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Disappointing and UnexpectedResults in Monte-Carlo Tree Search

O. Teytaud & colleaguesSilver Workshop, ECML 2012

In a nutshell:- the game of Go, a great AI-complete challenge- MCTS, a great recent tool for MDP-solving- negative results on MCTS are the most important stuff- considerations on academic publications (pros and cons)

Disappointing and UnexpectedResults in Monte-Carlo Tree Search

O. Teytaud & colleaguesSilver Workshop, ECML 2012

In a nutshell:- the game of Go, a great AI-complete challenge- MCTS, a great recent tool for MDP-solving- negative results on MCTS are the most important stuff- considerations on academic publications (pros and cons)

If you solve these weaknesses,even if it takes all your

time in all your research during 30years, it is worth being done.

Part I. A success story on Computer Games Part II. Two unsolved problems in Computer Games

Part III. Some algorithms which do not solve them

Part IV. Conclusion (technical)

Part V. Meta-conclusion (non-technical)

Part I : The Success Story(less showing off in part II :-) )

The game of Go is a beautifulChallenge.

Part I : The Success Story(less showing off in part II :-) )

The game of Go is a beautifulchallenge.

We did the first wins againstprofessional playersin the game of Go

Game o f Go (9x9 here )

Game o f Go

Game o f Go : count ing te r r i t o r ies( w h i t e h a s 7 . 5 “ b o n u s ” a s b l a c k s t a r t s )

Game of Go: the rulesBlack plays at the blue circle: the white group dies (it is removed)

It's impossible to kill white (two “eyes”).

“Superko” rule: we don't come back to the same situation.

(without superko: “PSPACE hard” with superko: “EXPTIME-hard”)

At the end, we count territories==> black starts, so +7.5 for white.

Coulom (06)Chaslot, Saito & Bouzy (06)Kocsis Szepesvari (06)

UCT (Upper Confidence Trees)(a variant of MCTS)

UCTKocsis & Szepesvari (06)

Exploitation ...

Exploitation ...

SCORE = 5/7 + k.sqrt( log(10)/7 )

... or exploration ?

SCORE = 0/2 + k.sqrt( log(10)/2 )

“UCB” ?• I have shown the “UCB” formula (Lai, Robbins), which is

the difference between MCTS and UCT



• The UCB formula has deep mathematical principles.




• But very far from the MCTS context.





• Contrarily to what has often been claimed, UCB is not central in MCTS.





• Contrarily to what has often been claimed, UCB is not central in MCTS.

• But for publishing papers, relating MCTS to UCB is so beautiful, with plenty of maths papers in the bibliography :-)

The great news:

● Not related to classical algorithms(no alpha-beta)

● Recent tools (Rémi Coulom's paper in 2006)

● Not at all specific from Go(now widely used in games,and beyond)

The great news:

● Not related to classical algorithms(no alpha-beta)

● Recent tools (Rémi Coulom's paper in 2006)

● Not at all specific from Go(now widely used in games,and beyond)

But great performance in Goneeds adaptations(of the MC part)...

We all have to write reports:

● Showing that we are very strong● Showing that our research has “breakthroughs”,

which destroy “bottlenecks”

So ok the previous slide is perfect for that

Part II: challenges

Two main challenges:● Situations which require abstract thinking

(cf. Cazenave)● Situations which involve divide & conquer (cf Müller)

Part I. A success story on Computer Games

Part II. Two unsolved problems in Computer Games Part III. Some algorithms which do not solve them



A trivial semeai(= “liberty” race)

Plenty of equivalentsituations!

They are randomlysampled, with

no generalization.

50% of estimatedwin probability!

Semeai



no generalization.


A trivial semeai



no generalization.


This is very easy.Children can solve that.

But it is too abstractfor computers.

Computers play“semeais” very badly.

It does not work. Why ?


In the first node:● The first simulations give ~ 50%● The next simulations go to 100% or 0% (depending on the chosen move)● But, then, we switch to another node (~ 8! x 8! such nodes)

And the humans ?


In the first node:● The first simulations give ~ 50%● The next simulations go to 100% or 0% (depending on the chosen move)● But, then, we DON'T switch to another node

Requires more than local fighting.Requires combining several local fights.Children usually not so good at this.But strong adults really good.And computers very childish.

Looks like abad move,“locally”.

Lee Sedol (black)Vs

Hang Jansik (white)

Requires more than local fighting.Requires combining several local fights.Children usually not so good at this.But strong adults really good.And computers very childish.

Looks like abad move,“locally”.


Part II. Two unsolved problems in Computer Games

Part III. Some algorithms which do not solve them (negatives results show that importance stuff is

really on II...)



Part III: techniques for addressing these challenges

1. Parallelization

2. Machine Learning

3. Genetic Programming

4. Nested MCTS

Parallelizing MCTS• On a parallel machine with shared memory: just many

simulations in parallel, the same memory for all.

• On a parallel machine with no shared memory: one MCTS per comp. node, and 3 times per second:

● Select nodes with at least 5% of total sims (depth at most 3)

● Average all statistics on these nodes

==> comp cost = log(nb comp nodes)

Good news: it worksSo misleading numbers...

Much better than voting schemes

But little difference with T. Cazenave (depth 0).

Every month, someone tells us:

Try with a biggermachine !

And win againsttop pros !

(I have believed that,at some point...)

In fact, “32” and “1”have almost the same level...

(against humans...)

Being faster is not the solution

The same in Havannah (F. Teytaud)

More deeply, 1(R. Coulom)

Improvement in terms of performance against humans

<<

Improvement in terms of performance against computers

<<

Improvements in terms of self-play

More deeply, 2

No improvement in divide and conquer.

No improvement on situations

which require abstraction.

Part III: techniques for adressing these challenges

1. Parallelization

2. Machine Learning


4. Nested MCTS

Machine learning

A lot of tuning of the MC is central.

It is a bit disappointing for thegenericity of the method.

Can we make thistuning automatic ?

A classical machine learning trick in MCTS: RAVE (= rapid action value estimates)

score(move) = alpha UCB(move)

+ (1-alpha) StatisticsInSubtree(move) Alpha2 = nbSimulations / ( K + nbSimulations)

Usually works well, but performs weakly on some situations.

weakness: - brings information only from bottom to top of the tree - does not solve main problems - sometimes very harmful ==> extensions ?

Here B2 is the only good move for white.But B2 makes sense only as a first move, and nowhere else in subtrees ==> RAVE rejects B2.

==> extensions ?

A classical machine learning trick in MCTS: RAVE (= rapid action value estimates)

score(move) = alpha UCB(move)

+ (1-alpha) StatisticsInSubtree(move) Alpha2 = nbSimulations / ( K + nbSimulations)

Usually works well, but performs weakly on some situations.[Müller]

4 generic rules proposed recently: - Drake [ICGA 2009]: Last Good Reply- Silver and others: simulation balancing - poolRave [Rimmel et al, ACG 2011]- Contextual Monte-Carlo [Rimmel et al, EvoGames 2010]- Decisive moves and anti-decisive moves

[Teytaud et al, CIG 2010]

==> significantly (statistics) ok, but far less efficient than human expertise

Part III: techniques for adressing these challenges

1. Parallelization

2. Machine Learning


4. Nested MCTS

We don't want to use expert knowledge.We want automated solutions.

Developing biases by Genetic Programming ?


Developing a MC by Genetic Programming ?

Looks like a good idea.

But importantly:

A strong MC part(in terms of playing strength of the MC part),

does not imply (by far!)a stronger MCTS.

(except in 1P cases...)


Developing a MC by Genetic Programming ?

Hoock et alCazenave et al

Part III: techniques for addressing these challenges

1. Parallelization

2. Machine Learning


4. Nested MCTS

Nested MCTS in one slide(Cazenave, F. Teytaud, etc)

1) to a strategy, you can associate a value function

-Value(s) = expected reward when simulation with strategy

from state s




from state s

2) Then define: Nested-MC0(state)=MC(state) Nested-MC1(state)=decision maximizing

NestedMC0-value(state.(state))...

Nested-MC.42(state)=decision maximizing NestedMC.41-value(state.(state))




from state s

2) Then define: NestedMC0(state)=MC(state) NestedMC1(state)=decision maximizing

NestedMC0-value(state+decision)...

NestedMC.42(state)=decision maximizing NestedMC.41-value(state+decision)

==> looks like a great idea==> not good in Go==> good on some less widely known testbeds (“morpion solitaire”, some hard scheduling pbs)


Part II. Two unsolved problems in Computer Games

Part III. Some algorithms which do not solve them



Part IV: Conclusions

Game of Go:

1- disappointingly, most recent progress = human expertise ==> we understood a lot by methods which do not work or work little ==> we understood a lot by

counter-examples, not by impressive performance


Game of Go:

1- disappointingly, most recent progress = human expertise

2- UCB is not that much involved in MCTS (simple rules perform similarly) “==> publication bias”


Recent “generic” progress in MCTS:

1- application to GGP (general game playing): the program learns the rules of the game just before the competition, no last-minute development (fully automatized) ==> not so well known, but really interesting


Recent “generic” progress in MCTS:

1- application to GGP (general game playing): the program learns the rules of the game just before the competition, no last-minute Development (fully automatized)

2- one-player games: great ideas which do not work in 2P-games sometimes work in 1P games (e.g. optimizing the MC in a

DPS sense)


Techniques whichoutperformed thestate of the art inMinesweeper were(negatively) tested on Go,and (positively) onindustrial problems.

Part V: Meta-Conclusion

Huge publication bias.People report only experiments which aresooooo great breakthrough.


Huge publication bias.People report only experiments which aresooooo great breakthroughs.But when you discuss with them they tellyou that there is publication andthere is reality.



At the end, we trust our friends, or publishedtheorems, but we don't trust experiments.

The most interesting MCTS results arenegative results:

Current main ML

techniques for MCTSdoes not work on this

Abstractthinking (lookslike theorem

proving)

Understanding this “combination of local stuff”is impossible for computers

There are several examples of MCTS papersin which problems were swept under the carpet,

for the sake of publication,whereas the dust was the interesting stuff.

Results are often difficult to reproduce,or unstable w.r.t. experimental conditions.

Examples:

“- I have truncated results to ..... because it was unstable otherwise.”

(cheat by using new version only for openings)

==> for any method, with enough tuning, you get positive results

Examples:

“- I have truncated results to ..... because it was unstable otherwise.”

(cheat by using new version only for openings)

“- I could make it work after a lot of tuning in 9x9, but I couldnot get positive results in 19x19”

(cheat by heavy tuning)==> for any method, with enough

tuning, you get positive results ==> you are more likely to publish “I used sophisticated method XXX and got positive results” than “I used plenty of dirty tuning

and got positive results”==> if method XXX has plenty of free parameters

it's ok at some point you will validate it

For mathematical works,sometimes people lie on motivations, trying

to justify that there is a real world application.



Sometimes it's true, but it's also often a lie.

A memory from a long time ago;I was working on pure theory stuff and I asked “I have read in the abstract that

this can be applied to biological problems.Can you explain ?”




A memory from a long time ago;I was working on pure theory stuff and I asked “I have read in the abstract that

this can be applied to biological problems.

Answer: “Wahaha he has believed it!”




In experiments, it's different: people often use experimental setups

for hiding the problems under the carpet.Mathematicians can not do that.



My conclusions:- don't trust publications too much, - I want to publish less- I want to publish (try to publish...) failures and disappointing results.


Huge publication bias.People report only experiments which aresooooo great breakthrough.But when you discuss with them they tellyou that there is publication andthere is reality.


We could apply inMineSweeper (1P)Ideas which do not

work in Go (2P)


Huge publication bias.People report only experiments which aresooooo great breakthrough.But when you discuss with them they tellyou that there is publication andthere is reality.


We could apply inMineSweeper (1P)Ideas which do not

work in Go (2P)

We could apply inEnergy Manag. (1P)Ideas which do not

work in Go (2P)


People in computer-games look much moreClever since they have been working on Go.

Much easier to write reports :-)Lucky, right place, right moment.

The progress in the game of Go does not cure cancer.The important challenges are still in front of us (don't trust

too much published solutions...).

Failed experiments on Go provide more insights than the success story (in which the tuning part, which is not so generic, is not visible...).

Yet games are great challenges.

When you play Go, you look clever & wise.

When you play StarCraft, you look like a geeky teenager.

Yet, StarCraft, Doom, Table Tennis, MineSweeper are great challenges.

Di f f i cu l t games : Havannah

Very difficult

for computers.

What else ? First Person Shooting(UCT for partially observable MDP)

Frédéric Lemoine MIG 11/07/2008 104

What else ? Real Time Strategy Game(multiple actors, partially obs.)

Frédéric Lemoine MIG 11/07/2008 105

What else ? Sports (continuous control)

“Real” games

Assumption: if a computer understands and guesses spins, thenthis robot will be efficient for something else than just games.

(holds true for Go)

“Real” games

Assumption: if a computer understands and guesses spins, thenthis robot will be efficient for something else than just games.

VS

What else ? Collaborative sports

Experimentalworks.

Difficult to reproduce(except games...)

Dust swept undercarpet / aesthetic

bias

Statisticalconscious or unconscious

cheating

Negative resultsunpublished

Moderately reliablepublication

Yet, academic papers are, I think, more reliable thanreports for billion-$ contracts ==> pressure by money

does not work :-(

Funding based onpublication records

For me, this is sourceof all evil.

Academics are, andshould remain,

the most independent and reliable people.

Should be refereesfor all important

industrial contracts.