pruning strategies in adaptive off-line auto-tuninglu li , usman dastgeer, christoph kessler...
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Pruning Strategies
in Adaptive O�-line Auto-tuning
Lu Li, Usman Dastgeer, Christoph Kessler
Linköping University
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Agenda
1 Motivation
2 Approach
3 Results
4 Conclusion
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Problem Background
Application needs tuned for optimal performance
Performance tuning is challenging
Heterogeneous processorsCon�guration diversity
Auto-tuning needed
Performance Portability
Approach: Implementation selection for a multi-variant
component
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Component Interface and Implementations
Implementation variantPlatforms (CPU, acceleratorcores)
Algorithms
Tunable parameter settings
Compiler transformations
...
Meta-dataDependencies
Resource requirements
Deployment descriptors
Performance prediction models
...
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Staged Composition
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Guiding Composition: Empirical Models
Analytical model
Empirical model
No or little understanding of the target architectureO�-line Empirical Models: Feed sampling data (trainingexamples) into a prediction model, e.g. SVM, C4.5
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O�-line Empirical Models: Pros and Cons
+ Avoid �cold start�
+ Controllable tuning process
- Tuning overhead
�Cold start� E�ect
Example from Dastgeer et al. (ParCo'2011) on SkePU/StarPU integration,
Coulombic potential grid execution, with 3 successive executions
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Zoom into the Cons
A closer look at o�-line overhead
Exhaustive execution is not feasiblePrevious work: Stargazer (random sampling)
Training examples (Sampling data) is vital for performance
prediction models
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Attack the Cons: Observations
In the context of performance tuning: a concrete example
(Matrix-matrix multiplication)
Smart sampling by heuristics
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Adaptive Sampling
Sample only vertices of a space
Recursive decomposition (cutting) for open spaces, controlled
by maximum depth, etc
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Adaptive Sampling
Sample only vertices of a space
Recursive decomposition (cutting) for open spaces, controlled
by maximum depth, etc
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Adaptive Sampling
Sample only vertices of a space
Recursive decomposition (cutting) for open spaces, controlled
by maximum depth, etc
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Adaptive Sampling
Sample only vertices of a space
Recursive decomposition (cutting) for open spaces, controlled
by maximum depth, etc
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Adaptive Sampling
Sample only vertices of a space
Recursive decomposition (cutting) for open spaces, controlled
by maximum depth, etc
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Adaptive Sampling
Sample only vertices of a space
Recursive decomposition (cutting) for open spaces, controlled
by maximum depth, etc
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Adaptive Sampling
Sample only vertices of a space
Recursive decomposition (cutting) for open spaces, controlled
by maximum depth, etc
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Adaptive Sampling
Sample only vertices of a space
Recursive decomposition (cutting) for open spaces, controlled
by maximum depth, etc
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Adaptive Sampling
Sample only vertices of a space
Recursive decomposition (cutting) for open spaces, controlled
by maximum depth, etc
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Adaptive Sampling
Sample only vertices of a space
Recursive decomposition (cutting) for open spaces, controlled
by maximum depth, etc
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Formalization: Runtime context (e.g. Input Size)
Context Property Value Space (PVS) is a n-dimensional�nite space
A run-time context instance consists of n context propertyvalues maps to a point in the PVSPVS has 2n vertices (corner points)
Closed and open subspaces
Closed subspace: a subspace where a variant wins on allvertices. It heuristically approximate �uninteresting� subspacesOpen subspace: otherwise
Recursive space decomposition
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Convexity Assumption from the Observation
�In real life, the world is smoothly changing, instances close by
most of the time have the same labels, and we need not worry
about all possible labelings.�
Ethem Alpaydin in �Introduction to Machine Learning, second edition�
Our Convexity Assumption
If all vertices of a subspace share the same winner, then thewinner wins in all points of the subspace statistically
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Adaptive Sampling In the Big Picture
O�-line: adaptive sampling, tree construction
On-line (Run-time)
Load the treePrediction
Closed space: look up winner on one vertexOpen space: Euclidean-based predictor
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Adaptive Sampling In the Big Picture
O�-line: adaptive sampling, tree construction
On-line (Run-time)Load the treePrediction
Closed space: look up winner on one vertexOpen space: Euclidean-based predictor
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Techniques for Adaptive Sampling
Light oversampling
Sample one extra point in the middle
Detect holes
Small increase in overhead
May increase prediction accuracy
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Further Techniques Based on Adaptive Sampling
Thresholding
Relative threshold: abs(vi − vmin)/vmin <= θStop splitting early
Reduce training overhead
May decrease prediction accuracy
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Further Techniques Based on Adaptive Sampling
Thresholding
Relative threshold: abs(vi − vmin)/vmin <= θStop splitting early
Reduce training overhead
May decrease prediction accuracy
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Further Techniques Based on Adaptive Sampling
Implementation Pruning
Only winners of the vertices will involve in the future sampling
of the subspace
Reduce overhead remarkably if many implementation variants
are available for an interface
May lead to loss of optimization potential
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Further Techniques Based on Adaptive Sampling
Implementation Pruning
Only winners of the vertices will involve in the future sampling
of the subspace
Reduce overhead remarkably if many implementation variants
are available for an interface
May lead to loss of optimization potential
Try 10 variantsfor each vertex
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Further Techniques Based on Adaptive Sampling
Implementation Pruning
Only winners of the vertices will involve in the future sampling
of the subspace
Reduce overhead remarkably if many implementation variants
are available for an interface
May lead to loss of optimization potential
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Further Techniques Based on Adaptive Sampling
Implementation Pruning
Only winners of the vertices will involve in the future sampling
of the subspace
Reduce overhead remarkably if many implementation variants
are available for an interface
May lead to loss of optimization potential
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Further Techniques Based on Adaptive Sampling
Implementation Pruning
Only winners of the vertices will involve in the future sampling
of the subspace
Reduce overhead remarkably if many implementation variants
are available for an interface
May lead to loss of optimization potential
Try 2 winner variantsfor each untested vertex
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Platform
Name CPU GPU OS CompilerCora 16 Intel(R) Xeon(R)
CPU X5550 @2.67GHz
3 GPUs: two nVidiaTesla C2050 andone Tesla C1060
RHEL5.6
gcc 4.1.2and nvccV0.2.1221
Fermi 8 Intel(R) Xeon(R)CPU E5520 @2.27GHz
two Tesla M2050GPUs
3.2.1-2-ARCH
gcc 4.6.2and nvccV0.2.1221
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Benchmarks
Benchmark Feature modeling Range Implementation variantsMatrix-matrixmultipli-cation(MM)
row size, columnsize of �rst ma-trix, column sizeof second matrix
(30, 30, 30) to(300, 300, 300)
Sequential implementation anda variant by loop rearrange-ment, CUDA impl., BLAS impl.,Pthread impl. and �ve of its vari-ants from loop rearrangement
Sorting(ST)
array size; discre-tization of arrayvalues distribu-tion (samplednumber of inver-sions)
(1,0) to(10k,10)
bubble sort, insertion sort,merge sort, quick sort
Path �nder(PF)
row; column (1,1) to(10k,20k)
OpenMP implementation,CUDA implementation
Backpropagation(BP)
array size (1k) to (100k) OpenMP implementation,CUDA implementation
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Prediction Accuracy (%) on Cora: Base-line adaptive o�-line sampling
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Prediction Accuracy (%) on Fermi: Base-line adaptive o�-line sampling
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Other Metrics
Absolute runtime overhead: 4 - 23 µs
Relative runtime overhead: 0.2%
Average sampling rate: 0.053%
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Test against Convexity Assumption
BP MM
PF ST
Accuracy(%) on closed space. Pecentage(%) on closed space. 22 / 40
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Test against Convexity Assumption
BP MM
PF ST
Accuracy(%) on closed space. Pecentage(%) on closed space. 23 / 40
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Test against Convexity Assumption
BP
Accuracy(%) on closed space. Pecentage(%) on closed space.
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Thresholding E�ect: Training Time
BP: Depth 4 MM: Depth 4
PF: Depth 1 ST: Depth 4 25 / 40
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Thresholding E�ect: Prediction Accuracy
BP: Depth 4 MM: Depth 4
PF: Depth 1 ST: Depth 426 / 40
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Thresholding E�ect: Prediction Accuracy
BP: Depth 4
MM: Depth 4
PF: Depth 1 ST: Depth 4 27 / 40
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Thresholding E�ect: Prediction Accuracy
BP: Depth 4
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Oversampling E�ect: Prediction Accuracy
BP MM
PF ST
Adaptive Sampling. Adaptive Sampling with light oversampling.
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Oversampling E�ect: Prediction Accuracy
BP MM
PF ST
Adaptive Sampling. Adaptive Sampling with light oversampling.
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Oversampling E�ect: Prediction Accuracy
BP
Adaptive Sampling. Adaptive Sampling with light oversampling.
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Oversampling E�ect: Training Time
BP MM
PF ST
Adaptive Sampling. Adaptive Sampling with light oversampling.
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Implementation Pruning E�ect: Training Time
BP MM
PF ST
Adaptive Sampling. Adaptive Sampling with impl pruning.
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Implementation Pruning E�ect: Prediction Accuracy
BP MM
PF ST
Adaptive Sampling. Adaptive Sampling with impl pruning.
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Combo E�ect: Training Time
BP MM
PF STAdaptive Sampling. Adaptive Sampling with the combo of oversampling
and impl pruning.
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Combo E�ect: Prediction Accuracy
BP MM
PF STAdaptive Sampling. Adaptive Sampling with combo of oversampling
and impl pruning.36 / 40
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Adaptive Sampling vs Random Sampling
BP MM
PF STRandom Sampling Adaptive Sampling Adaptive Sampling with the combo
of oversampling and impl pruning.
37 / 40
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Adaptive Sampling vs Random Sampling
BP MM
PF STRandom Sampling Adaptive Sampling Adaptive Sampling with the combo
of oversampling and impl pruning.38 / 40
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Adaptive Sampling vs Random Sampling
MMRandom Sampling Adaptive Sampling Adaptive Sampling with the combo
of oversampling and impl pruning.
39 / 40
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Conclusion
Convexity Assumption holds for all benchmarks used, more to
test
Three techniques help to decrease training time or increaseprediction accuracy
ThresholdingLight OversamplingImplementation pruning
The right combination can combine the advantages
Adaptive sampling shows bene�ts against random sampling
More questions please contact me: [email protected], +46704759692
40 / 40