾Ð¥ÎONfNN^jfÆÅN"¥>UNNj>j mf[ff>NNNNf Ã
{>«¬±XH¨ j\±fª¬°Ho§J¹Xf¨ Nã¹Xf¨ UvN¶£f°²o f>9ÇN±X¨ i±[¨ jÇ´ j}Df¶££ £«j¼ ¨ W¬£«L°I§J«Lª «
¯
ÈmÌ X ¼
¤*HmUÌ N£¼S½m¼jÞ £ß\Jà Uâ£ ¼DÐÑ¢9ff¦f>f¿)Nj S¿¿"ÁfNNjfSfmjf3¼ SW¬¨ f\¹[j«m ®
¯ ±[°I§J¹[¨Ç±X¨p´´}Á¹[¨N°I«¬¹³ L®RÉÈÌ á [ fà S¼
,6Ý
?>
3C `>
3
Þ
+i
+7
Ä
÷.
>
+567
,
ò8
0
Sá

Â
.

zà
>
, S0
?>
+4+*
0
0
>
.
Ni
0Ý
%à
þ

', S. ,
²Ý
0
S.
¬ þ+þ
S00
ÒFff
N5

Download Report

A MATHEMATICAL ANALYSIS OF ACTOR-CRITIC

Paperzz.com

Your Paperzz