supervised design space exploration by compositional approximation of pareto sets hung-yi liu 1,...
TRANSCRIPT
Supervised Design Space Exploration by Compositional Approximation of
Pareto Sets
Hung-Yi Liu1, Ilias Diakonikolas2,Michele Petracca1, and Luca P. Carloni1
Dept. of Computer Science, Columbia University1
Dept. of EECS, UC Berkeley2
DAC, June 8th, 2011
• Multi-core era demands novel design tools– build systems-on-chip by reusing soft IP [Borkar, DAC-
09]
– by 2020, 90% of design are reused IP to achieve a10X design productivity boost [ITRS]
• Synthesis-driven design methodology is crucial– time-consuming
synthesis tasks fornew technologies
– desirable fast system-level design space exploration
Motivation
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system designspace
soft IP design spaces
composition
Related Work
• Design space exploration– solution space reduction
• Givargis [TVLSI-02], Schafer [TCAD-10]
– local search heuristics• Eeckelaert [DATE-05], Tiwary [DAC-06]
– cost/performance estimation• Ascia [J. Syst. Architect.-07], Beltrame [TCAD-10], Palermo [TCAD-09]
– representative Pareto sets• Bordoloi [DAC-09], Singhee [DAC-10]
• Advances in multi-objective optimization– approximate Pareto sets
• Papadimitriou [FOCS-00], Diakonikolas[SODA-08, SIAM J. Computing-09],Vassilvitskii [Theo. Comp. Science-05]
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Problems:• long runtime• uncertain quality• inaccurate result• not general
Advantages:• succinct Pareto sets• guaranteed quality
Supervised Design Space Exploration
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CAPS
Oracle≤ k queries
feedback
C: components with design parametersε: system error tolerancek: max number of queries
..
.system Pareto curve with error ≤
ε
component Pareto curves
(implementations)
Compositional Approximation of Pareto Sets (CAPS)
- Primal Problem:Given ε, minimize k- Dual Problem:Given k, minimize ε
• For objectives x and y, given x-constrained y-minimizing oracles, which return points pi
• Error metrics bounded by q Q and p P– E(q, p) = max{ px/qx-1, py/qy-1, 0 }
• i.e. max x, y error ratio between two points
– E(q, P) = min p P E(q, p) error between q & closest p P
– E(Q, P) = max q Q E(q, P) error between Q & P
Approximating Design Quality
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• No design point exists in the yellow region• Pareto points exist only in the blue region
y
x
q1
q2
p1
p2
p3
• Given extreme points p1 & p2, bi-partition and iterate into regions w/ max errors until– max error small enough or– max query number reached returned by
oracle
Opt. Online Algo.: Single Component
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y
x
q1
q2
p1
p3
p2
y
x
p1
p2q1
• initial error = E(q1, {p1,p2})
• current error = E({q1, q2}, {p1, p2, p3})
p3x
E1
E2
• let p3x = (p1x+p2x)/2 be thenext oracle query input
• E1 = E(q1, {p1, p3}), E2 = E(q2, {p2, p3})• if E1 (E2) > ε, bi-partition and iterate on the left (right) blue regions
Opt. Online Algo.: System Composition
• Afford only 1 component query per iteration– pick the one w/ max potential error reduction
• System composition functions– fx = max, e.g. clock period
– fy = sum, e.g. area/power
• Estimate component query result1.assume oracle returns qa1
2.combine qa1 w/ pb1 & pb2
to derive system points& evaluate system error
3.repeat for qb1
4.pick best error reduction
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y
x
p1
p2q1
y
x
pa
1
pa2qa1
y
x
pb1
pb2qb1
system curve
component a curve
component b curve
derived points
Experiments: Power vs. Performance
• Oracle– commercial logic synthesizer
• Design (8 components)– MPEG2 encoder @ 45nm
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adaptive component queries
system curve w/ ε < 3%
Experiments: Error Convergence
• Actual error εa
– E(exact Pareto curve, CAPS approximation)
– εa ≤ ε (CAPS guaranteed)
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Query # required(only 7%-19% of exhaustive
search)
CPU time (hours) required(only 8%-39% of exhaustive
search)
Conclusions
• Novel supervised design space exploration framework– no a-priori knowledge about oracles
• Optimal online algorithm for compositional approximation of Pareto sets– intelligent component space sampling
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Thank you & see you in the poster session• more theoretical & experimental results• what if oracles are not “ideal”?