2 Combining machine learning with deduction for SAT solvers (Презентации лекций)

COMBINING MACHINE LEARNINGWITH DEDUCTION FOR SAT SOLVERSVijay Ganesh(Slides courtesy Jia Hui Liang)Improve the performance andunderstanding of SAT solvers usingmachine learning techniques2“The speed and degree of improvements is declining.Now we seem to have faced one of the ceilings thatcalls for a breakthrough.”-Chanseok OhBetween SAT and UNSAT: The Fundamental Difference in CDCL SAT (2015)3WHY MACHINE LEARNING?MB/sec ofnew dataEffective(LRB)RichLiteratureTheoryUnexplored4SAT OVERVIEWHow to pickdecisions?StudentDecisionPropagationPartial Assignment: A=false, B=true, C=false, …Learnt Clause: A or CTeacherClause LearningNothing5HISTORY OF BRANCHING HEURISTICS6LEARNING RATE OPTIMIZATIONPartial AssignmentStudentLearnt ClausePrunessearchspaceTeacherNothingMaximize the probability Teacher responds with Learnt Clause7LEARNING BY TRIAL AND ERRORA = false, B = true, C = falseStudentA = false, C = true, D = falseTeacherStudentLearnt Clause: A or CLearnt Clause: A or DA = false, B = true, D = trueStudentB = true, D = trueTeacherNothingTeacherStudentTeacherNothinglearning_rate(X) = ℙ(X is in learnt clause | X is assigned & in conflict)8MULTI-ARMED BANDITpp$p$sample average =1/3 × $4exponential moving average =(1 – α)2 × $4$Best slotmachine+ to play1/3 × $3(for+ (1now)– α)1 × $3Lessweight+1/3 × $1+ (1 – α)0 × $1)Moreweight9LRB EXAMPLEA is assignedA is assignedB or DA or DA or BB or CB or EC or DA or EA is unassignedA is unassignedlearning_rate(A) = 2/3exponential moving average = (1 – α)1 × 2/3C or Elearning_rate(A) = 1/3+(1 – α)0 × 1/310EXTENSIONSReason Side Rate•  Prefer variables close in proximityto learnt clause variables.Locality•  Prefer recently assigned variables.11EXPERIMENTAL EVALUATION  5000VSIDSCHBLRB  4500  4000  3500Time  (s)  3000  2500  2000  1500  1000  500  0  0  200  400  600  800#  of  Solved  Instances  1000  1200  140012FUTURE WORK: QUALITY OF LEARNINGOBJECTIVEPartial AssignmentStudentLearnt ClausePrunessearchspaceHow “good”is thepruning?TeacherNothing13FUTURE WORK: VARIABLE RANKINGINITIALIZATIONInstances14FUTURE WORK: OPTIMIZE CONFLICTANALYSIS CUTPartial AssignmentStudentTeacherLearnt ClauseNothing15.