AI-Augmented Algorithms –How I Learned to Stop

Worrying and Love ChoiceLars Kotthoff

University of Wyominglarsko@uwyo.edu

St Andrews, 25 July 2018

Outline

▷ Big Picture▷ Motivation▷ Algorithm Selection and Portfolios▷ Algorithm Configuration▷ Outlook

2

Big Picture▷ advance the state of the art through meta-algorithmic

techniques▷ rather than inventing new things, use existing things more

intelligently – automatically▷ invent new things through combinations of existing things

3

Big Picture▷ advance the state of the art through meta-algorithmic

techniques▷ rather than inventing new things, use existing things more

intelligently – automatically▷ invent new things through combinations of existing things

3

Motivation – What DifferenceDoes It Make?

4

Prominent Application

Fréchette, Alexandre, Neil Newman, Kevin Leyton-Brown. “Solving theStation Packing Problem.” In Association for the Advancement of ArtificialIntelligence (AAAI), 2016.

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Performance Differences

0.1

1

10

100

1000

0.1 1 10 100 1000

Virt

ual B

est S

AT

Virtual Best CSP

Hurley, Barry, Lars Kotthoff, Yuri Malitsky, and Barry O’Sullivan. “Proteus:A Hierarchical Portfolio of Solvers and Transformations.” In CPAIOR, 2014.

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Leveraging the Differences

Method Mean PAR10 Number SolvedVB Proteus 97 1493Proteus 1774 1424VB CSP 3577 1349VB SAT 17373 775VB DirectOrder Encoding 17637 764VB Direct Encoding 21736 593VB Support Encoding 21986 583

Hurley, Barry, Lars Kotthoff, Yuri Malitsky, and Barry O’Sullivan. “Proteus:A Hierarchical Portfolio of Solvers and Transformations.” In CPAIOR, 2014.

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Performance Improvements

Configuration of a SAT Solver for Verification [Hutter et al, 2007]

Ran FocusedILS, 2 days × 10 machines

– On a training set from each benchmark

Compared to manually-engineered default

– 1 week of performance tuning

– Competitive with the state of the art

– Comparison on unseen test instances

10−2

10−1

100

101

102

103

104

10−2

10−1

100

101

102

103

104

SPEAR, original default (s)

SP

EA

R, optim

ized for

IBM

−B

MC

(s)

4.5-fold speedup

on hardware verification

10−2

10−1

100

101

102

103

104

10−2

10−1

100

101

102

103

104

SPEAR, original default (s)

SP

EA

R, optim

ized for

SW

V (

s)

500-fold speedup won category

QF BV in 2007 SMT competitionHutter & Lindauer AC-Tutorial AAAI 2016, Phoenix, USA 17

Hutter, Frank, Domagoj Babic, Holger H. Hoos, and Alan J. Hu.“Boosting Verification by Automatic Tuning of Decision Procedures.” InFMCAD ’07: Proceedings of the Formal Methods in Computer Aided Design,27–34. Washington, DC, USA: IEEE Computer Society, 2007. 8

Common Theme

Performance models of black-box processes▷ also called surrogate models▷ replace expensive underlying process with cheap approximate

model▷ build approximate model based on real evaluations using

machine learning techniques▷ no knowledge of what the underlying process does required

(but can be helpful)▷ allow better understanding of the underlying process through

interrogation of the model

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Algorithm Selection

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Algorithm Selection

Given a problem, choose the best algorithm to solve it.

Rice, John R. “The Algorithm Selection Problem.” Advances in Computers15 (1976): 65–118.

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Algorithm Selection

Portfolio

Algorithm 2Algorithm 1 Algorithm 3

Training Instances

Instance 2Instance 1 Instance 3

Algorithm Selection

Performance Model

Instance 4Instance 5Instance 6

...

Instance 4: Algorithm 2Instance 5: Algorithm 3Instance 6: Algorithm 3

...

Feature Extraction

FeatureExtraction

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Algorithm Portfolios

▷ instead of a single algorithm, use several complementaryalgorithms

▷ idea from Economics – minimise risk by spreading it outacross several securities

▷ same for computational problems – minimise risk of algorithmperforming poorly

▷ in practice often constructed from competition winners

Huberman, Bernardo A., Rajan M. Lukose, and Tad Hogg. “An EconomicsApproach to Hard Computational Problems.” Science 275, no. 5296 (1997):51–54. doi:10.1126/science.275.5296.51.

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Algorithms

“algorithm” used in a very loose sense▷ algorithms▷ heuristics▷ machine learning models▷ consistency levels▷ …

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Parallel Portfolios

Why not simply run all algorithms in parallel?▷ not enough resources may be available/waste of resources▷ algorithms may be parallelized themselves▷ memory contention

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Building an Algorithm Selection System

▷ most approaches rely on machine learning▷ train with representative data, i.e. performance of all

algorithms in portfolio on a number of instances▷ evaluate performance on separate set of instances▷ potentially large amount of prep work

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Key Components of an Algorithm Selection System

▷ feature extraction▷ performance model▷ prediction-based selector/scheduler

optional:▷ presolver▷ secondary/hierarchical models and predictors (e.g. for feature

extraction time)

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Types of Performance Models

Regression Models

A1

A2A3

A1: 1.2A2: 4.5A3: 3.9

Classification Model

A1A3 A1

A2 A1

Pairwise Classification Models

A1 vs. A2

A1A2 A1

A1

A1 vs. A3

A1A1 A3

A3 …A1: 1 voteA2: 0 votesA3: 2 votes

Pairwise Regression Models

A1 - A2

0

A1 - A3

0…

A1: -1.3A2: 0.4A3: 1.7

Instance 1Instance 2Instance 3

...

Instance 1: Algorithm 2Instance 2: Algorithm 1Instance 3: Algorithm 3

...

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Benchmark Library – ASlib

▷ currently 29 data sets/scenarios with more in preparation▷ SAT, CSP, QBF, ASP, MAXSAT, OR, machine learning…▷ includes data used frequently in the literature that you may

want to evaluate your approach on▷ performance of common approaches that you can compare to▷ http://aslib.net

Bischl, Bernd, Pascal Kerschke, Lars Kotthoff, Marius Lindauer, YuriMalitsky, Alexandre Fréchette, Holger H. Hoos, et al. “ASlib: A BenchmarkLibrary for Algorithm Selection.” Artificial Intelligence Journal (AIJ), no. 237(2016): 41–58.

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(Much) More Information

http://larskotthoff.github.io/assurvey/

Kotthoff, Lars. “Algorithm Selection for Combinatorial Search Problems: ASurvey.” AI Magazine 35, no. 3 (2014): 48–60. 20

Algorithm Configuration

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Algorithm Configuration

Given a (set of) problem(s), find the best parameter configuration.

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Parameters?

▷ anything you can change that makes sense to change▷ e.g. search heuristic, variable ordering, type of global

constraint decomposition▷ not random seed, whether to enable debugging, etc.▷ some will affect performance, others will have no effect at all

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Automated Algorithm Configuration

▷ no background knowledge on parameters or algorithm▷ as little manual intervention as possible

▷ failures are handled appropriately▷ resources are not wasted▷ can run unattended on large-scale compute infrastructure

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Algorithm Configuration

Frank Hutter and Marius Lindauer, “Algorithm Configuration: A Hands onTutorial”, AAAI 2016

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General Approach

▷ evaluate algorithm as black box function▷ observe effect of parameters without knowing the inner

workings▷ decide where to evaluate next▷ balance diversification/exploration and

intensification/exploitation

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When are we done?

▷ most approaches incomplete▷ cannot prove optimality, not guaranteed to find optimal

solution (with finite time)▷ performance highly dependent on configuration space

→ How do we know when to stop?

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Time Budget

How much time/how many function evaluations?▷ too much → wasted resources▷ too little → suboptimal result▷ use statistical tests▷ evaluate on parts of the instance set▷ for runtime: adaptive capping

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Grid and Random Search▷ evaluate certain points in parameter space

Bergstra, James, and Yoshua Bengio. “Random Search forHyper-Parameter Optimization.” J. Mach. Learn. Res. 13, no. 1 (February2012): 281–305.

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Model-Based Search

▷ evaluate small number of configurations▷ build model of parameter-performance surface based on the

results▷ use model to predict where to evaluate next▷ repeat▷ allows targeted exploration of new configurations▷ can take instance features into account like algorithm selection

Hutter, Frank, Holger H. Hoos, and Kevin Leyton-Brown. “SequentialModel-Based Optimization for General Algorithm Configuration.” In LION 5,507–23, 2011.

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Model-Based Search Example

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yei

−1.0 −0.5 0.0 0.5 1.0

0.0

0.4

0.8

0.000

0.005

0.010

0.015

0.020

0.025

x

type

● init

prop

type

y

yhat

ei

Iter = 1, Gap = 1.9909e−01

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Model-Based Search Example

●

●

●

●

●

yei

−1.0 −0.5 0.0 0.5 1.0

0.0

0.4

0.8

0.00

0.01

0.02

0.03

x

type

● init

prop

seq

type

y

yhat

ei

Iter = 2, Gap = 1.9909e−01

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Model-Based Search Example

●

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yei

−1.0 −0.5 0.0 0.5 1.0

0.0

0.4

0.8

0.000

0.002

0.004

0.006

x

type

● init

prop

seq

type

y

yhat

ei

Iter = 3, Gap = 1.9909e−01

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Model-Based Search Example

●

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●

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yei

−1.0 −0.5 0.0 0.5 1.0

0.0

0.4

0.8

0e+00

2e−04

4e−04

6e−04

8e−04

x

type

● init

prop

seq

type

y

yhat

ei

Iter = 4, Gap = 1.9992e−01

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Model-Based Search Example

●

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yei

−1.0 −0.5 0.0 0.5 1.0

0.0

0.4

0.8

0e+00

1e−04

2e−04

x

type

● init

prop

seq

type

y

yhat

ei

Iter = 5, Gap = 1.9992e−01

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Model-Based Search Example

●

●

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yei

−1.0 −0.5 0.0 0.5 1.0

0.0

0.4

0.8

0.00000

0.00003

0.00006

0.00009

0.00012

x

type

● init

prop

seq

type

y

yhat

ei

Iter = 6, Gap = 1.9996e−01

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Model-Based Search Example

●

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yei

−1.0 −0.5 0.0 0.5 1.0

0.0

0.4

0.8

0e+00

1e−05

2e−05

3e−05

4e−05

5e−05

x

type

● init

prop

seq

type

y

yhat

ei

Iter = 7, Gap = 2.0000e−01

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Model-Based Search Example

●

●

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●

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yei

−1.0 −0.5 0.0 0.5 1.0

0.0

0.4

0.8

0.0e+00

5.0e−06

1.0e−05

1.5e−05

2.0e−05

x

type

● init

prop

seq

type

y

yhat

ei

Iter = 8, Gap = 2.0000e−01

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Model-Based Search Example

●

●

●

●

●

yei

−1.0 −0.5 0.0 0.5 1.0

0.0

0.4

0.8

0.0e+00

2.5e−06

5.0e−06

7.5e−06

1.0e−05

x

type

● init

prop

seq

type

y

yhat

ei

Iter = 9, Gap = 2.0000e−01

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Model-Based Search Example

●

●

●

●

●

yei

−1.0 −0.5 0.0 0.5 1.0

0.0

0.4

0.8

0e+00

1e−07

2e−07

3e−07

4e−07

x

type

● init

prop

seq

type

y

yhat

ei

Iter = 10, Gap = 2.0000e−01

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Benchmark Library – AClib

▷ ASP, MIP, planning, machine learning, …▷ 4 algorithm configuration tools from the literature already

integrated▷ https://bitbucket.org/mlindauer/aclib2

Hutter, Frank, Manuel López-Ibáñez, Chris Fawcett, Marius Lindauer,Holger H. Hoos, Kevin Leyton-Brown, and Thomas Stützle. “AClib: ABenchmark Library for Algorithm Configuration.” In Learning and IntelligentOptimization, 36–40. Cham: Springer International Publishing, 2014.

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Outlook

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Quo Vadis, Software Engineering?

Run

Hoos, Holger H. “Programming by Optimization.” Communications of theAssociation for Computing Machinery (CACM) 55, no. 2 (February 2012):70–80. https://doi.org/10.1145/2076450.2076469.

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Quo Vadis, Software Engineering?

Run

+ AI

Hoos, Holger H. “Programming by Optimization.” Communications of theAssociation for Computing Machinery (CACM) 55, no. 2 (February 2012):70–80. https://doi.org/10.1145/2076450.2076469.

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Meta-Algorithmics in the Physical Realm – AI and Lasers

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Tools and Resources

LLAMA https://bitbucket.org/lkotthoff/llamaSATzilla http://www.cs.ubc.ca/labs/beta/Projects/SATzilla/

iRace http://iridia.ulb.ac.be/irace/mlrMBO https://github.com/mlr-org/mlrMBO

SMAC http://www.cs.ubc.ca/labs/beta/Projects/SMAC/Spearmint https://github.com/HIPS/Spearmint

TPE https://jaberg.github.io/hyperopt/

autofolio https://bitbucket.org/mlindauer/autofolio/Auto-WEKA http://www.cs.ubc.ca/labs/beta/Projects/autoweka/

Auto-sklearn https://github.com/automl/auto-sklearn

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Summary

Algorithm Selection choose the best algorithm for solving aproblem

Algorithm Configuration choose the best parameter configurationfor solving a problem with an algorithm

▷ mature research areas▷ can combine configuration and selection▷ effective tools are available▷ COnfiguration and SElection of ALgorithms group COSEAL

http://www.coseal.net

Don’t set parameters prematurely, embrace choice!

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I’m hiring!

Several funded graduate positions available.

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