Frédéric Saubion LERIA Learning and Intelligent OptimizatioN Conference Autonomous Search.
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Transcript of Frédéric Saubion LERIA Learning and Intelligent OptimizatioN Conference Autonomous Search.
Frédéric Saubion LERIA
Learning and Intelligent OptimizatioN Conference
Autonomous Search
Based on joint works on this topic with :
G. Di TolloA. Fiahlo Y. Hamadi F. Lardeux J. Maturana E. MonfroyM. SchoenauerM. Sebag
Learning and Intelligent OptimizatioN Conference
1. Introduction2. Main Ideas3. Taxonomy of AS4. Focus on examples5. Conclusion and challenges
Outline
IntroductionGeneric modeling tools for engineers
(Decision) VariablesDomains Constraints Mathematical
Model
Solver
Solving Constraint Optimization and Satifaction Problems
IntroductionMap coloring problem
Satifaction Problems
IntroductionMap coloring problem
Satifaction Problems
IntroductionMap coloring problem
Satifaction Problems
Introduction
Optimization Problems
Travelling Salesman Problem : finda round trip across cities with minimal cost
Introduction
Optimization Problems
Travelling Salesman Problem : finda round trip across cities with minimal cost
Introduction
Optimization Problems
Travelling Salesman Problem : finda round trip across cities with minimal cost
IntroductionSearch landscapes are difficult to explore
Many variablesComplex constraints
Problems are more and more complex
IntroductionSearch landscapes are difficult to explore
Exploration vs. Exploitation Balance
Problems are more and more complex
Boolean Variable {0,1}
IntroductionAn illustrative example : solving SAT
SAT CNF instance
Devising more and more complex Solving algorithms
ba
ca
cba
Litterals
Clauses
Assignment
(1 0 0)
Introduction
Devising more and more complex Solving algorithms
How to explore the binary search space (assignments) to find a solution ?
Introduction
Devising more and more complex Solving algorithms
Use Local Search
Introduction
Devising more and more complex Solving algorithms
Basic Local Search
0 1 0 1 1
Choose a random initial assignment
Introduction
Devising more and more complex Solving algorithms
Basic Local Search
Compute the number of true and false clauses
Introduction
Devising more and more complex Solving algorithms
Basic Local Search
Try to improve by changing a value (flip)
0 1 0 1 1
0 1 1 1 1
Move to a neighbor
Introduction
Devising more and more complex Solving algorithms
Basic Local Search
Until finding a solution
Introduction
Devising more and more complex Solving algorithms
Short overview of the story : a first greedy version GSATBart Selman, Hector J. Levesque, David G. Mitchell: A New Method for Solving Hard Satisfiability Problems.AAAI 1992: 440-446
A first boat for binary seas
Introduction
Devising more and more complex Solving algorithms
10 1 0 1 1 0 0
1 1 1 1
0 0 0
Problem : Many possible moves (many variables)
Introduction
Devising more and more complex Solving algorithms
Restrict neighborhoodSelect a false clause C
fda a b c d e f g
0 1 0 1 1 0 0
Introduction
Devising more and more complex Solving algorithms
Get stuck in local optima
Introduction
Devising more and more complex Solving algorithms
Add pertubationsSelect a false clause C
With a random probability p Perform a random flip for C
With (1-p) Select the variable with best IMP Perform best move
If solution then stopElse go on
Parameter !
Introduction
Devising more and more complex Solving algorithms
Use restarts
False Clauses
Iterations
Parameter !
Introduction
Devising more and more complex Solving algorithms
WalkSAT : adding a noise and random restart
Henry A. Kautz, Bart Selman: Noise Strategies for Improving Local Search..AAAI 1994
Introduction
Devising more and more complex Solving algorithms
How to break ties ?
0 1 0 1 1 0 0
+3 +3
+3
Introduction
Devising more and more complex Solving algorithms
Add more sophisticated heuristics Compute the age of the variableIf the best variable is not the most recent then flipElseWith a random probability p’
Perform a random flip the second best
With (1-p’) Flip the best
Parameter !
Introduction
Devising more and more complex Solving algorithms
Novelty : using more strategies to perform improvements (age of the variable)D.A. McAllester, B. Selman and H. Kautz. Evidence for invariant in local search.In Proceedings of AAAI-97, AAAI Press 1997, pages 321-326.
Introduction
Devising more and more complex Solving algorithms
And improvements go on …
Novelty +,Novelty ++, …, TNM, Sattime…
Introduction
Devising more and more complex Solving algorithms
Captain Jack : many indicators and thus selection strategies
Dave A. D. Tompkins, Adrian Balint, Holger H. Hoos: Captain Jack: New Variable Selection Heuristics in Local Search for SAT. SAT 2011: 302-316
IntroductionAdding more parameters and heuristics
Devising more and more complex Solving algorithms
More flexible algorithms Fit to different instances
Set parameters/heuristics values Understand the behavior
John Rice. The algorithm selection problem. Technical Report CSD-TR152, Computer science department, Purdue University, 1975.
The Algorithm Selection Problem
Main ideas
John Rice. The algorithm selection problem. Technical Report CSD-TR152, Computer science department, Purdue University, 1975.
The Algorithm Selection Problem
Main ideas
Tuning the parameters
Related Questions
Main ideas
Using several algorithms for solving a classof problems
Tuning the parameters
Related Questions
Main ideas
Adjusting the parametersof one algorithm
Tuning the parameters
Main Objectives
Main ideas
Need for more autonomous solving tools
Increasing number of works in this trend : LION, Specialsessions in EA conferences (GECCO,…) …
Tuning the parameters
Ideas for More Autonomous Solvers
How to use an algorithm that includes
•Many parameters
•Many possible heuristics or components
Ideas
Tuning the parameters
Ideas for More Autonomous Solvers
How to use an algorithm that include
•Many parameters
•Many possible heuristics or components
How to automate all these choices ?
Ideas
Tuning the parameters
Off-line Automated Tuning
Ideas
Run your solver on some problems
Experiment automatically parameters values
Tuning the parameters
Off-line Automated Tuning
Ideas
Run your solver on new problems with these parameters values
Tuning the parameters
Off-line Automated Tuning
Ideas
Question : Generality of the parameters ?
Tuning the parameters
On-line Parameter Control
Ideas
Try to react during the resolution by changing the parameter
Tuning the parameters
On-line Parameter Control
Ideas
Example : try to increase some parameter when possible
Tuning the parameters
On-line Parameter Control
Ideas
Question : How to react efficiently ?
Tuning the parameters
Hyper Heuristics
Ideas
Combine basic solving heuristics
Tuning the parameters
Hyper Heuristics
Ideas
Get new solvers
Tuning the parameters
Hyper Heuristics
Ideas
Question : How to learn the suitable solver ?
Tuning the parameters
Portfolios Based Solvers
Ideas
Use different types of solvers
Tuning the parameters
Portfolios Based Solvers
Ideas
Learn how to select the right solver for a given problem
Tuning the parameters
Portfolios Based Solvers
Ideas
Question : Reliability of the learning process ?
Evolutionary ComputationA. E. Eiben, R. Hinterding, and Z. Michalewicz. Parameter control in
evolutionary algorithms. IEEE Trans. Evolutionary Computation,
3(2) :124141, 1999.
Reactive Search Battiti R, Brunato M, Mascia F (2008) Reactive Search and Intelligent
Optimization, ORCS interf., vol 45. Springer
Hyper-HeuristicsBurke EK, Hyde M, Kendall G, Ochoa G, Ozcan E, Woodward J
Handbook of Meta-heuristics, chap A Classification of Hyper-heuristics Approaches
Portfolios methodsGagliolo M, Schmidhuber J (2008) Algorithm selection as a bandit problem with unbounded losses. Tech. rep., Tech.
report IDSIA - 07
Why introducing the concept of Autonomous Search ?
Taxonomy
Taxonomies
Classification : Solving
Solving MethodsTree-Based Search
MetaheuristicsSLS EA
On-
line
Off-
line Au
to
Complete/incomplete search,Model representationOther optimization paradigms (e.g., ACO )
Taxonomy
Classification : Parameters
Solving MethodsTree-Based Search SLS EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
StructuralBehavioral
Numerical/discrete valuesComponents of the solverVs. Configuration of the solver
Taxonomy
Classification : Settings
Solving MethodsTree-Based Search EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
•Experiment-based•Feedback Control •Measures and learning techniques(reinforcement learning, statistical learning, case-base reasonning…)
Taxonomy
Related Approaches
Solving MethodsTree-Based Search
MetaheuristicsSLS EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
StructuralBehavioral
Taxonomy
Parameter Setting in Evolutionary Computation
Related Approaches
Solving MethodsTree-Based Search
MetaheuristicsSLS EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
StructuralBehavioral
Taxonomy
Parameter Setting
ParameterTuning
ParameterControl
Deterministic
Adaptive Self-adaptive
Related Approaches
Solving MethodsTree-Based Search
MetaheuristicsSLS EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
StructuralBehavioral
Taxonomy
Optimization of algorithms (automated tuning)
Related Approaches
Solving MethodsTree-Based Search
MetaheuristicsSLS EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
StructuralBehavioral
Taxonomy
Optimization of algorithms (automated tuning)
SLS Based (ParamILS)Frank Hutter, Holger H. Hoos, Kevin Leyton-Brown, Thomas Stützle: ParamILS: An Automatic Algorithm Configuration Framework. J. Artif. Intell. Res. (JAIR) 36: 267-306 (2009)
GA Based (Revac)Volker Nannen, A. E. Eiben: Efficient relevance estimation and value calibration of evolutionary algorithm parameters. IEEE Congress on Evolutionary Computation 2007: 103-110
Racing techniquesMauro Birattari, Thomas Stützle, Luis Paquete, Klaus Varrentrapp: A Racing Algorithm for Configuring Metaheuristics. GECCO 2002: 11-18
…
Related Approaches
Solving MethodsTree-Based Search
MetaheuristicsSLS EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
StructuralBehavioral
Taxonomy
Reactive SearchLearning for SLS
Related Approaches
Solving MethodsTree-Based Search
MetaheuristicsSLS EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
StructuralBehavioral
Taxonomy
Hyper heuristics
Hyper Heuristics
Taxonomy
Two possible views
• heuristics to choose heuristics
• heuristics to generate heuristics
Burke EK, Hyde M, Kendall G, Ochoa G, Ozcan E, Woodward JHandbook of Meta-heuristics, A Classification of Hyper-heuristicsApproaches
Proposing a general view of AS
Solving MethodsTree-Based Search
MetaheuristicsSLS EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
StructuralBehavioral
Taxonomy
Autonomous Search
Autonomous Search Genesis
Taxonomy
Gather works from the CSP solving community
Workshop “Autonomous Search” CP 2007, Providence (RI)
Autonomous Search Genesis
Taxonomy
Identify common concepts, goals andchallenges for future works
Tuning the parameters
Requirements for an Autonomous Search SystemParameters
Taxonomy
Modify its internal components
•Parameters•Fine grain heuristics•Coarse grain solving techniques•Model representation
React to external forces and opportunities
•Search landscape analysis (quality, diversity,...)•External knowledge (prediction models, rules, ...)
Tuning the parameters
CS Related Areas
Taxonomy
Solving Techniques Point of View
•Constraint Programming•Operation Research•Evolutionary Computation
Adjustment Techniques Point of View
•Reinforcement Learning•Statistical Learning•Information Theory
Tuning the parameters
CS Related Areas
Taxonomy
Solving Techniques Point of View
•Constraint Programming•Operation Research•Evolutionary Computation
Adjustment Techniques Point of View
•Reinforcement Learning•Statistical Learning•Information Theory
Not limited to…
Examples of works
Solving MethodsTree-Based Search
MetaheuristicsSLS EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
StructuralBehavioralExamples
Examples of works
Examples
Solving MethodsTree-Based Search
MetaheuristicsSLS EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
StructuralBehavioral
Manual Empirical TuningDeciding the Size of a Tabu List
Mazure B, Sais L, Gregoire E, Tabu search for sat. In : AAAI/IAAI,pp 281285, 1997
Examples of works
Examples
Solving MethodsTree-Based Search
MetaheuristicsSLS EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
StructuralBehavioral
Automated Parameter Tuning(SLS based)Hutter F, Hoos H, Stutzle T Automatic algorithm configuration based on local search. AAAI 2007
Examples of works
Examples
Solving MethodsTree-Based Search
MetaheuristicsSLS EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
StructuralBehavioral
Portfolios ApproachesFeatures based linear regression and classiers
Xu L, Hutter F, Hoos HH, Leyton-Brown K Satzilla : portfolio-based algorithm selection for sat. JAIR 2008
Examples of works
Examples
Solving MethodsTree-Based Search
MetaheuristicsSLS EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
StructuralBehavioral
Learning Combinations of Well-known Heuristics
Epstein S, Freuder E, Wallace R Learning to support constraint programmers. Comput Intell 2005
Examples of works
Examples
Solving MethodsTree-Based Search
MetaheuristicsSLS EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
StructuralBehavioral
Discovering heuristics(variable selection in SAT SLS)
Alex S. Fukunaga : Automated Discovery of Local Search Heuristics forSatisability Testing. Evolutionary Computation 2008
Examples of works
Examples
Solving MethodsTree-Based Search
MetaheuristicsSLS EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
StructuralBehavioral
Automated TuningAdjusting the size of a Tabu List
R. Battiti, G. Tecchiolli : The Reactive Tabu Search. INFORMS Journal on Computing 6(2): 126-140 (1994)
Examples of works
Examples
Solving MethodsTree-Based Search
MetaheuristicsSLS EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
StructuralBehavioral
Controlling Variable Orderings and Values Selection inSearch Heuristics
Boussemart F, Hemery F, Lecoutre C, Sais L Boosting systematic search by weighting constraints. ECAI2004 2004
Examples of works
Examples
Solving MethodsTree-Based Search
MetaheuristicsSLS EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
StructuralBehavioral
Adaptive Genetic Algorithms
A.E. Eiben, Z. Michalewicz, M. Schoenauer, J. E. SmithParameter Control in Evolutionary Algorithms.In Parameter Setting in Evolutionary Algorithms
2007
Focus on an example : how to design an AS system ?
Generic Evolutionary Algorithm for Constraint Satisfaction Problem
Focus
Population
Apply variation operator
New Population
Solution ?
Focus on an example
Generic Search Algorithm for ConstraintSatisfaction Problem
Focus
Configuration
Apply variation operator
New configuration
Solution ?
Question : How to choose the suitable operator at each iteration ?
Focus on an example
Idea
Associate a probability of application to each operator (parameter)
Select an operator according to thisprobability scheme
Focus
Focus on an example
Question : how to set the probabilities(parameters of the algorithm) ?
Focus
Focus on an example
Use a principled approach to tune yourparameter
•Search in the parameters space
•Assess the performance of each setting through runs of the algorithm on selected Instances
ParamILS, REVAC, F-Race …
Focus
Focus on an example
Second idea:
Control the probability during the run
•Evaluate the performance of each operator after application
•Adjust the parameters according to the performances
Focus
General process for control(Automated Operator Selection)
Focus
Focus on an example
What are the suitable criteria ?
-Quality -Fitness diversity -Genotypic diversity -Time -…
Focus
Focus on an example
What are the suitable criteria ?
-Quality -Fitness diversity -Genotypic diversity -Time -…
Focus
Different performnce mesearues
Focus
1 2 3 4 5 6 70
2
4
6
8
10
12
14
16
Op1Op2
Sliding Windows
Mean or Max ?
How to measure the impact ?
Focus on an example
What is the performance of the operators ?
•Fix a search policy•Dynamic policy •Values against rank •…
Focus
Focus on an example
What is the performance of the operators ?
Fix a search policy
Focus
Focus on an example
What is the performance of the operators ?No values :
Pareto rank of the operatorsArea under the curve
Focus
Estimating efficience of operators
How to reward the operators ?
Proportionally to their performance
Focus
Estimating efficience of operators
Using UCB (Upper Confidence Bound)(reinforcement learning technique)
Exploration + Exploitation of the operators
Choosing the operator having the best UCB
Focus
to
ktk
to n
nCr
,
,
,
)log(
Estimating efficience of operators
Warning : UCB converge asymptotically toGain for the MAB
But here we have dynamic changes
Use of statistical test to restart learning.
Focus
Different selection processes
Focus
UCB PM Uniform0
2
4
6
8
10
12
14
16
18
Op1Op2Op3Op4
Instances ?
Comparisons ?
Induced new parameters ? ?
Reliability ?
How to assess the performances of your system ?
Focus
What’s next ?
Solving MethodsTree-Based Search
MetaheuristicsSLS EA
Para
met
er s
etting
met
hod
On-
line
Off-
line Au
to
Parameter type
StructuralBehavioral
Focus
Conclusion
Many different possible approaches
Guidelines for designing new autonomousSolvers
Off-line/On-lineBehavioural parameters/componentsControl of the efficient heuristics/discovering new heuristics
…
Conclusion
Challenges
Comparing performances
•Autonomous vs. ad-hoc
•Off-line Tuning vs. On-line control
•Representative benchmarking
Conclusion
Challenges
Comparing performances
•Methodologies for comparisons
•New competitions Chesc (Cross-domain Heuristic Search Challenge)
G. Ochoa and her team
•Related to No Free-Lunch TheoremsMore reliable on more problems
Conclusion
Challenges
Parameters induced by the AS system
•Abstract parameters should be more easy to control (e.g., EvE balance)
•New parameters should be less sensitive than original ones
•Fewer paramaters are easier to adjust
Conclusion
Challenges
Learning
•Interactions solving-learning
•Improving learning off-line
•Short term (react) vs. long term (prediction)
•Continuous search (Arbelaez, Hamadi & Sebag)
Conclusion
Challenges
Distributed and parallel computing
•Improving algorithm’s space exploration
•Sharing information on parameters
•Sharing information on problems
Conclusion
Challenges
Towards more generic on-line control tools
•Identify generic control techniques andmeasures
•Control various components type (behavioral parameters, objective functions, heuristics…)
Conclusion
Of course all LION Proceedings …
Some books to read
Conclusion
And ;-)
Conclusion
So
Sorry for missing references and works
Conclusion
I will not forget important works and references I will not forget important works and references I will not forget important works and references I will not forget important works and references I will not forget important works and references I will not forget important works and references I will not forget important works and references I will not forget important works and references
So
Questions
Conclusion
I will not forget important works and references I will not forget important works and references I will not forget important works and references I will not forget important works and references I will not forget important works and references I will not forget important works and references I will not forget important works and references I will not forget important works and references