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Using Artificial Markets to Teach Computer Science Through Trading Robots

Using Artificial Markets to Teach Computer Science Through Trading Robots. How to get students interested in algorithms, combinatorial optimization and software development. Karl Lieberherr, Northeastern University, Boston. Outline. Specker Derivative Game (SDG) history example, bottom up

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Using Artificial Markets to Teach Computer Science Through Trading Robots

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  1. Using Artificial Markets to Teach Computer Science Through Trading Robots How to get students interested in algorithms, combinatorial optimization and software development Karl Lieberherr, Northeastern University, Boston SDG Mittagsseminar

  2. Outline • Specker Derivative Game (SDG) • history • example, bottom up • top-down • derivatives, raw materials, finished products • Risk analysis for a derivative • Problem reductions – noise elimination • SDG(MAX-SAT): risk analysis using polynomials • Conclusions SDG Mittagsseminar

  3. History • Diplomarbeit with Ernst Specker on two-dimensional automata. • Around 1975: working on non-chronological backtracking for MAX-SAT for my PhD with Erwin Engeler. • Ernst Specker analyzed MAX-SAT which lead to the Golden Ratio Result: joint FOCS 79 and JACM 1981 paper. Ideas applicable to MAX-CSP. • 2006: sabbatical at Novartis reactivated my interest in MAX-SAT. • 2007: Turned Golden Ratio Result into a game SDG(Max) parameterized by a maximization problem Max. • 2007/2008: Taught SDG to students who had a lot of fun trying to produce a winning robot. SDG Mittagsseminar

  4. SDG Example • derivative(CNF{(2,0),(1,1)}, 0.70) • 4 variables maximum • would you like to buy it? • you will get two rights • you will receive a CNF R of the given type. • if you can satisfy fraction q of clauses in R, I will pay back q to you. SDG Mittagsseminar

  5. CNF{(2,0),(1,1)} raw materials 2: a 2: b 2: c 1: !a !b 1: !b !c 2: a 2: b 3: c 1: d 3: !a !b 9: !a !c 7: !b !c 1: !a !d 6: !b !d 6: !c !d 2: a 3: b 1: c 8: !a !b 6: !b !c 1: a 1: b 8: !a !b SDG Mittagsseminar

  6. CNF{(2,0),(1,1)} raw materials,finished products 2: a 2: b 2: c 1: !a !b 1: !b !c 2: a 2: b 3: c 1: d 3: !a !b 9: !a !c 7: !b !c 1: !a !d 6: !b !d 6: !c !d 6/8=0.75 2: a 3: b 1: c 8: !a !b 6: !b !c 17/20=0.85 price of 0.7 seems fair!? 1: a 1: b 8: !a !b 9/10=0.9 35/40 = 0.875 SDG Mittagsseminar

  7. Oops • Our analysis was not thorough enough! • 2 kinds of uncertainty: • worst formula? • best assignment? SDG Mittagsseminar

  8. Playing with the weights x: a x: b x: c x: d y: !a !b y: !a !c y: !b !c y: !a !d y: !b !d y: !c !d x =1, y=1 best assignment a=1, b=0, c=0, d=0: (1+6)/10=7/10=0.7 x = 2, y=1 best assignment a=1, b=1, c=0, d=0: (4+5)/14=9/14=0.64 derivative(CNF{(2,0),(1,1)}, 0.70) LOSS: 0.06 SDG Mittagsseminar

  9. The SDG Game: Two high level views • Financial: Implement trading robots that survive in an artificial derivative market through offering derivatives, and buying and processing derivatives produced by other trading robots. • Biological: Implement organisms that survive in an artificial world through offering outsourced services, and consuming and processing outsourced services produced by other organisms. SDG Mittagsseminar

  10. Derivative: (pred, p, s) bought by b • Max is an NP-hard maximization problem with objective function range [0,1]. • Buyer b buys derivative at price p. • Seller s delivers raw material R (instance of Max) satisfying predicate pred. • Raw material R is finished by buyer with outcome O of quality q and seller pays q to buyer. • Buyer only buys if she thinks q > p. • Uncertainty for buyer: which raw material R will I get? Only know the predicate! What is the quality of the solution of Max I can achieve for R? SDG Mittagsseminar

  11. Buyer b Seller s (pi,p,s) SDG Mittagsseminar

  12. Buyer makes profit of 0.8 - 0.7 = 0.1 0.8 (p2,0.9,s) Buyer b Seller s O 0.8 O 0.8 R R (p1,0.7,s) sold Derivatives R satisfies pi 0.7 SDG Mittagsseminar

  13. Artificial markets • Trading Robots that survive in a virtual world of an artificial market of financial derivatives. • Trading Robots that don’t follow the world rules don’t survive. • Trading Robots are ranked based on their bank account. • Teaches students about problem solving, software development and analyzing and approximating combinatorial maximization problems. SDG Mittagsseminar

  14. Survive in an artificial market • Each robot contains a: • Derivative buying agent • Derivative offering agent • Raw material production agent • Finished product agent (solves Max) • Winning in robot competitions strongly influences the final grade. • Game is interesting even if robots are far from perfect. • Focus today: how to play the game perfectly (never losing) SDG Mittagsseminar

  15. SDG(Max) • Derivative = (Predicate, Price in [0,1], Player). • Players offer and buy derivatives. • Buying a derivative gives you the rights: • to receive raw material R satisfying the predicate. • upon finishing the raw material R at quality q (trying to find the maximum solution), you receive q in [0,1]. SDG Mittagsseminar

  16. To play well: solve min max maximum solutions instances selected by predicate (an infinite set) 0.91 0.62 0.8 0.618 0.619 minimum Analysis for one Derivative SDG Mittagsseminar

  17. To play well: solve min max maximum solutions instances selected by predicate (an infinite set) 0.91 0.62 0.8 0.618 0.62 0.619 minimum small subset of raw materials guaranteed to contain minimum of maxima Analysis for one Derivative Noise SDG Mittagsseminar

  18. Raw material selected all possible finished products 0.7 0.7 0.7 small subset of finished products guaranteed to contain maximum Noise SDG Mittagsseminar

  19. Risk analysis • Life cycle of a derivative (pred,p) • offer • risk high if I can find rm and fp with q(fp) > p • buy • risk high if I can find rm and fp with q(fp) < p • raw material (rm) • finished product (fp ,quality q(fp)) • Two uncertainties • raw material is not the worst (uncertainty_rm) • finished product is not the best (uncertainty_fp) SDG Mittagsseminar

  20. To play SDG perfectlyeliminate risk • buy • break-even price • sell • break-even price • produce • efficiently find worst case example • process • efficiently achieve break-even quality SDG Mittagsseminar

  21. Goal: never lose with offer/buy • Choose algorithms RM and FP SDG Mittagsseminar

  22. Analysis of SDG(Max) tpred = inf all raw materials rm satisfying predicate pred max all finished products fp produced for rm q(fp) SDG Mittagsseminar

  23. Analysis of SDG(Max) tpred = lim n -> ∞ min all raw materials rm of size n satisfying predicate pred max all finished products fp produced for rm q(fp) SDG Mittagsseminar

  24. Spec for RM and FP tpred = lim n -> ∞ min all raw materials rm of size n satisfying predicate pred and having property WORST(rm) max small subset of all finished products fp produced for rm q(fp) SDG Mittagsseminar

  25. Analysis of SDG(Max) tpred = lim n -> ∞ min all raw materials rm of size n produced by RM satisfying predicate pred max all finished products fp produced for rm by FP q(fp) SDG Mittagsseminar

  26. Hope • Max is NP-hard • SDG(Max) simplifies Max if our goal is to never lose. SDG Mittagsseminar

  27. SDG(MAX-SAT) • Predicates using clause types. • Example predicate PairSat = All CNFs with clauses of any length but clauses of length 1 must contain one positive literal. • What is the right price p for derivative (PairSat, p, Specker) SDG Mittagsseminar

  28. SDG(MAX-SAT) • Predicate space: any subset of clause types of PairSat • t all PairSat = (√5 -1)/2 • t {(2,0),(1,1)} = (√5 -1)/2 • t {(100,50), (3,2), (2,0),(1,1)} = (√5 -1)/2 Noise for the purpose of constructing raw material. SDG Mittagsseminar

  29. SDG(MAX-SAT) • t {(2,0),(1,1)} = t SYM{(2,0),(1,1)} = (√5 -1)/2 • SYM stands for Symmetrization: Idea: if you give me a CNF with a satisfaction ratio f, I give you a symmetric CNF with a satisfaction ratio <= f. • For a CNF in SYM{(2,0),(1,1)}, the MAX-SAT problem reduces to maximizing a polynomial. SDG Mittagsseminar

  30. Students need to implement trading robots • Fall semester (undergraduates): SDG(MAX-SAT) • Spring semester (graduates): SDG(MAX-CSP) SDG Mittagsseminar

  31. Opportunities for learningExample SDG(MAX-SAT) • Abstraction: What is important to play the game well. • Game reductions: To play game SDG(MAX-SAT) well, it is sufficient to play game SDG(X) well, where X is simpler than MAX-SAT. SDG Mittagsseminar

  32. Complexity theory connection • Break-even prices are not only interesting for the SDG game. • They also have complexity-theoretic significance: they are critical transition points separating P from NP (for “most” predicates). SDG Mittagsseminar

  33. General Dichotomy Theorem MAX-CSP(G,f): For each finite set G of relations there exists an algebraic number tG For f ≤ tG: MAX-CSP(G,f) has polynomial solution For f≥ tG+ e: MAX-CSP(G,f) is NP-complete, e>0. 1 hard (solid) NP-complete polynomial solution: Use optimally biased coin. Derandomize. P-Optimal. tG = critical transition point easy (fluid) Polynomial 0 due to Lieberherr/Specker (1979, 1982) SDG Mittagsseminar

  34. Other break-even prices(Lieberherr/Specker (1982)) • G = {R0,R1,R2,R3}; Rj : rank 3, exactly j of 3 variables are true. tG= ¼ SDG Mittagsseminar

  35. Other break-even prices(unpublished)(Lieberherr/Specker (1982)) • G(p,q) = {Rp,q = disjunctions containing at least p positive or q negative literals (p,q≥1)} • Let a be the solution of (1-x)p=xq in (0,1). tG(p,q)=1-aq SDG Mittagsseminar

  36. Lessons learned from SDG • Developing trading robots and make them survive in an artificial market is very motivating to students • Students learn experientially about many important topics driven by the single goal of making their robots competitive • software development • problem solving by reduction (noise reduction) • combinatorial optimization • game design • sub-optimal playing is very educational too! SDG Mittagsseminar

  37. Noise reduction: important topic • seen in solving minimization and maximization problems • To implement trading robots, we use a tool called DemeterF which is good at noise reduction during programming process: focus on important classes and eliminate noise classes SDG Mittagsseminar

  38. Conclusions • SDG(Max) is an interesting tool for teaching a wide variety of topics. • It helps if you give your students a robot that knows the basic rules. Then the students can focus on improving the robots rather than getting all robots to communicate properly. SDG Mittagsseminar

  39. Conclusions • SDG(Max) is an interesting tool for research. • Does it always turn an NP-hard maximization problem into a polynomial time approximation algorithm? SDG Mittagsseminar

  40. References • Lieberherr/Specker (1979, 1981) FOCS and Journal of the ACM • Lieberherr (1982) Journal of Algorithms • Workshop paper: • DemeterF home page SDG Mittagsseminar

  41. Obstacles to finding p • Try to find a CNF satisfying PairSat in which only a small percentage of the clauses can be satisfied. • Challenge of finding the worst case. • Even if we find the worst case, we might not find the maximum assignment for that case. SDG Mittagsseminar

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