CS 744: DRF Shivaram Venkataraman Fall 2020 ML knowledge - - PowerPoint PPT Presentation

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CS 744: DRF Shivaram Venkataraman Fall 2020 ML knowledge - - PowerPoint PPT Presentation

Aug 23, 2023 624 likes •889 views

! morning good CS 744: DRF Shivaram Venkataraman Fall 2020 ML knowledge ADMINISTRIVIA q TEY Attend tM%L - - - Assignment 2 out! fainted Piazza , systems - Course Project students - Form groups? Cloud ~ 3 Google Form

slide-1
SLIDE 1

CS 744: DRF

Shivaram Venkataraman Fall 2020

good

morning

!

slide-2
SLIDE 2

ADMINISTRIVIA

  • Assignment 2 out!
  • Course Project
  • Form groups?
  • Project list by Monday (9/28)
  • Submit project bids by Thursday (10/1)
  • Assigned project by Friday (10/2)

q

ML knowledge

TEY

  • →

Piazza

Attend tM%L

,

fainted

→

systems

~ 3

students

→ Google Form

Google Cloud

~ 2 months

to

work
  • n
the

project

slide-3
SLIDE 3

SETTING: FAIR SHARING

Equal Share Max-Min Share Maximize the allocation for most poorly treated users Maximize the minimum

z users

networking

OS →

lottery scheduling

earlier

5dm!.us

u → to

handle

different

  • demands
across users
slide-4
SLIDE 4

MOTIVATION: MULTI RESOURCES

Memory

Cpu

Cpu

manifested

÷÷:÷÷÷¥F÷÷

slide-5
SLIDE 5

DRF: MODEL

Users have a demand vector <2, 3, 1> means user’s task needs 2 R1, 3 R2, 1 R3 Resources given in multiples of demand vector i.e., users might get <4,6,2>

  • -
→
  • ne task

←

2 tasks with their

demand

  • shot

based

model

= , are No containers
  • g. war

;

" MMM

"

isan:

egroups
  • 2
reduce

linux

slots

slide-6
SLIDE 6

PROPERTIES

Sharing Incentive Strategy Proof Pareto Efficiency Envy free

User

should

get

you

can't lie about

what

you

need to get

.at?east

. 1am?
  • orison
. ? more
  • No
worse
  • ff
than Heir

Incentivizey

truth
  • wn
cluster

within

resources

telling

If

you

allocate

more users

should

not

envy

for

  • ne
user , You need

allocation

  • f
another

to take

away from
  • thers
user
  • .
  • utilization
slide-7
SLIDE 7

PROPERTIES

Sharing Incentive User is no worse off than a cluster with 1/n resources Strategy Proof User should not benefit by lying about demands Pareto Efficiency Not possible to increase

  • ne user without

decreasing another Envy free User should not desire the allocation of another user

slide-8
SLIDE 8

DRF: APPROACH

Dominant Resource

Resource user has the biggest share of Total: <10 CPU, 4 GB> User 1: <1 CPU, 1 GB> Dominant resource is memory

Dominant Share

Fraction of the dominant resource user is allocated E.g., for User 1 this is 25% or 1/4

  • "

Hare ÷

men share
slide-9
SLIDE 9

DRF: APPROACH

Equalize the dominant share of users

Total: <9 CPU, 18 GB> User1: <1 CPU, 4 GB> dom res: mem User2: <3 CPU, 1 GB> dom res: CPU

User Allocation Dominant Share User1 <0 CPU, 0 GB> User2 <0 CPU, 0 GB>

Cl Cpu ,

49137

2/9

< 2. CPU , 8GB? 419

  • ← ICH , 129135J

61g

  • I
  • 53cm ,
19137

3/9

Total

used

:

gcpu ,

14GB

k£00

, 29137T

61g

slide-10
SLIDE 10

DRF: APPROACH

Total: <9 CPU, 18 GB> User1: <1 CPU, 4 GB> per task <3 CPU, 12 GB> for 3 tasks dom res: mem dom share: 12/18 = 2/3 User2: <3 CPU, 1 GB> <6 GPU, 2 GB> for 2 tasks dom res: CPU dom share: 6/9 = 2/3

  • D
.

→ tonnage

  • is unallocated
  • O
slide-11
SLIDE 11

DRF ALGORITHM

Whenever there are available resources: Schedule a task to the user with smallest dominant share

slide-12
SLIDE 12

DRF ALGORITHM

→

cluster

config

→

running sum

→

initialization

→

track

resources given to each user
  • ←< lcpu , 49137
rn I

= ]→ if

  • ne
resource is

fill

you

can

still

  • ffer
resources to

tasks that

don't

need R ,
slide-13
SLIDE 13

COMPARISON: ASSET FAIRNESS

Asset Fairness: Equalize each user’s sum of resource shares Violates Sharing Incentive

Consider total of 70 CPUs, 70 GB RAM U1 needs <2 CPU, 2 GB RAM> per task U2 needs <1 CPU, 2 GB RAM> per task Asset Fair Allocation: U1: U2:

  • =

4

units
  • f resource
÷ 3 units
  • f
resource = = 15

tasks

for

u ,

43

, ' : iii. iz '

:

. . ?:O e w tasks

for

us
slide-14
SLIDE 14

COMPARISON: ASSET FAIRNESS

Asset Fairness: Equalize each user’s sum of resource shares Violates Sharing Incentive

Consider total of 70 CPUs, 70 GB RAM U1 needs <2 CPU, 2 GB RAM> per task U2 needs <1 CPU, 2 GB RAM> per task Asset Fair Allocation: U1: 15 tasks: 30 CPU, 30 GB (Sum = 60) U2: 20 tasks: 20 CPU, 40 GB (Sum = 60)

  • u ' Ii't
be . YI

Hunter

rat

is

dedi at

= =

slide-15
SLIDE 15

COMPARISON: CEEI

CEEI: Competitive Equilibrium from Equal Incomes

  • Each user receives initially 1/n of every resource,
  • Subsequently, each user can trade resources with other users in a

perfectly competitive market

  • Computed by maximizing product of utilities across users
slide-16
SLIDE 16

COMPARISON: CEEI

Total: <9 CPU, 18 GB> User1: <1 CPU, 4 GB> User2: <3 CPU, 1 GB>

dominant

resource
  • .
CEE I

f f

  • Cpu
Mem

454

. X
  • 4.05
,

y = l

  • 62
  • q t .
'↳
slide-17
SLIDE 17

CEEI: STRATEGY PROOFNESS

Total: <9 CPU, 18 GB> User1: <1 CPU, 4 GB> User2: <3 CPU, 2 GB> Total: <9 CPU, 18 GB> User2 Before: CEEI: 55% CPU, 9% mem

  • x. y
used to be

higher

y

= 1.62 X ' 4.05

3.6 tasks

? ?

↳ discrete

nursery

tasks ?!

f

  • →
.

nt3y

I

9 max X
  • Y
,

fatty

E 18 x
  • 3.6

g

y

  • I -8
slide-18
SLIDE 18

COMPARISON

slide-19
SLIDE 19

SUMMARY

DRF: Dominant Resource Fairness Allocation policy for scheduling Provides multi-resource fairness Ensures sharing incentive, strategy proofness

→

generalizes

max - min fairness
slide-20
SLIDE 20

DISCUSSION

https://forms.gle/i7m7xXxKhtfvL9UD9

slide-21
SLIDE 21

Consider a system with 100 units of CPU, 50 units of memory and 200 units

  • f disk. Consider three users with the following requirements

Alice (4 CPU, 1 memory, 1 disk) Bob (1 CPU, 4 memory and 4 disk) Carol (1 CPU, 2 memory and 16 disk) List the dominant resource as defined in DRF for Alice, Bob and Carol

  • Z
s

Alice

. CPO

450 Bob

:

Memory

4150 Carol

e .

Disk 4150

slide-22
SLIDE 22

What would be the final task allocation in the given cluster for Alice, Bob and Carol ?

X ,

y

, z nun tasks
  • f

Alice

, Bob , card

Every

time

Alice

is

allocated

  • nto

8/200

44

44

16¥

  • =
  • Bob
. . Card = 1640 100 50 200

A-lice

get

two turns

4kt

y +2

1100

'

i:*;:*: : ..Y÷÷÷

" ".! :* :*

.

  • .

Alice

  • 12
Bob . 6 ,

Carol

: 6

XE

12-5
  • yr
.

6.25--2

I

either

44,6 , b)

  • r ( 12,6, 7) ✓
slide-23
SLIDE 23

What could be one workload / cluster scenario where DRF implemented on Mesos will NOT be optimal?

If

there

aren't

enough

resources →

if

at

least

  • ne

task

can run →

Heterogeneous tasks

→

Instantaneously

[ over

time

? ]

fair

. ?
  • 71

Locality

pref

?

slide-24
SLIDE 24

NEXT STEPS

Next Week: Machine Learning Assignment 2 out!

Mesos : resource Offer ( 9900, 18GB) → task IN, 318dB > at Ext

R : ( 21 , 21 >

I

Dl

:

22,27

: Dal I. 17 3 tasks 3 tasks =

Eisa

Zita

  • #

strategy proof

:

assuming

rational

actor Dpr

allocation DRF

starvation :-)

  • ne

long running

tasks) D1 : 3121

&

very

highly

contended cluster

pz

:

4M

F

DI ' r 6/21
  • n

me....

are.

÷÷

. :÷÷f÷÷÷÷ subject to
  • IIe
? ? resource

constraints