Cross Channel Optimized Marketing by Reinforcement Learning Naoki Abe, Naval Verma and Chid Apte
Robert Schroko
Mathematical Sciences Dept. IBM T. J. Watson Res. Ctr. Yorktown Heights, NY 10598
Database Marketing Saks Fifth Avenue 12 E. 49th Street, New York, NY 10017
nabe, nverma,
[email protected]
Robert
[email protected]
ABSTRACT
!"# $%&'( $%*) *$% +"',! -/.0 1 2$% $%34 !5& 36 7 "'& $87 /! ' '3$29$%5;: A@ +"9CBDFEGH A3 5I3934JK.L*" M4N"O) ! P Q)R ' N 9% + % &/.0 *$%34 !8' ST
U"&($%.L V; K>A VR Q)*WL ' YX4 + Z: >AW[X\@ DEG 39 G!JL.0] 34 S N ] ' S S;^_ 5S3 ^_SM46 /.0-Ea`0>b=c 5 d!"HeV5[f( -g7)5 h &5)R 4! !33'5!MGBA \ i ' BA ; 5!.0 "*3 M$%D &M 83 M$j.0I AS M4"Y_ 8 8) 96 9 3 $%k%"' $2l5$83 $2( $Am5$%k5 * c3 U ?A n Z!GD0o'"5 _B- 3 M'$p $%$% * ; 6q!?AJ.'*.0h5rtsRu vxw/yRz!z!{v sR|}}ua~ v sR|R~_~ua}auaJ\" I ]/VY ?m53%V56 hM4G.0S $2! VR I! 0VR8'; i99" 8 $%[ 34 [ M"H Do-h3 Q)5"] _ n [3 M$pM9 "* * "O"2. 5 Y _ $%5h'+ 4D-0 '6qG!M4 ! B-m34 '$85 )
!' 9 S I $%\ S"90 .P ! !7$h P%n *[34?5? 5! 8A Z3 U 5 M4Im534 "JxM5B-$83 QBH%$2!'34 'Bd $2 5!'B "MBA [$8 +" BDh % n U $p ! 33
%\)"%8"5n. % K L!x ! ' 7] [ 5!x.0 "D Categories and Subject Descriptors
EDDS &Qt9tl5ttt
59RQ/5 ' General Terms
m534 $%5 Keywords
$80_ '$8) +J4AJ 0 )R75!
J 6 ( $%55!
J! "]$2 VR '
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. KDD’04, August 22–25, 2004, Seattle, Washington, USA. Copyright 2004 ACM 1-58113-888-1/04/0008 ... 5.00.
1. INTRODUCTION
h 7 \ n!9 O!"2 $%'( $%0) 0$% +"'%! 0 " M "B7/.0 ? \$% 9$%34 6 5? 3' "S $8 G! 3*$A!$85 : A@n +"9CBDWL 3' A ."6q 3 5"!iV5 ."$85 c $%34 5J h9? M4P7 ! BA ' 6 * ] 8 n'* h$2! VRD[EG2$2!BA+ J4)R" 3 Q)5"K_ 0 M c!5 $8"JM 3 Q)5"[ % 34/!'6q3 34 &!B5 D g733B5[m5 n"9[!B5 0 + 0. L( B8)R S5 "Y"9DIZZM45 ;m5' A + 8" A '3S 3 $%k?"' I$AV5S 34 )R!'L_ $2!m$%k5! * c_ h3 U %! 7"4 5?i9DKEG 83 53!34Jl.LS3 34 Z Q)R\ Y 9n 5! nG.0 8'$834 5 1 U"]_!$%.L VD 23 34 "F #]M9 "d d &5 &.0 VH %335 & l ( $85'+ 8 h 5 5 /4 6 ' )Rh" ' A$2V5/D0E/A 3934J?.n!7"$% 6 "* 9?M5B] $ZM'; ( $8575 -"A +6 M8"![$%I J4" ' [ !S! 8 3 6 $%k"*. - 34[ I' & $pM4U 75*M4A! $A 6 5!'B& "2 ''B&_ $ "9S9B5 DLo- h) /! x KM! n i ' B; 834 _ $¡ $8'(n $%[) $% +"'n2L 6¢! 4J
!"% 3 $%k$2! VR ' ?. 34 % % $AJ5$h 6qi9£3 U D o-9 )h " "1[^_ 57 "BIM4G.L2Ea`0>¤= 5! i " eV59f_ hg7)5 c 75)R 4! 0 n335M'/Bh B] P73 5!93 M$2J5.A.0.' 34 ? ¥ ; 5n3!34DIIM Z3 M$¦.L; "F! ? M4"&( K5)R 4! ] 9K x 3 $%k%5 6 LM4/.0% " \$A
x"% i9/D 0\ 8) [!'n L $8n n !;e!V f_ Ag)R5 .%!" 34 J 1 n.0M9J $2! 6 VR 4Jx" 8$2!'H"Y ; +J.L& & A( + 8 8'5 ! nM4G.L- %/ n/.0 &i9JlM9 " n G! )R5 )
!' 9 Y"] 5"' ? n ')
! "!D 2/ M ' !&.LC"#d ]4 && !'h! & h8 6q!0 9 4J!"¥h !5 c [$% [!335! ' \) )5'[ 6¢! 5 D9?3 M$2J.i;.0?5!'\rtsu vxw/yRz!z%v s|R}}ua~ v sR|R~_~ua}auaJc L/VZ
m53'V5'7M4/.08 0$2 VR 6 ' [!VRA2 Z!"2 34 ;:_3 U h .[ "@ M"Y'd D;h /! JxY36 5Jc )R B¥ .¡ / ; M )R"PM4G.L1$2! VR ' ;!"A 74 S [!'DK _ 5Jc33B56 46q 6q 4 I$% +"L $% +"
? .n "n!
7( )
! ' ) /M'J?VRB& %3 +" I$8 +" 9'"34"7 8$2 VR '1 ' J 5 n'+" 8 ?$2 V % 'D o; )R& 8!'&MB*5)R V52 ; _ $%5 5! BJ
"S")5 IK5 $hM4c £$% +"'U5 H'D§0¥ 8 Y$% +"U5! ' JnM! ", ¨Tm5' $8 +"d n _ $%I5 15"©|Rª«a|R}rt|RauY¬ªR|r { ® }?'¯!/J+\3! ' / B% M5DxEG\$290 n ') ? !ci9SMBA( + A -5! ] Aª ® ° u w ua}±!un' 4 0 ; ? .n! "K $%34 &! JR M5B8M5B56 39 ? 7 ! L $2! 8 5 \ B[ .n "( ' D o2 " "Om534 $%5![) ! ' # A3 34 " $8 +"n ¥ 9c $%n5 ' ¥"!h( $²eV5 f( Pg)R5 +D]; Z ? h6q/M4 B-)
! m34 '$85 x x l.0\5!hm34!x$h I9 Z934 5 5 L' \ L3 U M5B7$%3 QB5' ' ! $2 5!'BY3 +" "¥M5B h$% +" BJh $83 " * ; 58$2!'-34 B¥ "T eV5D2 & $³ I U $p 9 S33 4!i*n)
!'"*"5&.' n !K´ ! ?'] [ 5!x.L "D 2 ] h 2334&] 4!k"µ&_ ' Q.Do-2M46 M5B]" M& ZM 73 M$ 9.0A!"" J
' eQ De *¯3 5 \ $% +" B%' "n"6 !'"]" 3 K .B%")5' "&$% +"DeQ ;¶h.' " M4; %m34 '$85 n.0S " "O"- % h.L M!'"DeQ 1·? "?. 1? $%$2! BD 2.
PROBLEM DESCRIPTION
2.1 The business problem
2M &3 M'$¸.LN"" I'& !I 3 $%k " n$2!'\5! S$2!' )n$Z '385!$%3!'J $Am5$%kS Z4[ - 83 U ¹! )R5 Z M" Yi9/D gPe!V5Af'( ,g)R5 )PºO$AQ^( 2"6 n$2\5$83] % " "*5!i¥B5D S5!$%6 392)
! BF( $»$2!'* %!Z Y5! - 34U? n39 G!L3 +" c 3J iA\.0 $8¼ !339 ?!"A $% D%eQ $%] Z 5 +$%39J4 i !¥AW7X. A n 6¢!x ! h 3 5!6 9De M!"&34 BSh?$2!33Z( $´ $% M h)R [ J
'5*M4h 5"'BA ! / "2 _6q & GB5n _ nY!BI +D 3.2 Q-learning with variable time intervals
g78.0 $% "PNE/ +" J_ S %3 M'$b% B Am5 " *>AW[X1_!$%.0 V¥ PZ( $h / 5)R )5h)
! G!M7 $%7'5 )DxS«a| w ® |RÂa~uhr ® ¾8u ® }rtu w «a|~ Ã ÄÅ .0h '"7 h'"5 5 ; h !"9 "2" $%>AW[X£J£m3 !)R B*)R5nh '$8"D;À7 S.L-! 6 $8 !S $%P!I ] / A;º4J[!"N M 5 5%)R5 S.'7C)R 34 ' )RA $%P! +/ "d.
$2DLZ3 + ?'A $%h' G!9 ÆÇ7ÈÇÉ1º4J !"¥ - S5 Z 345 "B!VR& Jx ' A' 5 A & 9J ! 5J .n! "©"d $%25 !" 3J Ê :!ÆËCÌ/Í£Ë/Ì/Î+Ë/Ì/ÈiË/@!ÏiÐ ËÒÑ Ç D&I 4! S5! Z'Z -"U" !Z S$2m5$%k5! ' Y S L" 5 "¥ .[ "Jx.' [" 5 " C " $%"Y!8?_ & 9 [ $% " ! ' D9!KJR'K Z$2m5$%k[ $h / )R .n! " Ó J Ð Ó É Ô ÎË : Ø@ Ë_Ñ Ç+Õ9Öt× on n n$% +".0n5 +" n "4 5_ $ !" '$83h %m h>AW[XY 8 5 5 $%] ¥5D
D,e>AW7X#3 34 "HM5BF ¶/JLH 9%.LA ' ! $%h" h $% 3J C)5S) /M'5 ) 9D 8!'S*")5 -5! &$% +"* 8) 6 !M8 $%Z )
!?>AW[X-n'2" $%& ., h .n! " )
! ' n $%%5 )[ "M48 $2k"9Jl- "n * 4 c Z5 +" " M5BI n) B5S5 ) 9D1f
% $2! '¥ &$%$%"G! .[ "JcS'S'+ 9[ 8 .[ "* )R"H $%%5 )9+-M4h $26 k"AMBI")5"S?M5BI '$8h5 )/D\f ? $2 ; Ù\{ «a|R~¬5uÚ ¬}±ar ® y }A:_ nm534 " $h / )R .[ "@ J.i ? n M^( )R_ ]'Y1>AW[X£J+ n ! A _6 5!5 'B$% I $%35 "D EG¥39 G!J9.0;$Z ! 5 ( ! !Jl!5BS5! % ! J+ )
!4 ) .iZ K"' 5 "h .[ "c $8$%"A:_( ?!33 Qm5$2 Z) h( @c7 $%5 "DKf
$8 5J h46 )R8'5 )c&4 "¥M5BA %5! ] 5J£ '*h/! 5! n! 34 "L S 'n 5! \.05 c [ .n "K ')"S !05 h _ 5DÀ .0?3 34 %K 6 $Ak5 i$%hA.i2M4 A c h ! S hVR 5 ] 5KI" $8' 4 )R? $%75 )4 hM4
"Y_ Z $2!'k+ 9DP>8 & 34U5!'BJx.LI #!6 34"9 8 %_ n % $2!'k5! ¥C J0 9[( SÛ06q) ? $2 +Dc7 ' 8) /5K x M! i-Û06 5! ;$% +"A_ )
! G!M $%'5 ) 6q 39J5Ü7 6 =: Ûn@ JQ03 5 "SIf 8ØD:_? 34"9 L_ 0M4 Û06q) J5Ý9ËtÞá ßâ à J£"& $2!'k+ C J9ã[ËqÞ'á ßâ à Jl! []M' +V ¶
D7 73 " 6q +"5D@ 3.3 Batch Advantage Updating
g©5 $hM47 K3! [3!34 nC)R "" "* Z3 M$³ m "]Û06q5! &"; 0 / "I5! h$% +"K ) /!M $%5 )"S$8 B% n 5 5 $%&
J\5D 4Dd¯J\¶/Dd0? +Jc &.L VYM5Bd`K! "¯ n L39 /!n'5 [ & J
'8[ d3345 n M4-"" BP G! "P3 M$%8 * ; ].L& 6 B; !5_ Y33 Qm$2! YÛ06q5! %5)R ')5 ) /!MZ $%h5 )
!7 _ A"¿% ?" h S h6 +" "¥M5B S)
! B]5 )
!D-`K!' "Y3 34 8 Q)R $8 +"9J55!'"P|RªR«a|R}rt|RauS¬ªR|Rr ® }aJ. 8'+ G! )RA!")5h L $%34 -! [P5B]')2 5D n3 +" ) "n9 )5I Im53 'B2 $2! % Û06 ) 0_ J M5B[M5B53! ' 0 B $2 Z3 M6 $AD*o-;M 'äB-" M4I 8$% +"T"Y $%&$% +"U+6 .0$2!"[ %$AVRn.0 VI( ? ?3 M'$2D g")5Z 34"! ';'7M "* Z 2 n|RªR«a|}rt|Rau K! &Í8 /! ')7 ? 3 '$A\ ' ¥!nK)RI ! ÆaJ4. -å8:!ÆQÌ¢Íl@ D[%( .A'7 8 n! ! ')%"U6
æ Q çlèxé9Qên ëaìIí[î/ï;ð X£ $% 5 g,M! n5 'S$% +" 5J`0 5J5_ ? A)R9D EG3 0"ñpÉ Êò Ë/ó ô É#ØRÌaõõõÌGö1Ï?. ò ËÉ Ê÷ ÆËqá âÌ/Í£Ëtá âQÌGÎ+Ëtá âaÌ/ÈËtá âaø ó ù É#ØRÌõõõÌGúGËGÏ : ò Ë ô 6q ]3' +"5Jx!"]ú Ë ' [ ò Ë D@ ØD9f
h! ò ËûSñ ØDØ7f
ù É#Ø Sú Ë Jlü7È Ëtá â ÉYÈ Ëqá â ý Çþ È Ëtá â D9f
h! ò Ë ûSñ DØ7f
ù É#Ø Sú Ë þ1Ø ã ËqÞá ÿâ à É#ü7È Ëtá â Ý ËqÞáÿâ à ÉYÎ Ëtá â ñ Ë Þÿà É Ê÷ :!Æ Ëtá â Ì/Í Ëqá â @!Ì ø ó ù É#ØRÌaõõõÌGú Ë Ï × Þÿà @ ¯
D Þÿà É`K! 5 : ËÒÑ Ç á á × ñ¥ Ë ¶4D9f
ZÉFØ? ¶
DØSe ß J5+D
D ß É Ç ß ¶
D7f
h!' ò Ë9û;ñ f
ù É#Ø Sú Ë þ1Ø ã[ËqÞ'á ßâ à É#: Øþ ß @!ã[ËqÞ'á ßâ Ç à ß : ü7ÈiËqá â ãnËtÞ'á ßâ! ý Ç Ç à @ Ý9ËqÞ'á ßâ à ÉF: Ø? þ ß @ Þ'ß Ç à :!ÆËtá âaÌ/Í£Ëqá â@ ãnËtÞá ß â Õ Ç à Ö × m ! Þ'ß Ç à :!ÆËqá â ý Ç Ì¢Í@ ã ËtÞ'á ß â! ý Ç Ç à @ ß :ÒÎ+Ëtá â $A Õ Ö × #"$ ñ Ë Þ'ßà É Ê÷ :!ÆaËtá âaÌGÍ£Ëqá â@!Ì # "% ø ó ù É#ØÌaõ'õõÌGúGË
þPØÏ × ¶
D¯ Þßà É`K! 5 : Ë_Ñ Ç á á × ñ Ë Þ'ßà @ ·D0 3 K [U9l $2!'k" $% +"/J5/D 5D #Þ &Kà ã 'Þ &Kà D ( t
éx)+*%ênQt+,xt .-¥Atl5/0,921HïnëatQ9t943
5 !5 '/BD å65R:!ÆQÌ/Íl@cÉ ü7Ø È7 :ÒÎ : @ 7$: q@_£þ@;A5R:!ÆQ@ @ Õ Ö$89 EGn ?M4 Q)R5J \ !B; 5 "U";!; 5 :!ÆQ@ÉY$2!m 5 :!ÆQÌ¢Íl@ J . 5 :!ÆQÌ/Íl@lK ZÛ06q) ? 0; 3 $2434 'BDxo " ü7CÈ 7c h" [ 7 $%[5 )£$%$%"G! B;_ Q.S ÆaJx!"PÆ > 8" n ! n 5"P!_ %ÆaDcg ! ')BJ S")5!n5! M4[. $8? 9 6q) MB : ¯@ åD5+:!ÆÌqÍl@\É ü7Ø ÈC7 : 5+:!ÆQÌ¢Íl@xþ $2!: m 5R:!ÆÌ¢Í+>q@ @ \5 5 GBncm5 $%'Bh5 [( \ ( \G.0 7 5 EGnC Z n %"34"Z K %)
! %( ' ¥ $%[5 )/J£|R}ª7 & [ 5 D E0)RI & !")6 5Jl|RªR«a|R}rt|Rau8¬ªR|Rr ® }0hI 6¢5 '8$% +"I 5 Z h( - ! )RBJM5BNZ 3" 34"9 S( S ] $2! S_ ;å !F " ;hJ?"; $Ak5 3A( [å 5 :!ÆQÌ/Íl@.iA" ')$Am : å 5 :!ÆÌ¢Í > @ .[ "7k
D o-7m5MZM! i&)R ] 9 '$% +"] f ID gj 3- 8 $% +"U5! ' 2.0 - BJ7M4_ /.0 $% +"\^_ L3 "JÜ7 6i=: Ûn@c"SM 6q g GSJ " M4n$2!" %.0 V&! BDn0[$% +"U5! ' A! " . \' G!'k+ Z \ 95 xM4? '$A " S ?G.L n$% +"J ZÛ06q)
! Z"Sg76q)
! 5JQ $86 3 5! $Z G! )R .n! "\ M )R"%% K"!J! c 9 ;$%$%"/ ; .[ " hY ; 9K 6q';$% +"D 8 [$% +"U5 -'I!' Q.] 3 7335 _ d33 Qm5$2 9Jl5D
D033B5]( d!33 m5$2!6 1Y)R I B H46¢ Y ! DPWL I 2 39I'$8'! J.0 . $%S ]"; &$% +"U+ Jn"P (S 5!" % 5! 34 ZØ/D
æ Q ç£R5è9é9QKJ821ëaL X4 $% 5 g,M9 n5! S$% +" 5Jl`K +J_ A)RD E/3 K"!ñ É Ê!ò ËGó ô ÉFØÌaõõ'õÌGö1Ï. ò Ë9É Ê÷ ÆËtá âQÌ¢ÍlËtá âQÌ/Î+Ëqá âQø ó ù ÉFØÌaõõ'õÌGú/ËGÏ : ò Ë ô 6q ]3 +"5J" ú Ë n ] ò Ë D@ ØD9f
Z ò Ë9û;ñ ØDØ7f
ù É#Ø Sú Ë Jlü7È Ëqá â ÉYÈ Ëtá â!ý ÇcþAÈ Ëtá â D9f
Z ò Ë û;ñ ñ¥Ë Þÿà É Ê÷ :!ÆËqá âQÌ/Í£Ëtá âQ@!N Ì M ø ó ù É#ØRÌaõõõÌGúGË/Ï ¯Då Þÿà É`K! 5 : ËÒÑ Ç á á Öt× × ñ Ë Þÿà @ ¶4D9f
Z ò Ë û;ñj" _ ù É#Ø Sú Ë þ1ØJ5' G!'k ¶4DØ[å&ËtÞ ÿá â à ÉYå Þÿà :!ÆËtá âaÌ/Í£Ëqá â@ ¶4D[P å O&RÍ Q0ËqÞÿá â à É¥$2!m : å Þ ÿà :!ÆËqá âÌ/Í > @ ¶4DS ¯ ;%ËtÞá âÿà ÉYP å O]RÍ Q0ËtÞ ÿá â à ·D9f
T ZÉ#Ø ·DØSe ß JRU ß !"V ß J+5D 4DW ß ÉXU ß ÉYV ß É Ç ß ·D7f
8! ò Ë ûSñ f
ù ÉFØ? SúGË
þPØ å ËqÞ'ßá â à É#: Ø?þZ ß @Òå ËqÞ'ßá â Ç à ý\[?]W^ `_ #"baWcc' _ #"aWc# å O]RÍ Q ËtÞáß â Ç à M ß :ÒP @ × ed × ñ¥Ë Þßà É Ê÷ :!ÆËqá âÌ/Í£Ëtá âa@!Ì¢å&ËtÞ'áßâ à ø ó ù É#ØRÌaõõõ×ÌGÖt×úG Ë
þPØÏ × ·D¯[å Þßà É`K! 5 : ËÒÑ Ç á á ñ¥Ë Þ'ßà @ ·D ¶Sf
8! ò ËûSñj" _ ù É#Ø Sú/Ë4þ1ØJ+ 34"! å&ËtÞ'áßâ à É1å Þ'ßà :!ÆaËtá âaÌ/Í£Ëqá âQ@ å O]RÍ Q ËtÞßá â à É¥$2!m : å Þ'ßà :!Æ Ëqá â Ì/Í > @ P ; ËqÞ'á â ßà É#: ØþU ß @f; ËqÞá â ß Ç à lk #"% lk #"baWc' Ç U ß :hgji m gj" i ; ËqÞá âß à @ ·D·7f
8! ò ËûSñj× " _ ù × É#Ø Sú/Ë4þ1ØJ+ $Ak å&ËtÞ'áßâ à ÉF: Ø?Z þ V @Òå&ËtÞ'áßN å O]RÍ Q0ËtÞáßâ à @ â à V :ÒåIËqÞ'áßâ à þAP D0 3 0 [Uß 0")
!5ß n$8 +"/J5å 'Þ &Kà D ( t
éxn4*oJ8212Q5tqp¢ç
QRR-¥5t5Q9t9S,9sra5èç
2èë /l
Aéqc t è9t943
4.
EXPERIMENTS
o Y) ! " Y3 34 "$% +"* 98 6 $%&'5 ! F"!A( $ e!V&f_ #g7)R A_ $ 39 IBR5! D ` Q.p.L2.'" M42 A"9].L* "O( Zm534 $%! ¥Y $8I"/DIY.0S.K"' Z!'h.0h !82) ! ; $% +" ;3! "9Do[ ]" M4h [m534 $%5! D 4.1 Data
g0M 'äB%m53G!";;EG5 +" J "9K.0 ";( "!%9B5 ?+ M4[+ k"A5 % 7_ Q.;_ /B534D ØD v ¬ z r y ¾8u w ªR|Rrt|?( [ØD$8' I $% J. 7 5 5 £ 34"m5""Y !'] "Dx !H"$% 31"P S/B5348 7( $2! ' Z $% DZo% 8 !n3 )BA ')%6 _ $2 P.[Z '334"¥ NM4( I B2.L & "¥( "!%9B5 D S D u w |R} z |R±ar ® y } ªR|Rrt|_ L "ØDK$%' & $8 0( I3! 8 ;BR5 DAI N"92 I $% $834"©"O 5!'# A5 ' 234 '5; !']"!J
' "'] 85! 'Z 03 i9 " $%I"! 3 5Jl$% S 'D ¯D v |R¾?| ® a}YªR|Rrt|8_ %$2a^_ 5$%39Z( 8BR5 ºº
D8 %.0 *Áh+$%39D8 %"9 5 '$8' $A'4Ja" JQGB534 5!' 5J
"%3 +" c 3[:_"')5 @£M4n ";MB [5!$%3!D ¶4D Å w/y ªR¬5±ar]ªR|Rrt|-( * ¥3 ! ", $%2 ¥ 6 2"D ¥ 5!',m5 $hBd'_ $2 * $2J4&5 / /B*( $³3 +" [ 3 " Q. 8 Iwe v6GF)R/D Z"9[.0 h A "A ;! Z $%h $%34"* 6 5 \_5! %)R 5'] $%$2 k"( $2!6 ¥ Y S' B 6q!05 DIS_5!6 \.LK! "2"% "% 7 5J 3 5 [ K h8 $8&&5B*)R¥34 ¥ $%5J0 ; $%$A k" AM ØDne: x7 n 9? _+ S ; !'5 S( ?GB534 "'S % 7"? D@ x7 Z 98[ "2 $8*2!M Ø[ Z / +¿85 %M4G.L15!iP I_+ 2"P & 34 ) /M'Z:_ .[ "9@L! ? "9DxÀ7 5J 34 )
! /M?.n! 5!' / "N $%3BYM5B- $%$%* I M )R"P3 U 8P "!J+ Q)RhUm"&34 +"& 9 $%n n [ $%[ 9 7$26 A¥5 ' JL"-'" +Z m 'B* 34 "Y ±a¬5¾8¬5~|Rr ® «auSª ® z ± y ¬}rtu!ªS wGzy y r z .0h. ;$2!m$%k+D?EG n.0
J£ J4 !;h)R B . / ¥ M )R"AM4G.02 5 )
! G!M]:_$2- 9@7!" 34 ?)
! /M5J4!0 $%3! "; n $%? l \_5!6 D0 5 9)
! /Mh! h "A' Q.L 7 / +¿85: Kº
D ºº4@ J£";K$2!' "0' Q.LK !; GB53'+:_ ! ' O!"25!$%3!'@L(5 D?[m53/ n9 n ?rtsRuS± w/yRz!z{ ±asR|R}}ua~c±asR|R~_~ua}auaJx!" A39 /! .5BS.0[ "I 8h$% +"l 9K"34"50 x 7 6 c) /M5Jl..L% Hh !"9 "* ¥% $% +" n 34 n)
! /MI!%( ] n(5 D 4.2 Evaluation
g $8$% F3 M$¸'#34 ( $2!-)
! T Z 6 _ $%\5 n$% +"cL 9c ( Sc'\"¿% c \'$86 34 M'0 ? " 5+_0m534 $%5x.Z L5! $% +"?C)R& [ S 6q'Z5 ! . A &>AW[X£D 0 \ 5[!335! ' ;" $A; L "S"!M! 7$2! 6 VR &[ &m53 9D79 ] " 34 ( $2!8)
!6
! O /MBN '¥ BN ! 'A 5"!&I I MS!'5D\3 M$¡ 9?.0" %) 9 34 B "2M5B] h5! I3 +" h ; 'B&3! "!JK.O3 $2!MBN.L 2 "d Y $%234 B !"'4 5_ $¡D À7 [.0[3 34 I? ' % '3 M'$2J£"& [ " [34 ( $2!8)
! ( n [$% +" ' BD;0 ' -[M9 "* H * B 3 34 "M5Z B vI!V
!" "]K_ "1x+" y ~ ® ± {8|RªR«a|R}rt|RauaJ9"YM/ 6 i5 [M9 " $%34 !!$%3
J5D D?غGDco- /M4 ] M4 .hD f J9.0I"U%" I $%&) 1 ? ; 1 |RªR«a|}rt|Rau +" "&5! '8:_ D£¯@ JR. ] 34 A!5B 34
B |0D å }:!ÆQÌ/Íl@\É }:!ÆQÌ/Íl@xþ]$2f:!m }:!ÆQÌ/sÍ >q@ T :_¶4@ 8 L34 B&")
!!K L.¥34 'B| > . Z 34 * "H:_ [!$%3
@034 B|F"*' /!\ ! %" M
~hfbbf
`
% b?
bff %
% bf
ff l. ` ?f w
% ¢`f b¢
= ª b¢
= ® ¯ b¢
= © b¢
= ª b¢
= b P `¢`
% f b¢
= ª f b¢
= ® ¯ f b¢
= © f b¢
= ª f b¢
= b `¢`
= b ± f ª f ® ¯ f © f b f f ª f f ® ¯ f f © f f % fb
Bf
fbb`
%fw
%
b`f TR %T
bbb?w
%
%f l.!b ?f l%
%f£¤qf¥§¦
%2¨ Dw
!
«Dwb Dw
!
«®¯DDw%TRfw Dw
!
«©DDw%TRfw Dw
!
«f %bjD`2 b¢
!£T¯P?b
¨ %D `¢
bf
0!D%TRfw
b¢
bAP2
WP2%N!?`fw«2
b b¢
bAP2
W®e¯DDwbTfbf2«w
b¢
bAP2
We©DDwbTfbf2«w
b¢
bAP2
Aª?!?`fw«2
b %bj`¢
bDw!fbf2w
%bj`¢
bDw!w
T± w=¥Rf ?%f
B
b?w«T
bWD2% w=¥Rf ?%f
B
b?w«T
bW®¯DDwb w=¥Rf ?%f
B
b?w«T
bW©DDwb %bjwA¥f fbf
f2 w=¥Rf ?%f
B
b?w«T
bWD2%N%f%6fb?w«w
w=¥Rf ?%f
B
b?w«T
bW®¯DDwbbbfb6fbfww
w=¥Rf ?%f
B
b?w«T
bW©DDwbbbfb6fbfww
%bjwA¥f fbf
f2%fb`6?`fw«2
b %DD+«%DD
4 ¡ © ¬ °¬ ª® ª¯° ª ¡ ° ¬ °ª ª®¬ ª¡ °¯ 5 ®ª ®¬ ©¯ ¬© ®¬ ® ©® ©® ¬
² s ,9t³)4* ( 5é9QRr¥éqra5è´t´ç
éxNR´\t\5Q.-¥5lCr* ( 5é9Qrµ;C1xtPè9RraRQ.t9tçqrµ&9è´C1xtPRç
QQ5ttçqrY¶%tC1´C1x QR¶hQèxtè3 ² 19!p/5é9QRr7Q%t.raèAt·I
Qç
éqtqr*&îb)ð7Réqraç4-¥5Dp¢é9QRr¸îbn
ðQqraRtç
¹p/5é9QRr¸îbº
ðR+-»txt
p¢5éxRrK ¸ 9èî%·
ðNt9Qç£è9é9RSçéqt¼rtc5Rt9]+-»t9t
@p/5é9Qr3Aîb½-IHR´l+-»t9t&Rç
QQ5ttç
¾/té9 .rZ´\19.,9tè@p¢ç
raR4/ 5Q/p 5é9Q8 r ç4 p l9 1 .S r z¿\c t Rt3 ð À J5. ' åT} á Á :| > @ J+'"U"Y!?( Q.D å } á Á5:| > c@ É 7«} á Á5 Â}w: Þ Ã 7 à å } :!ÆQÌ/Íl@_ 9 9
: ·@ E/5 )RBJ 34 B]")
!!K$85 c Q.1$Z i ")6 !h52 M5B] 3/I & 2 \ "234 B M5B 9% 7 ].¡34 BT2;" $¤ "HM5B¥ !$%3234 'BJx.'-K ] ' Z $21 i9" :_ 34U"IM5B% ?$%3'834 'B@ DxE/I $%[ 5JR K$%+6 Z5 95 U? Q.,$h A +5$%3 Q)R$%5?S !"2M5B !' & "N34 'BYM5B I.´34 'BJ! $%* ! n Q)R Ç n" M ? U5!5 'B¥4 " M5B 95D &34 'B#")
!!I51M4; $2! "N 2 'B-" "¥M5BA 8$83 34 'K B |LJ
¥hM/!h i5 [M9 " ]$%34 h!$%3A?_ Q.D å} á Á :|>¢@cÉ 7 á «} á Á | |0> :Ò:ÒÍ Í ó ó ÆaÆQ@ @ å}:!ÆQÌ/Íl@_ : @ 9 x n 9 | > :ÒÍ ó Æa@x'V5 Q.& 'n' ;:_34 MBI +i9 6 5@034 'BA "M5B ( $85n'+ 4J4M D |0:ÒÍ ó Æa@ "&M4n $2 "]_ $¡ ["!J+ n.L[" % V5 Q.d !$%3734 Bm53 'BD£EG9 '"ZM4K34 5 "h 9 ! 5 95 GB%M4 $%0'$834 Mn h $2 _ h" : $% !$%3A34 'BJ ; 8M/h Y ! } } Þ Ãà 7 7 à "6 Þ 34à B ) &_ Y ' ]ÍP)RIi dM5BP A!$%31 |LDEGA 5!.0 "* J Q.0)J Z_ $2 _ 8 x ¿%5 " $8'K 0i Z" $%6 5!'BJ?' [5 ]
D Ç vIV"%"&K_ "1£C)R M' "Y 5l 6 [.*$%3'[ !S[.T34 BA. N34 ' )Rh34 B !")585!-M4Z "* &"U .,34 BJ£.i*3 Q)56 !MBIM4 34 _ $2 & n '"]34 BD
4.3 Experimental Results
o-Z " %)
!' 9 $% +"-^_ n +" "J4$8B ! MG! " $2! ' A 934 'B¥!")5[ "!JR 8)"! [ 34 _ $2[ x 3 34 "&$% +"D o-A "OM4 H n A3 34 "O$8 +"J0Ü[! '6i=: Ûn@S!" `K! i6¢ g G%DEG;M4 ;5! J+.07 ";Ea`K>A¼ 5!/M[ 5JZX£ M h> JZ/J8!] M9 T$% +" 5D f
nM4 *$% +"J£.L% " %_5! % & /kS Û06 ) 7"Zg6¢) \ '$A ' L$%3 55_K $%L)
!6
Dxg7 4J( KM4 S$% +"J.L "S 3 ; L33B5 _ !33 Qm5$2 !%)R B-_ N5! * D EG] ?) ! J.L" $%B&$%3'"P33 Qm$2! B1ØD º 34 x 0")5'" !R $% ( $ L5 0"9?: 36 3 Qm5$2 'BYØn "A $% [( $ ØD$8' 9@ D? 3' +"]"!%.0 & Y! "J9( % &1 4JMB " $%BS 2 M6¢3 +" x -غ :_ ' % غA)R5 @K 34 "'2 5Y S$%3'"Y'")5" 6 DSg 39! S "h ' A ·J ººº2" $%B "8"')5" 99.[? $%3'"8_ 95!' / 7 034 6 BH")5!5D%S34 'BO!")5S.n5! / "Y h")5'" !"97 Q)R n I75$%39J" _ 5!iN'+ Y' 9J0 ] ;.0 PC)R!"H )*غ " $¡ D S n) 9 F! Sm5M "'-f' &¯ "%¶4Dlf' Z¯03 \ Q.N 34 B !")5 4 34 B 3 7M5B ZÜ[! 6=: Ûn@$% +"!;n 85! O3 &&/B35 9DNf A¶¥ Q.; 9 Z3_ h %M! i6qA g G$% +"DEG5- K !3J+ B6i!mL'0 ?34 B*")
!!? Q.K 34 6 5!% Q)R7 h)
!' 8 0 Z "*34 BD;e BA 345V5
J .!KK Q.I I ?m56!m5'0'0 L $ZM4L x J M L! L0 ?5 $hM4\ £ $%K( ' 33 Qm$2! ; 34 ( $%"9D9EG]M4 &+ J5.0n 7 % I_ ¥33 Qm56 $2 P)R BS( 5 'S 9D
4! JQ.0" U" c3 M$ $%$% 8 [$8 +" 6¢!5 ! J"Z3 34 "2\ ' %M9 "Z "H"*., i5 \ _ $%7'+ 4Do !' 3 Q)5""- & 8 7$838M/3 M$´I) !6 % 45 "S34 J4"% "%\ 7)
! 3 34 " 33
D2e $%% h_ _ S) 4 ¥ "S _ ' Q.
2: Ø@ ! '2"3' QB5$%5M5B " ' ;"¥ $%kR Æ: @xÀ%"'8) i9£ 5 ' "6 %M " !'5 w Æ 6. ACKNOWLEDGMENTS
( t
éxTº4* ² 19tcç
tt¿Aè/
Np¢ç
[C1x/ts,9t8.-¥ tl5/ Kï[ëQt5Q9t9I-¥5C19ç£èî/tN-?¿Ät9t0Qé93tð
o-8.' - ] !VN`0f
!V5I"deQ coO l6 E0CB* e !V5f_ 2g)R5 n( 7 7m5 )R5" 32A$2V5 ]^_ 5I3 ^_;34 'M5D#o1 Y. d ¥ 9V ". X" S"N`/+Å Çl" k5B \Ea`0>b=c 5 N¾ " Èi !_ "* \EZ%A 1!ºº¶
D !I8EGµX£ J Q)ØÁÁ·D ·!nDlXlhD vI'M'4J>AD5KD5' $AJl"]g%D5oDl>8 + +D =c_ $%55 4xgF )B4D Ó y ¬ w }|R~ y Ú Ê w r ® y ± ® |~ Ë }rtua~Ò~ ® aua}±!T u Ô\u z u!| w ±asRJ¶
JØÁÁD !IehD vIV"S» " ÈRD+( "D5g733 Qm5'$A B; 3 '$A 33 Qm$2! n ( $85?5!
DE/ Å wGy ±!u!uª ® } zy Ú rtsRT u ÕÖrtÅ s Ë }rtu w }|r ® y }|~ vxy }Ú u w ua}±!u y } à |R±as ® }u × u!| w } ® }aÄJ Èi B-ºº4D !I=D xS!a^ !P" DlX"9 'Dle$%5 "& ' $2 ( ?$2 )Rn"9 D5EG» Éu!± y }Ø ª É+Ë Ê Ã Ë }rtu w }|Rr ® y }|R~ vxy }Ú!u w ua}±!u y } Ä |Rrt| à ® } ® }aJ+g ' J Ü7 /Jxºº4D 2!3345!D ! DlX"9 'hJ xSDRgM45J`0ÄD Çl" k5BJRÀSD+od!4J+oD+fc9J "¥