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Virtual Scientific Communities for Innovation

Supported by Novartis and GMO

- Karl Lieberherr
- Northeastern University
- College of Computer and Information Science
- Boston, MA
- joint work with
- Ahmed Abdelmeged and Bryan Chadwick

Introduction

- Problems to be solved:
- Optimal assembly of a system from components
- hardware
- software
- Maximum constraint satisfaction problem (MAX-CSP)
- Transporting goods minimizing energy consumption
- Schedule tasks minimizing cost

Innovation

Introduction

- Solve optimization problems in a domain X (X-problems).
- Find a feasible solution of good quality efficiently.
- Scholars to play the Specker Challenge Game (X) [SCG(X)]. Repeat a few times.
- Within the group of participating scholars, the winning scholar has the
- best solver for X-problems
- best supported knowledge about X

Innovation

Introduction

- Players share hypotheses about "the approximability of problems in certain niches of the problem domain"
- Administrator reconciles inconsistencies between shared hypotheses => Condensing knowledge/stirring progress
- Player with the strongest correct hypothesis gains reputation, the other player receives targeted feedback / gains knowledge

Introduction

- The game is designed to exclude situations where it is impossible to give useful targeted feedback and/or it's possible to gain reputation without sharing the strongest correct hypothesis, e.g.: proposing strong obvious hypothesis, avoiding involvement with other players, mirroring, ... etc => Fair assessment

Benefits of SCG

- Social Welfare
- Supported knowledge
- Hypotheses are challenged and strengthened.
- Better supported knowledge comes from better algorithms and software.

Innovation

SCG(X)

Scholar

Alice

Scholar

Bob

Scholars

Design Problem Solver

Develop Software

Deliver Agent

I am the best

No!!

Agent Alice

Agent Bob

Let’s play constructively

Administrator

SCG police

Innovation

Social Engineering

- Why develop problem solving software through a virtual scientific community?
- Evaluates fairly, frequently, constructively and dynamically. Encourages retrieval of state-of-the-art know-how, integration and discovery.
- Challenges humans, drives innovation, both competitive and collaborative.
- Agents point humans to what needs attention in problem solution / software.

Innovation

Software Development

- Software developers are knowledge integrators: Requirements, contextual information (lectures, papers), behavior of program in competition, etc.

Innovation

Scholars and virtual Scholars!

- Are encouraged to
- offer results that are not easily improved.
- offer results that they can successfully support.
- strengthen results, if possible.
- publish results of an experimental nature with an appropriate confidence level.
- stay active and publish new results or oppose current results.
- be well-rounded: solve posed problems and pose difficult problems for others.
- become famous!

Innovation

Agent Design

- How to Design an artificial organism?
- needs introspection to give it an ego.
- has a basic need: maximize reputation.
- has a rhythm: every round the same activity.
- interacts with other agents by proposing and opposing hypotheses.
- makes agent vulnerable.

Innovation

competitive / collaborative

Agent Alice: claims hypothesis H

loses reputation r

wins knowledge k

Agent Bob: challenges H, discounts: provides

evidence for !H

wins reputation r

makes public knowledge k

Innovation

Definitions

- A hypothesis H offered by Alice is constructively defendable by Alice against Bob if Alice supports H when Bob challenges H.
- The constructive defense is determined by an interactive protocol between Alice and Bob.
- A hypothesis H1 is stronger than hypothesis H2 if H1 implies H2.
- Successfully opposing is a form of proposing: strengthening a hypothesis means to propose a new one. Discounting a hypothesis means to propose its complement.

Innovation

SCG is sound

- The SCG game is sound, i.e., agent Alice wins with proposed hypothesis H against opponent Bob iff
- H is stronger than what Bob could constructively defend and
- H is constructively defendable by Alice against Bob.

Innovation

GIGO: Garbage in / Garbage out

- If all agents are weak, no useful solver created.
- WEAK against STRONG:
- STRONG accepts a hypothesis that is not discountable but WEAK cannot support it. Correct knowledge might be discounted.
- STRONG strengthens a hypothesis too much that it becomes discountable, but WEAK cannot discount it. Incorrect knowledge might be supported.

Innovation

What is the purpose of SCG?

- The purpose of playing an SCG(X) contest is to assess the "skills" of the players in:
- "approximating" optimization problems in domain X,
- "figuring-out" the wall-clock-time-bounded approximability of niches in domain X,
- "figuring-out" hardest problems in a specific niche, and
- "being-aware" of the niches in which their own solution algorithm works best.
- This multi-faceted evaluation makes SCG(X) more superior to contests based on benchmarks that only test the player's skills in approximating optimization problems. During the game, players cross-test each others' skills.

Innovation

How to use SCG(X)

- ABB needs new ideas about how to solve optimization problems in domain X.
- Define hypothesis language for X
- X-problems
- hypotheses, includes protocol
- Submit hypothesis language definition to SCG server.

Innovation

How to use SCG(X)

- Offer prize money for winner with conditions, e.g., performance must be at least 10% higher as performance of agent XY that ABB provides.
- 10 teams from 6 countries sign up, committing to 6 competitions. Player executables become known to other players after each competition. One team from ABB.
- The SCG server sends them the basic agent and the administrator for testing.

Innovation

How to use SCG(X)

- Game histories known to all. Data mining!
- First competition is at 23.59 on day 1. Registration starts at 18.00 on same day. The competition lasts 2.5 hours.
- Repeat on days 7, 14, … 42.
- The final winner is: Team Mumbai, winning 10000 Euro. Delivers source code and design document describing winning algorithm to ABB.

Innovation

Benefits for ABB of using SCG(X)

- Teams perform know-how retrieval and integration and maybe some research.
- Participating teams try to find the best knowledge in the area.
- Hypothesis language gives control!
- The non-discounted hypotheses give hints about new X-specific knowledge.
- A well-tested solver for X-problems that integrates the current algorithmic knowledge in field X.

Innovation

Disadvantages of SCG

- The game is addictive. After Bob having spent 4 hours to fix his agent and still losing against Alice, Bob really wants to know why!
- Overhead to learn to define and participate in competitions.
- The administrator for SCG(X) must perfectly supervise the game. Includes checking the legality of X-problems.
- if admin does not, cheap play is possible.
- watching over the admin.

I am

perfect

Innovation

How to compensatefor disadvantages

- Warn the scholars.
- Use a gentleman’s security policy: report administrator problems, don’t exploit them to win.
- Occasionally have a non-counting “attack the administrator” competition to find vulnerabilities in administrator.
- both generic as well as X-specific vulnerabilities.

Innovation

Experience block

Innovation

Experience

- Used for 3 years in undergraduate Software Development course. Prerequisites: 2 semesters of Introductory Programming, Object-Oriented Design, Discrete Structures, Theory of Computation.
- Collect and integrate knowledge from prerequisite courses, lectures, and literature.
- Teach it to the agent.

Innovation

Experience MAX-CSP

- MAX-CSP Problem Decompositions
- T-Ball (one relation), Softball (several relations, one implication tree), Baseball (several relations).
- ALL, SECRET

Innovation

Stages for SECRET T-Ball

- MAXCUT
- R(x,y)= x!=y
- fair coin ½
- maximally biased coin ½
- semi-definite programming / eigenvalue minimization 0.878

Innovation

Stages for SECRET T-Ball

- One-in-three
- R(x,y,z) = (x+y+z=1)
- fair coin: 0.375
- optimally biased coin: 0.444

Innovation

Stages for ALL Baseball

- Propose/Oppose/Provide/Solve
- based on fair coin
- optimally biased coin
- correctly optimize polynomials
- correctly eliminate noise relations
- correctly implement weights
- …

Innovation

How to model a scholar?

- Solve problems.
- Provide hard problems.
- Propose hypotheses about Solve and Provide (Introspection).
- Oppose hypotheses.
- Strengthen hypotheses.
- Challenge hypotheses.
- Supported challenge failed.
- Discounted challenge succeeded.

Innovation

How to model a hypothesis

- A problem space.
- A discounting predicate on the problem space.
- A protocol to set the predicate through alternating “moves” (decisions) by Alice and Bob. If the predicate becomes true, Alice wins.

Innovation

How to model a hypothesis

- Proposing and challenging a hypotheses is risky: your opponent has much freedom to choose its decisions within the game rules.
- Alternating quantifiers.
- Replace “exists” by agent algorithm kept by administrator.

Innovation

Hypothesis

- Alice’ Hypothesis: There exists a problem P in niche N of X s.t. for all solutions SBob searched by the opponent Bob in T seconds. Quality(P, SBob) < AR * Quality(P, SAlice).
- Hypotheses have an associated confidence [0,1].
- Hypothesis: <N, AR, Confidence>.

Innovation

1in3 niche

Truth Table 1in3

000 0

001 1

010 1

011 0

100 1

101 0

110 0

111 0

- Only relation 1in3 is used.
- 1in3 problem P:

v1 v2 v3 v4 v5

1in3( v1 v2 v3)

1in3( v2 v4 v5)

1in3( v1 v3 v4)

1in3( v3 v4 v5)

secret1 0 0 1 0

Secret quality SQ = 3/4

Innovation

1in3 Hypothesis

- 1in3 hypothesis H proposed by Alice: exists P in 1in3 niche so that for all SBob that opponent Bob searches in time t (small constant) seconds: Quality(P,SBob) < 0.4 * Quality(P,SAlice).
- H = (niche = (1in3), AR =0.4, confidence = 0.8)
- Bob has clever knowledge that Alice does not have. He opposes the hypothesis H by challenging it using his randomized algorithm.

Innovation

Bob’s clever knowledge4/9 for 1in3

- 4/9 for 1in3: For all P in 1in3 niche, exists S so that Quality(P,S) >= 0.444 * SQ.
- Proof: la(p)=3*p*(1-p)2 has the maximum 4/9.
- argmaxp in [0,1] la(p) = 1/3.
- Without search, in PTIME.
- Derandomize
- Bob successfully discounts
- Alice gets a hint
- Was Bob just lucky?

Truth Table 1in3

000 0

001 1

010 1

011 0

100 1

101 0

110 0

111 0

Innovation

End

Innovation

Reputation Gain

- Hypothesis have credibility [0,∞]. The credibility of a hypothesis is proportional to agent’s confidence in the hypothesis and agent’s reputation.
- Reputation gain is proportional to the discounting factor and the hypothesis credibility.
- The discounting factor [-1,1]. 1 means the hypothesis is completely discounted.

Innovation

Discounting Factor

- H1 = ((1in3), AR = 1.0, confidence = 1.0)
- H1 proposed by Alice: exists P in 1in3 niche so that for all S that opponent Bob searches: Quality(P,S) < 1.0 * SQ.
- This is a reasonable hypothesis if Alice is sure that her secret assignment is the maximum assignment when she provides a sufficiently big problem to Bob.

What we did not tell you so far

- A game defines some configuration constants:
- a maximum problem size
- For example, all problems in the niche can have at most 1 million constraints.
- A maximum time bound for all tasks (propose, oppose, provide, solve), e.g. 60 seconds.
- An initial reputation, e.g., 100. When reputation becomes negative, agent has lost.

Discounting Factor: ReputationGain for Strengthening

- H1 = ((1in3), AR = 1.0, confidence = 1.0)
- H1 proposed by Alice: exists P in 1in3 niche so that for all S that opponent Bob searches: Quality(P,S) < 1.0 * SQ.
- Bob thinks he can strengthen H1 to H2 = (MAXCSP, niche = secret ExistsForAll (1in3), AR = 0.9, confidence = 1.0).
- DiscountingFactor 1.0-0.9 = 0.1.
- ReputationGain for Bob = 0.1 * 1.0 * AliceReputation.
- Alice gets her reputation back if she discounts H2.

Discounting FactorReputationGain for Discounting

- H = ((1in3), AR = 0.4, confidence = 1.0)
- H proposed by Alice: exists P in 1in3 niche so that for all S that opponent Bob searches: Quality(P,S) < 0.4 * SQ.
- Bob knows he can discount H based on this knowledge: 4/9 for 1in3.
- Let’s assume he achieves 0.45 on Alice’ problem.
- DiscountingFactor 0.45 – 0.4 = 0.05 .
- ReputationGain for Bob = 0.05*1.0*AliceReputation.

Discounting FactorReputationGain for Supporting

- H = ((1in3), AR = 0.4, confidence = 1.0)
- H proposed by Alice: exists P in 1in3 niche so that for all S that opponent Bob searches: Quality(P,S) < 0.4 * SQ.
- Bob knows he can discount H based on this knowledge: 4/9 for 1in3.
- Let’s assume he achieves 0.3 on Alice’ problem. Bob has a bug somewhere!
- DiscountingFactor 0.3 – 0.4 = -0.1
- ReputationLoss for Bob = -0.1*1.0*AliceReputation.

Mechanism Design

- The exact SCG(X) mechanism is still a work in progress.
- SCG(X) mechanism must be sound:
- Encourage productive behavior and discourage unproductive behavior of scientists.
- The agent with best heuristics wins.

Innovation

Tools to facilitate use of SCG(X)

- Definition of X.
- Generate a client-server infrastructure for playing SCG(X) on the web.
- Administrator enforces SCG(X) rules: client.
- Baby agents: servers. They can communicate and play an uninteresting game.
- Baby agents get improved by their caregivers, register with Administrator and the game begins at midnight.

Innovation

Scholars and virtual Scholars!

- Are encouraged to
- offer results that are not easily improved.
- offer results that they can successfully support.
- quote related work and show how they improve on previous work.
- publish results of an experimental nature with an appropriate confidence level.
- stay active and publish new results or oppose current results.
- be well-rounded: solve posed problems and pose difficult problems for others.
- become famous!

Innovation

Productive Scientific Behavior (1)

- The agents propose hypotheses that are difficult to strengthen or challenge (i.e. non-trivial yet correct). Otherwise, they lose reputation to their opponents.
- Offer results that cannot be easily improved.
- Offer results that they can successfully support.

Innovation

Productive Scientific Behavior (2)

- Agents are encouraged to propose hypotheses they are not sure about. But they need to fairly express their confidence in their hypotheses.
- If the confidence is inappropriately high, they lose too much reputation if the hypothesis is successfully discounted.
- If the confidence is inappropriately low, they don’t win enough reputation if the hypothesis is successfully supported.
- publish results of an experimental nature with an appropriate confidence level.

Innovation

Productive Scientific Behavior (3)

- Agents stay active. In each “round”, they must propose new hypotheses and oppose other agents hypotheses.
- stay active and publish new hypotheses or oppose current hypotheses.
- Agents maximize their reputation.
- become famous!

Innovation

Productive Scientific Behavior (4)

- When Alice loses reputation to Bob, Alice can learn from Bob:
- Alice has a bug in her software.
- Bob has skills superior to hers. Alice should try to acquire Bob’s skills.
- Learn from mistakes.
- Be careful how you oppose a Nobel Laureate. The risks are high.

Innovation

Unproductive Scientific Behavior

- Cheating is forbidden: you can only succeed through good scientific behavior (by adding useful hypotheses or by successfully opposing hypotheses in the knowledge base).

Innovation

Fair Scientific Community

- All agents start with the same initial reputation.
- The winner has the best skills in domain X within the set of participating agents.

Innovation

Improving the research approach

- Problem to be solved: Develop the best practical algorithms for solving NPO X.
- Standard solution: Write hundreds of papers on the topic with isolated implementations. What are the best practical algorithms?
- Our solution: Use the virtual scientific agent community SCG(X) with a suitably designed hypotheses language to compare the algorithms. The winning agent has the best practical algorithms.

Innovation

Teaching: Survival Skills in SCG(X)

- Needed when agent caregiver is human.
- Knowledge about domain X needs to be developed by students or taught to them and understood and put into algorithms (propose-oppose(strengthen-challenge)-provide-solve) that go into the agent.
- This tests both whether the knowledge about X is understood as well as the programming skills.

Innovation

Teaching: Survival Skills in SCG(X) [cont.]

- [Scientific Innovation in X] Agents get skills programmed into them by clever scientists in domain X. Scientists use data mining to learn from competitions and manually improve the agents.
- [Machine Learning Innovation in X] Agents get skills programmed into them by an agent caregiver programmed with learning skills and data mining skills for domain X. Agent gets updated automatically between competitions and they improve automatically.

Innovation

SCG(X) produces history

- Proposer’s reputation: 120
- Hypothesis10 proposer1 opposer2 confidence 1
- Problem delivered
- Solution found: discountFactor = 1
- Opposer: increase in reputation: 1 * 1 * 120 = 120

Innovation

Blame assignment

- Where is the proposer to blame?
- Bad hypothesis that is discountable.
- Bug in problem finding algorithm.
- Bug in problem solving algorithm used to check proposed hypothesis.

Innovation

Propose, Oppose, Strengthen, Challenge, Provide,

Solve

Creating Agents- An agent is composed of 6 components: Agent = <Prop, Opp, Str, Cha, Prov, Sol>.
- Components can refer to each other.
- Given a set of agents: Agent1 ... Agentn
- Composed agent is a 12-tuple: <PropI, PropO, OppI, OppO, StrI, StrO, ChaI, ChaO, ProvI, ProvO, SolI, SolO>.
- <Prop3, (01101),Opp4, (00000), …>

1=own

0=other

Innovation

Creating Agents [cont.]

- PropI, OppI, StrI, ChaI, ProvI, SolI ∈ [1..n].
- PropO consist of 5-bits, each denote one of the other components. The first bit describes whether to use the opposition component of agent PropI or agent OppI.

Innovation

Conclusions

- We have shown how a virtual scientific community of agents can foster the development and innovation of heuristics for approximating NPOs.
- We need your input on how DM and ML could help with evolving the agents.

Innovation

Discounting

- If Alice offers the belief (FourColorConjecture, confidence = 1.0), she must be ready to support it.
- The opponent Bob gives Alice a planar graph.
- Alice must deliver a 4-coloring.
- If she does not, Bob has successfully discounted Alice’ belief and Alice loses reputation and Bob gains.
- If she does, Alice has successfully defended her belief and Alice wins reputation and the opponent Bob loses.
- Note that discounting is different from finding a counterexample. If Alice loses she has a “fault” in her coloring algorithm.

10/16/09

Can DM and ML help?

Beliefs: Four color conjecture

- FourColorConjecture: For all graphs g satisfying the predicate planar(g) there exists a 4-coloring of the nodes of g such that no two adjacent nodes have the same color.
- ForAllExists belief: For all problems p satisfying predicate pred(p) there exists a solution s satisfying a property(p,s).

10/16/09

Can DM and ML help?

Undiscounted beliefs represent the accumulated shared knowledge gained from the game. (Requires negation and reoffer of discounted beliefs?)

Innovation

Improving the research approach

- Problem to be solved: Develop the best practical algorithms for solving NPO X.
- Standard solution: Write hundreds of papers on the topic with isolated implementations. What are the best practical algorithms?
- Our solution: Use the virtual scientific agent community SCG(X) with a suitably designed hypotheses language to compare the algorithms. The winning agent has the best practical algorithms.

Innovation

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