Evolving SolutionsMachine Learning

Programs that Search for SolutionsSearching Random Points

Recursive Descent / AscentSub-Optimization

Faulty AnalogiesFitness

Genetic AlgorithmsParticle Swarm Optimization

Simulated Annealing

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Basic Concepts

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Learning ==> Improvement

Some quality is being improved.

There is some measure of good / bad.

There is some way to move toward good.

Change position

Change behavior

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Learning ==>Some quality is being improved.

Implies / Assumes:

There is consensus about good versus bad.

There is some way to measure good / bad.

Give that measure a name: “Fitness”

Analogy to nature and evolution concept.

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Searching for BetterRandom Search

Randomize values in degrees of freedom.

Compare resulting fitness.

Pick the best results.

And then what?

Recursive Descent / Ascent

Assumes that solution space has a gradient.

Assumes there are minima / maxima.5Monday, January 14, 13

Seeker:When do you quit searching?

Infinite Loop versus “Stopping Condition”

Eventually we run out of time / resource / energy.

Complications:

Sometimes “Best” is not well-defined.

The solution space is continuously changing.

The shape (gradient qualities) of space is unknown.

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Faulty Analogs

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EvolutionThere is some way to measure “fitness”

Fitness is a function of a set of objects that can vary over individual instances.

Call the objects “genes” to use genetic analogy.

Mutation ==> Changing the values of “genes”.

Sexual Reproduction ==> Merging gene “sequences.”

Next Generation <== keep most fit, cull least fit.8Monday, January 14, 13

Genetic AlgorithmDefine degrees of freedom ==> genes.

Produce first generation with randomized genes.

Evaluate fitness of each individual

Calculate / Run a simulation of environment.

Keep most fit <==> Cull least fit.

Populate the next generation. ( mutate and/or splice )

Repeat until “done”

Note: Real environments change over time. 9Monday, January 14, 13

Main Loop In Smalltalk

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Next Generation

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Mutation

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Degrees Of Freedom

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See Also: Java Examplefor

Traveling Salesman

http://code.google.com/p/java-traveling-salesman/source/checkout

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Insect (Swarm) Behavior

Swarms search for “food” / Encounter “intruders”-- mostly random search.

Insects communicate with their buddies.

Their buddies re-direct their paths to gather / fight.

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Particle Swarm OptimizationMixed Analogy: Particle <==> Flying insect.

Particles have “position” in multi-dimensional space.

Assign each particle to a group “swarm” (at random).

After fitness is evaluated, particles move toward the most fit particle in their swarm.

The most fit particle in the swarm can stay where it is, ascend, or dither (random move).

Recursive ascent / descent may guide movesif the space is believed to be reasonably continuous.

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http://vimeo.com/17407010

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Stopping ConditionsHow good is good enough?

Genetic Algorithms and Particle Swarm Optimizationcan provide multiple solutions.

Stop when best fitness is no longer improving.

Stop when move method is no longer moving anything.

Stop at some arbitrary limit:

Number of generations.

Time limit.

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Simulated AnnealingConcept: Temperature ==> Energy Available.

Energy ==> speed of movement.

Speed == How much change from step to step?

Annealing == Cooling at controlled rate ==> The allowed change decreases from step to step.

Stopping Condition:

Temperature (Change/Step) goes to zero.

Other stopping conditions may also apply.

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Gotcha’sExperts refuse to say “optimum / optimal / optimized”

No way to verify solution is best possible.

Parameters selected may not cover everything.

Say “sub-optimal” or “satisfices” (good enough)

Solution is only good inside your simulation.

Real world is certainly different.

Don’t over-train: Solution may lack flexibility.20Monday, January 14, 13

VisualizationHow do you visualize position in hyperspace?

Assign each degree of freedom to some geometry.

3 degrees (x,y,z) ==> position

2 degrees (angle, angle) ==> orientation of “axis”

additional degrees ==> shape dimensions

Example: Torus (donut) Shape -- 9 shape dimensions

Radius, Eccentricity, Angle (?), r, e, a

frequency of: twist, wave, bulge21Monday, January 14, 13

http://megaswf.com/serve/

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Lessons LearnedI did not and do not expect this to work.It is just something I always wanted to tinker.

Best fitness for 2007-2008: Stay out of the market!

“When-to-buy” was competing with “when-to-sell” and producing counter-productive results.==> Need more complex strategy ==> more parameters.

Very compute intensive (generation takes way too long)==> Need faster data structure ==> Refactor database.==> Squeak VM is single-thread ==> Port to Erlang ???==> Potential GPU application.

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