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Supervised Design Space Exploration by Compositional Approximation of Pareto Sets

Supervised Design Space Exploration by Compositional Approximation of Pareto Sets. Hung-Yi Liu 1 , Ilias Diakonikolas 2 , Michele Petracca 1 , and Luca P. Carloni 1 Dept. of Computer Science, Columbia University 1 Dept. of EECS, UC Berkeley 2. DAC, June 8th, 2011. Motivation.

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Supervised Design Space Exploration by Compositional Approximation of Pareto Sets

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  1. 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

  2. Motivation • 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-consumingsynthesis tasks fornew technologies • desirable fast system-level design space exploration system designspace composition soft IP design spaces CAPS @ DAC-11

  3. 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] • Problems: • long runtime • uncertain quality • inaccurate result • not general • Advantages: • succinct Pareto sets • guaranteed quality CAPS @ DAC-11

  4. Supervised Design Space Exploration C: components with design parametersε: system error tolerancek: max number of queries - Primal Problem: Given ε, minimize k - Dual Problem: Given k, minimize ε Oracle ≤ k queries CAPS feedback ... system Pareto curve with error ≤ ε component Pareto curves (implementations) Compositional Approximation of Pareto Sets (CAPS) CAPS @ DAC-11

  5. Approximating Design Quality • 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  PE(q, p)  error between q & closest p  P • E(Q, P) = max q  Q E(q, P)  error between Q & P p1 y • No design point exists in the yellow region • Pareto points exist only in the blue region p2 q1 p3 q2 x CAPS @ DAC-11

  6. Opt. Online Algo.: Single Component • 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 p1 p1 y y p3 E1 q1 E2 q1 p2 p2 q2 x x p3x • initial error = E(q1, {p1,p2}) • current error = E({q1, q2}, {p1, p2, p3}) • 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 CAPS @ DAC-11

  7. 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 result • assume oracle returns qa1 • combine qa1 w/ pb1 & pb2to derive system points& evaluate system error • repeat for qb1 • pick best error reduction p1 derived points y q1 p2 x system curve y y pb1 pa1 pb2 pa2 qb1 qa1 x x component a curve component b curve CAPS @ DAC-11

  8. Experiments: Power vs. Performance • Oracle • commercial logic synthesizer • Design (8 components) • MPEG2 encoder @ 45nm system curve w/ ε < 3% adaptivecomponent queries CAPS @ DAC-11

  9. Experiments: Error Convergence • Actual error εa • E(exact Pareto curve, CAPS approximation) • εa ≤ ε(CAPS guaranteed) Query # required (only 7%-19% of exhaustive search) CPU time (hours) required (only 8%-39% of exhaustive search) CAPS @ DAC-11

  10. 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 • Thank you & see you in the poster session • more theoretical & experimental results • what if oracles are not “ideal”? CAPS @ DAC-11

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