Lecture 21: ML Optimizers Slides by Boehm and Surve

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Today DB optimizers ML programs Optimization Techniques

Section 1 1. DB Optimizers

Logical vs. Physical Optimization Section 1 Logical vs. Physical Optimization SQL Query Relational Algebra (RA) Plan Logical optimization: Find equivalent plans that are more efficient Intuition: Minimize # of tuples at each step by changing the order of RA operators Physical optimization: Find algorithm with lowest IO cost to execute our plan Intuition: Calculate based on physical parameters (buffer size, etc.) and estimates of data size (histograms) Optimized RA Plan Execution

Translating to RA Π 𝐴,𝐷 ( 𝜎 𝐴<10 𝑇⋈ 𝑅⋈𝑆 ) Π 𝐴,𝐷 R(A,B) S(B,C) Section 1 Translating to RA R(A,B) S(B,C) T(C,D) Π 𝐴,𝐷 R(A,B) S(B,C) T(C,D) sA<10 SELECT R.A,S.D FROM R,S,T WHERE R.B = S.B AND S.C = T.C AND R.A < 10; Π 𝐴,𝐷 ( 𝜎 𝐴<10 𝑇⋈ 𝑅⋈𝑆 )

Optimizing RA Plan Π 𝐴,𝐷 ( 𝜎 𝐴<10 𝑇⋈ 𝑅⋈𝑆 ) Section 1 Optimizing RA Plan Push down selection on A so it occurs earlier R(A,B) S(B,C) T(C,D) Π 𝐴,𝐷 SELECT R.A,S.D FROM R,S,T WHERE R.B = S.B AND S.C = T.C AND R.A < 10; sA<10 T(C,D) R(A,B) S(B,C) Π 𝐴,𝐷 ( 𝜎 𝐴<10 𝑇⋈ 𝑅⋈𝑆 )

Optimizing RA Plan Π 𝐴,𝐷 𝑇⋈ 𝜎 𝐴<10 (𝑅)⋈𝑆 Section 1 Optimizing RA Plan Push down selection on A so it occurs earlier R(A,B) S(B,C) T(C,D) SELECT R.A,S.D FROM R,S,T WHERE R.B = S.B AND S.C = T.C AND R.A < 10; Π 𝐴,𝐷 T(C,D) sA<10 S(B,C) Π 𝐴,𝐷 𝑇⋈ 𝜎 𝐴<10 (𝑅)⋈𝑆 R(A,B)

Optimizing RA Plan Π 𝐴,𝐷 𝑇⋈ 𝜎 𝐴<10 (𝑅)⋈𝑆 Section 1 Optimizing RA Plan Push down projection so it occurs earlier R(A,B) S(B,C) T(C,D) SELECT R.A,S.D FROM R,S,T WHERE R.B = S.B AND S.C = T.C AND R.A < 10; Π 𝐴,𝐷 T(C,D) sA<10 S(B,C) Π 𝐴,𝐷 𝑇⋈ 𝜎 𝐴<10 (𝑅)⋈𝑆 R(A,B)

Optimizing RA Plan Π 𝐴,𝐷 𝑇⋈ Π 𝐴,𝑐 𝜎 𝐴<10 (𝑅)⋈𝑆 Section 1 Optimizing RA Plan We eliminate B earlier! R(A,B) S(B,C) T(C,D) Π 𝐴,𝐷 In general, when is an attribute not needed…? SELECT R.A,S.D FROM R,S,T WHERE R.B = S.B AND S.C = T.C AND R.A < 10; T(C,D) Π 𝐴,𝐶 sA<10 Π 𝐴,𝐷 𝑇⋈ Π 𝐴,𝑐 𝜎 𝐴<10 (𝑅)⋈𝑆 S(B,C) R(A,B)

Physical Optimization Section 1 Physical Optimization Physical optimization: Find algorithm with lowest IO cost to execute our plan Intuition: Calculate based on physical parameters (buffer size, etc.) and estimates of data size (histograms) Index-based selections Different join algorithms

2. ML Programs

ML Program Compilation Section 2 ML Program Compilation

Distributed Matrix Representation Section 2 Distributed Matrix Representation

Distributed Matrix Representation (2) Section 2 Distributed Matrix Representation (2)

Common Workload Characteristics Section 2 Common Workload Characteristics

3. Optimization Techniques

SystemML’s Compilation Chain Section 3 SystemML’s Compilation Chain HOP = high-level operations LOP = low-level operations

Basic HOP and LOP DAG Compilation Section 3 Basic HOP and LOP DAG Compilation

Static and Dynamic Rewrites Section 3 Static and Dynamic Rewrites

Example Static Rewrites Section 3 Example Static Rewrites

Example Dynamic Rewrites Section 3 Example Dynamic Rewrites

Matrix Multiplication Chain Optimization Section 3 Matrix Multiplication Chain Optimization

Matrix Multiplication Chain Optimization (2) Section 3 Matrix Multiplication Chain Optimization (2)

Matrix Multiplication Chain Optimization (3) Section 3 Matrix Multiplication Chain Optimization (3)

Example Operator Selection: Matrix Multiplication Section 3 Example Operator Selection: Matrix Multiplication

Fused Operators: WSLoss Section 3 Fused Operators: WSLoss

Section 3 More optimizations Dynamic Recompilation to address unknown/changing sizes Sparsity of intermediates Decisions: Split HOP DAGs for recompilation Mark HOP DAGs with unknown sizes / sparsity

Section 3 Resource Optimizer

From SystemR to SystemML – A Comparison