Learning Automatic Schedulers through Projective Reparameterization

Ajay JainSaman Amarasinghe

Challenges in ML for Systems

Learning automatic schedulers through projective reparameterization Ajay Jain

Challenges in ML for Systems

1. Discrete search spaces

Learning automatic schedulers through projective reparameterization Ajay Jain

Challenges in ML for Systems

1. Discrete search spaces

2. Large, combinatorial search spaces

Learning automatic schedulers through projective reparameterization Ajay Jain

Challenges in ML for Systems

1. Discrete search spaces

2. Large, combinatorial search spaces

3. Highly constrained feasible sets

Challenging for supervised learning!

Learning automatic schedulers through projective reparameterization Ajay Jain

Motivating application: Instruction Scheduling

Learning automatic schedulers through projective reparameterization Ajay Jain

N! POSSIBLESCHEDULES

FEASIBLESCHEDULES

EFFICIENT SCHEDULES

Motivating application: Instruction Scheduling

• List scheduling with heuristics• Stochastic search & superoptimization• Integer linear programming• Reinforcement learning

Challenging for supervised learning!

Learning automatic schedulers through projective reparameterization Ajay Jain

Baseline: Sinkhorn iteration from ranking literatureà 16% of schedules are invalid

This work

• Introduce EPOCS operator

• General approach for learning under dynamic constraints

• Formulate instruction scheduling as relaxed integer program

• Imitate GCC compiler instruction schedules

Learning automatic schedulers through projective reparameterization Ajay Jain

Permutation matrix representation

Learning automatic schedulers through projective reparameterization Ajay Jain

Fixed constraints

Input dependent partial order

constraints

0 1 2 3 41 0 2 3 4

ranking, scheduling, packet switching, matching…

Learning automatic schedulers through projective reparameterization Ajay Jain

Learning automatic schedulers through projective reparameterization Ajay Jain

Sinkhorniteration

Fixed constraintsDynamic constraints

Fixed constraintsDynamic constraintsEPOCS operator

Learning automatic schedulers through projective reparameterization Ajay Jain

1) Normalize*

2) Normalize*

3) ReLU

4) Project

One iteration of EPOCS for scheduling

Learning automatic schedulers through projective reparameterization Ajay Jain

Correct the relaxation with matching(Hungarian algorithm)

Evaluation

Train POCSNet to imitate GCC 4.9.4 schedules77,202 basic blocks from SPEC2006, SPEC2017 [Mendis et al 2019]

Evaluate data dependency violations, accuracy

Baseline: Sinkhorn iteration

Learning automatic schedulers through projective reparameterization Ajay Jain

Learning automatic schedulers through projective reparameterization Ajay Jain

Fixed constraints only16% of predicted schedules are infeasible

+ Dynamic constraints with EPOCS/POPOCS

Imposing dynamic constraints reduces data dependency violations

Imposing constraints improves accuracy (+4%)

POCSNet schedule latencies are on par with GCC latencies

Learning automatic schedulers through projective reparameterization Ajay Jain

0.356

0.397

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

Accuracy of schedules

Dynamic constraintsEPOCS/POPOCS

Fixed constraintsSinkhorn iteration

Fixed constraints

Sinkhorn iteration

Dynamic constraintsEPOCS/POPOCS

Accuracy 35.6% 39.7%

Kendall tau distance 0.238 0.222

Learning automatic schedulers through projective reparameterization Ajay Jain

mov rdi, rbpmov rsi, rbxadd rsp, 0x18pop rbxpop rbp

Shuffled input block

add rsp, 0x18mov rsi, rbxmov rdi, rbppop rbxpop rbp

POCSNet scheduled block

Takeaways

• EPOCS: General purpose op for dynamic constraints on NNs

• One application: Job scheduling problems

• A step toward correct-by-construction ML for Systems:

Enforce known constraints end-to-end for accuracy boost + guarantees

Learning automatic schedulers through projective reparameterization Ajay Jain

Contact: ajayj@berkeley.edu

Learning automatic schedulers through projective reparameterization Ajay Jain

movsd xmm5, qword ptr [rsp+0x20]movsd xmm3, qword ptr [r13+0xa0]subsd xmm3, xmm5divsd xmm3, xmm8ucomisd xmm2, xmm3

movsd xmm3, qword ptr [r13+0xa0]movsd xmm5, qword ptr [rsp+0x20]subsd xmm3, xmm5divsd xmm3, xmm8ucomisd xmm2, xmm3

Shuffled input block

POCSNet scheduled block