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maximize Halo 6 ELI lb generalized p spin Hnlo Ico Wo W GOE n SK motel HIP Zt ERN TEL 0,8 28 I 8I Wftcz't Ef dt fs.gl s zo Nlo S 4v Lene Enl Eic p line ENKE I ENZI ZI Z Zf Z Nco QI Z LEI I Q is.t.is ELICZ s ZITI m fecz.at Want f mtttmt.ms set Ft II ztb mire T us eggs w NI N Nzt ut int Zf Uf Mst State evolution ME IT t U CZ's.is Z U em ECZE.is't's.is ECMEMssl o mt

maximize Halo generalized Ico Wo W

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Page 1: maximize Halo generalized Ico Wo W

maximize Halo 6 ELI lb generalized pspinHnlo Ico Wo W GOE n SK

motel

HIP ZtERN TEL0,8 28 I 8 I

Wftcz't Efdt fs.gl s zo NloS4v

Lene Enl Eicp line ENKE I ENZI ZI ZZf Z Nco QI Z LEI I

Q is.t.is ELICZ s ZITIm fecz.at Want

f mtttmt.ms set

Ft II ztbmire

Tus eggsw

NI N

Nztut int Zf Uf MstState evolution

ME IT t U CZ's.is Z U em

ECZE.is't's.is ECMEMssl omt

Page 2: maximize Halo generalized Ico Wo W

Claim Mst t Z't are MGoProof Sufficient to provefol Z

Saff to check ECZEZ's 9ft as o

By induction over t Assume true up totWTS E Z't Z g Igf Vs ft

8t E Us Hits Ut Zetas 2E b94 8 E.es CUsil7GExs 9E'to

How to choose USU's 95 87 491 59 t

g o

H Is

of uCXi s 2

v u Rio I REE't't's 9 as tas Z't Be BM

mmmm

F t.EE yTBssBdJs o XI Xtdxt vcxe.tl dttdBtMe _It dB

Page 3: maximize Halo generalized Ico Wo W

JoKlux si

Euctss5 i its ELMI t

Mt tightest uls Xs dBs

dxt vlt.xeldtVSFDBtmte.IRm Thresh Round20dL

Lem f Hulot's f Hnlm't touche

Lee f Hdmi Ecu v town

Ela v 13CHEUK It

Ahg designmaximize ECU vsubj to ECMI t M Eti D a s

ftn Relax2 UB via duality3 Dual PrimalECM l 11mn117N 3G Xyz VAL I

REL Ut EMFT J t OCLBB.at

mix Jo g Euedtsit Me 4545us dB M CC1,1

Mt EMIL t ft1 I

a

ot tL l

Page 4: maximize Halo generalized Ico Wo W

T o D R o ult f 36181st dsJr snapELI'sIttuttfult ni g CH 1 Jolt

Turinst f 3M at dB Eti N

REL f JrE vittlesHuf 1 dt E LL 3116186kg Hui 1 dsdtSZE

GirlsREMI s Is o

Dynamic programming

Jolt zI sup E fEglstust'zVG g eius 1 TdsatDC41Z st zt figs usdBs Eti 1

Tft z Max J lo y Jr Jr 10,01 UEDA0

O tOtt H JB equation

PDE for JrREL E Jolo 0

Legendre fenchel dual of Trol Ct x MIN Jr tf ZX t

of satisfies Parisi's PDEREL E EL

infif inf achieved at r

Page 5: maximize Halo generalized Ico Wo W

VC Vr t.xlnft.DEintesPch infupert

Q1 Complexity of solvingthese within Eerrot

Q dr I EE

f in TAP mi O

DCM HR oci

11µg Feller OG