Poor scaling of multiprocessing Pool.map() on a list of large objects: How to achieve better parallel scaling in python?

Question

Let us define :

from multiprocessing import Pool
import numpy as np
def func(x):
    for i in range(1000):
        i**2
    return 1

Notice that func() does something and it always returns a small number 1.

Then, I compare an 8-core parallel Pool.map() v/s a serial, python built in, map()

n=10**3
a=np.random.random(n).tolist()

with Pool(8) as p:
    %timeit -r1 -n2  p.map(func,a)
%timeit -r1 -n2  list(map(func,a))

This gives :

38.4 ms ± 0 ns per loop (mean ± std. dev. of 1 run, 2 loops each)
200 ms ± 0 ns per loop (mean ± std. dev. of 1 run, 2 loops each)

which shows quite good parallel scaling. Because I use 8 cores, and 38.3 [ms] is roughly 1/8 of 200[s]

Then let us try Pool.map() on lists of some bigger things, for simplicity, I use a list-of-lists this way :

n=10**3
m=10**4
a=np.random.random((n,m)).tolist()

with Pool(8) as p:
    %timeit -r1 -n2  p.map(func,a)
%timeit -r1 -n2  list(map(func,a))

which gives :

292 ms ± 0 ns per loop (mean ± std. dev. of 1 run, 2 loops each)
209 ms ± 0 ns per loop (mean ± std. dev. of 1 run, 2 loops each)

You see, parallel scaling is gone! 1s ~ 1.76s

We can make it much worse, try to make each sub list to pass even bigger :

n=10**3
m=10**5
a=np.random.random((n,m)).tolist()

with Pool(8) as p:
    %timeit -r1 -n2  p.map(func,a)
%timeit -r1 -n2  list(map(func,a))

This gives :

3.29 s ± 0 ns per loop (mean ± std. dev. of 1 run, 2 loops each)
179 ms ± 0 ns per loop (mean ± std. dev. of 1 run, 2 loops each)

Wow, with even larger sub lists, the timing result is totally reversed. We use 8 cores to get a 20 times slower timing!!

You can also notice the serial map()'s timing has nothing to do with a sub list size. So a reasonable explanation would be that Pool.map() are really passing the content of those big sub list around processes which cause additional copy?

I am not sure. But if so, why doesn't it passing the address of sub-list? After all, the sub-list is already in the memory, and in practice the func() I used is guaranteed not to change/modify the sub-list.

So, in python, what is the correct way to keep parallel scaling when mapping some operations on a list of large things?

Answer 1

your work function ends too soon:

In [2]: %timeit func(1)
335 µs ± 12.6 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

so you are basically measuring the overhead of multiprocessing.

change your work function to do more work, like loop 1000 * 1000 times rather than 1000 times, you will see it scales again, 1000000 loops cost roughly 0.4s on my mac, which high enough compared to the overhead.

below is the test result for different n on my mac, I use Pool(4) as I have 4 cores, test runs only once rather than multi times like %timeit, cause the difference is insignificant:

you could see the speedup ratio is increasing proportionally with n, the overhead of multiprocessing is shared by each work function call.

the math behind, assume per-call overhead is equal:

if we want ratio > 1:

approximately equal:

which means, if work function runs too fast compares with per-call overhead, multiprocessing does not scale.

Answer 2

_{Before we start
and dive deeper into any hunt for nanoseconds ( and right, it will soon start, as each [ns] matters as the scaling opens the whole Pandora Box of the problems ), lets agree on the scales - most easy and often "cheap" premature tricks may and often will derail your dreams once the scales of the problem size have grown into realistic scales - the thousands (seen above in both iterators) behave way different for in-cache computing with < 0.5 [ns] data-fetches, than once having grown beyond the L1/L2/L3-cache-sizes for scales above 1E+5, 1E+6, 1E+9, above [GB]s, where each mis-aligned fetch is WAY more EXPENSIVE, than a few 100 [ns]}

Q : "... because I have 8 cores, I want to use them to get 8 times faster"

I wish you could, indeed. Yet, sorry for telling the truth straight, the World does not work this way.

See this interactive tool, it will show you both the speedup limits and their principal dependence on the actual production costs of the real-world scaling of the initial problem, as it grows from trivial sizes and these combined effects at scale _{just click-it and play with the sliders to see it live, in action} :

Q : _(is)Pool.map() really passing the content of those big sub list around processes which cause additional copy?

Yes,
it must do so, by design
plus it does that by passing all that data "through" another "expensive" SER/DES processing,
so as to make it happen delivered "there".
_{The very same would apply vice-versa whenever you would have tried to return "back" some mastodon-sized result(s), which you did not, here above.}

Q : But if so, why doesn't it passing the address of sub-list?

Because the remote ( parameter-receiving ) process is another, fully autonomous process, with its own, separate and protected, address-space we cannot just pass an address-reference "into", and we wanted that to be a fully independent, autonomously working python process ( due to a will to use this trick so as to escape from GIL-lock dancing ), didn't we? Sure we did - this is a central step of our escape from the GIL-Wars ( for better understanding of the GIL-lock pros and cons, may like this and this ( Pg.15+ on CPU-bound processing ).

             0.1 ns - NOP
             0.3 ns - XOR, ADD, SUB
             0.5 ns - CPU L1 dCACHE reference           (1st introduced in late 80-ies )
             0.9 ns - JMP SHORT
             1   ns - speed-of-light (a photon) travel a 1 ft (30.5cm) distance -- will stay, throughout any foreseeable future :o)
?~~~~~~~~~~~ 1   ns - MUL ( i**2 = MUL i, i )~~~~~~~~~ doing this 1,000 x is 1 [us]; 1,000,000 x is 1 [ms]; 1,000,000,000 x is 1 [s] ~~~~~~~~~~~~~~~~~~~~~~~~~
           3~4   ns - CPU L2  CACHE reference           (2020/Q1)
             5   ns - CPU L1 iCACHE Branch mispredict
             7   ns - CPU L2  CACHE reference
            10   ns - DIV
            19   ns - CPU L3  CACHE reference           (2020/Q1 considered slow on 28c Skylake)
            71   ns - CPU cross-QPI/NUMA best  case on XEON E5-46*
           100   ns - MUTEX lock/unlock
           100   ns - own DDR MEMORY reference
           135   ns - CPU cross-QPI/NUMA best  case on XEON E7-*
           202   ns - CPU cross-QPI/NUMA worst case on XEON E7-*
           325   ns - CPU cross-QPI/NUMA worst case on XEON E5-46*
        10,000   ns - Compress 1K bytes with a Zippy PROCESS
        20,000   ns - Send     2K bytes over 1 Gbps  NETWORK
       250,000   ns - Read   1 MB sequentially from  MEMORY
       500,000   ns - Round trip within a same DataCenter
?~~~ 2,500,000   ns - Read  10 MB sequentially from  MEMORY~~(about an empty python process to copy on spawn)~~~~ x ( 1 + nProcesses ) on spawned process instantiation(s), yet an empty python interpreter is indeed not a real-world, production-grade use-case, is it?
    10,000,000   ns - DISK seek
    10,000,000   ns - Read   1 MB sequentially from  NETWORK
?~~ 25,000,000   ns - Read 100 MB sequentially from  MEMORY~~(somewhat light python process to copy on spawn)~~~~ x ( 1 + nProcesses ) on spawned process instantiation(s)
    30,000,000   ns - Read 1 MB sequentially from a  DISK
?~~ 36,000,000   ns - Pickle.dump() SER a 10 MB object for IPC-transfer and remote DES in spawned process~~~~~~~~ x ( 2 ) for a single 10MB parameter-payload SER/DES + add an IPC-transport costs thereof or NETWORK-grade transport costs, if going into [distributed-computing] model Cluster ecosystem
   150,000,000   ns - Send a NETWORK packet CA -> Netherlands
  |   |   |   |
  |   |   | ns|
  |   | us|
  | ms|

Q : " what is the correct way to keep parallel scaling when parallel mapping some operations on a list of large things? "

A )
UNDERSTAND THE WAYS TO AVOID OR AT LEAST REDUCE EXPENSES :

Understand all the types of the costs you have to pay and will pay :

• spend as low process instantiation costs as possible (rather expensive ) best as a one-time cost only
  

  _{On macOS, the spawn start method is now the default. The fork start method should be considered unsafe as it can lead to crashes of the subprocess. See bpo-33725.}

• spend as small amount of costs of parameter-passing as you must ( yes, best avoid repetitive passing those "large things" as parameters )
  

• never waste resources on things that do not perform your job - ( never spawn more processes than was reported by len( os.sched_getaffinity( 0 ) ) - any process more than this will but wait for its next CPU-core-slot, and will but evict other, cache-efficient process, thus re-paying all the fetch-costs once already paid to re-fetch again all data so to camp-em back in-cache for a soon to get evicted again in-cache computing, while those processes that worked so far this way were right evicted (for what good?) by a naive use of as many as multiprocessing.cpu_count()-reported processes, so expensively spawned in the initial Pool-creation )
  
• better re-use a pre-allocated memory, than keep spending ad-hoc memory allocation costs ALAP
  
• never share a bit, if The Performance is the goal
  
• never block, never - be it python gc which may block if not avoided, or Pool.map() which blocks either

B )
UNDERSTAND THE WAYS TO INCREASE THE EFFICIENCY :

Understand all efficiency increasing tricks, even at a cost of complexity of code ( a few SLOC-s are easy to show in school-books, yet sacrificing both the efficiency and the performance - in spite of these both being your main enemy in a fight for a sustainable performance throughout the scaling ( of either of problem size or iteration depths, or when growing both of them at the same time ).

Some categories of the real-world costs from A ) have dramatically changed the limits of the theoretically achievable speedups to be expected from going into some form of [PARALLEL] process orchestrations ( here, making some parts of the code-execution got executed in the spawned sub-processes ), the initial view of which was first formulated by Dr. Gene Amdahl as early as 60+ years ago ( for which there were recently added two principal extensions of both the process instantiation(s) related setup + termination add on costs ( extremely important in py2 always & py3.5+ for MacOS and Windows ) and an atomicity-of-work, which will be discussed below.

Overhead-strict re-formulation of the Amdahl's Law speedup S:

S   = speedup which can be achieved with N processors
s   = a proportion of a calculation, which is [SERIAL]
1-s = a parallelizable portion, that may run  [PAR]
N   = a number of processors ( CPU-cores ) actively participating on [PAR] processing

               1
S =  __________________________; where s, ( 1 - s ), N were defined above
                ( 1 - s )            pSO:= [PAR]-Setup-Overhead     add-on cost/latency
     s  + pSO + _________ + pTO      pTO:= [PAR]-Terminate-Overhead add-on cost/latency
                    N               

Overhead-strict and resources-aware re-formulation:

                           1                         where s, ( 1 - s ), N
S =  ______________________________________________ ;      pSO, pTO
                   | ( 1 - s )             |               were defined above
     s  + pSO + max|  _________ , atomicP  |  + pTO        atomicP:= a unit of work,
                   |     N                 |                         further indivisible,
                                                                     a duration of an
                                                                     atomic-process-block

---

Prototype on target CPU/RAM device with your python, scaled >>1E+6

Any simplified mock-up example will somehow skew your expectations about how the actual workloads will perform in-vivo. Underestimated RAM-allocations, not seen at small-scales may later surprise at scale, sometimes even throwing the operating system into sluggish states, swapping and thrashing. Some smarter tools ( numba.jit() ) may even analyze the code and shortcut some passages of code, that will never be visited or that does not produce any result, so be warned that simplified examples may lead to surprising observations.

from multiprocessing import Pool
import numpy as np
import os

SCALE = int( 1E9 )
STEP  = int( 1E1 )
aLIST = np.random.random( ( 10**3, 10**4 ) ).tolist()

#######################################################################################
#   func() does some SCALE'd amount of work, yet
#                                                passes almost zero bytes as parameters
#                                                allocates nothing, but iterator
#                                                returns one byte,
#                                                invariant to any expensive inputs
def func( x ):  
    for i in range( SCALE ):
        i**2
    return 1

A few hints on making the strategy of scaling less overhead-costs expensive :

#####################################################################################
#   more_work_en_block() wraps some SCALE'd amount of work, sub-list specified
def more_work_en_block( en_block = [ None, ] ):
    return [ func( nth_item ) for nth_item in en_block ]

If indeed must pass a big list, better pass larger block, with remote-iterating its parts ( instead of paying transfer-costs for each and every item passed many many more times, than if using sub_blocks ( parameters get SER/DES processed ( ~ the costs of pickle.dumps() + pickle.loads() ) [per-each-call], again, at an add-on costs, that decrease the resulting efficiency and worsen the overheads part of the extended, overhead-strict Amdahl's Law )

#####################################################################################
#   some_work_en_block() wraps some SCALE'd amount of work, tuple-specified
def some_work_en_block( sub_block = ( [ None, ], 0, 1 ) ):
    return more_work_en_block( en_block = sub_block[0][sub_block[1]:sub_block[2]] )

---

Right-sizing the number of process-instances :

aMaxNumOfProcessesThatMakesSenseToSPAWN = len( os.sched_getaffinity( 0 ) ) # never more

with Pool( aMaxNumOfProcessesThatMakesSenseToSPAWN ) as p:
     p.imap_unordered( more_work_en_block, [ ( aLIST,
                                               start,
                                               start + STEP
                                               )
                                           for start in range( 0, len( aLIST ), STEP ) ] )

Last but not least, expect immense performance boosts from smart use of numpy smart vectorised code, best without repetitive passing of static, pre-copied (during the process instantiation(s), thus paid as the reasonably scaled, here un-avoidable, cost of thereof ) BLOBs, used in the code without passing the same data via parameter-passing, in a vectorised ( CPU-very-efficient ) fashion as read-only data. Some examples on how one can make ~ +500 x speedup one may read here or here, about but ~ +400 x speedup or about a case of just about a ~ +100 x speedup, with some examples of some problem-isolation testing scenarios.

Anyway, the closer will the mock-up code be to your actual workloads, the more sense the benchmarks will get to have ( at scale & in production ).

Good luck on exploring the World, as it is,
not as a dream if it were different,
not as a wish it were different or that we would like it to be

_:o)

Facts and Science matter - both + together

Records of Evidence are the core steps forwards to achieve as high performance as possible,
not any Product Marketing,
not any Evangelisation Clans wars,
not any Blog-posts' chatter

At least don't say you was not warned

_:o)