Ariel Procaccia Center for Research on Computation and Society Harvard SEAS

1. AI AND ECONOMICS THE DYNAMIC DUO Ariel Procaccia Center for Research on Computation and Society Harvard SEAS

2. Theme The interaction between AI and economics leads to new paradigms that can change the way we think about fundamental issues in AI and in economics

3. The Game Plan MAS AI ML Game Theory Game Theory econ Planning Social choice UAI KR

4. Game Theory “Game theory is a sort of umbrella ... for the rational side of social science, where ‘social’ is interpreted broadly” [Aumann 1987]

5. Fun and Games • Chess • Poker [Sandholm+] • Pool [Shoham+]

6. AI and Game Theory • GT offers: principles of rationality • AI offers: rational agents [Rosenschein+Genesereth, IJCAI’85] • GTPlanning: Planning games [Brafman+, IJCAI’09] • AI also offers: new ways of thinking about rationality • UAIGT: Dynamic incentive mechanisms [Parkes+]

7. Small Example: Incentives in ML MAS AI AI ML ML Game Theory Game Theory econ Planning Dekel+Fischer+P Incentive Compatible Regression Learning JCSS 2010 Social choice UAI KR

8. Super Simplified model • Input space X • Each player i controls input point xi (public) and label yiR(private) • Function class F of f:XR • Given reported labels, choose a function fF • Players want to minimize |f(xi)-yi| • Designer wants to minimize i|f(xi)-yi|

9. Let the Games Begin 1 2 3 4 4 5

10. If the Shoe Fits • Strategyproof mechanism = player never gains from misreporting private information • Group strategyproof mechanism = members of coalition cannot all gain from misreporting private information • Theorem: Assuming one point per player and convex function class, best fit is group strategyproof • Follows immediately from known results for F = constant functions (single peaked preferences) • Nontrivial for general convex function classes

11. Simplified model • Each player i controls input points xi1, xi2,... (public) and real labels yi1, yi2,... (private) • Players want to minimize k|f(xik)-yik| • Designer wants to minimize ik|f(xik)-yik|

12. A Whole New Ball Game 1 1 2 1 1 2

13. Project-and-Fit • Project-and-Fit: Project labels of each player onto closest fit, then fit with projected labels • SP and gives quality guarantees for some function classes

14. Project-and-Fit Illustrated 1 1 1 2 1 1 2 2

15. Slightly Simplified Model • Each player has a distribution i over X and target function oi:XR • Distributions sampled and labeled by players • Players want to minimize expected error wrt i and oi • Designer wants to minimize expected error wrt average player • Theorem (informal): For any ,,given enough samples, results from previous model carry over up to  with prob. 1-

16. Late Motivation: Zara • Optimizing distribution process of Zara [Caro+Gallien, OR 10] • Regression learning is used to predict demand based on orders from store managers • “... Zara’s inventory distribution process could be further improved in the future by introducing explicit incentives for the stores to contribute accurate forecasts.”

17. Can GT Enable AI? • Classic AI seeks to design intelligent robots/agents • Some of modern AI studies agent societies • GT distills rationality • Rationality is perceived as intelligence • Game-theoretic MAS may be perceived as intelligent • GT enables AI on the multiagent level!

18. The Game Plan MAS AI ML Game Theory econ Planning Social choice Social choice UAI KR

19. Social Choice Theory Social choice theory is a theoretical framework for measuring individual interests, values, or welfares as an aggregate towards collective decision

20. AI and Social Choice • CS + SC = computational social choice • SC offers: preference aggregation • SCMAS: Restricted communication [Caragiannis+P, AAAI’10] • AI offers: complex preferences • KRSC: Voting on multiattribute domains with CP-nets [Lang, IJCAI’07]

21. The basics • Set of nvoters: {1,...,n} • Voters are honest! • Set of malternatives: {a,b,c,...} • Each voter ranks the alternatives • Preference profile = collection of rankings • Voting rule selects alternative given profile • Plurality: each voter awards one point to top alternative • Borda count: each voter awards m-k points to alternative ranked k’th

22. Majority Consistency Voter 3 Voter 1 Voter 2 a a b b b c c c d d d a

23. Big Example:Dynamic Social Choice MAS AI AI ML Game Theory econ Planning Parkes+P Dynamic Social Choice Working paper Social choice Social choice UAI UAI KR

24. Motivation: MoveOn • Online public policy advocacy group • 5 million members, handful of staffers • Causes stem from preferences of members • Short time frames • Acting on a cause changes preferences, affecting next cause

25. Social Choice MDPs b b a a a b a,0 b,½ a,1 b,½ a a b ½ b b a 1 1 ½ ½ a a b b a a a b b b b b b ½ a a a a,1 b,½ a,1 b,½ a,½ b,½ a,0 b,½ b b a b a b a b a a b a b ½ a b a a,0 b,½ a,½ b,½ 1 1 ½ ½ b a a a b b Voters 1+2 Voter 3 a b b ½ b a a

26. Rewards and Policies • MDP components: states, actions, transitions, rewards • Reward function specifies (designer’s) reward for each state and action • Favorite alternative • Social consensus • (Deterministic stationary) policy selects action/alternative at each state/profile

27. Take-Home Message “A policy in a social choice MDP is a voting rule”

28. Rewards and Policies • MDP components: states, actions, transitions, rewards • Reward function specifies (center’s) reward for each state and action • Favorite alternative • Social consensus • (Deterministic stationary) policy selects action/alternative at each state/profile • Maximize infinite sum of discounted rewards... • ... subject to social choice constraints!

29. Exploiting Symmetries • In general finding an optimal policy is easy • First obstacle: state space is exponential in n and m • Assume constant m and constant #transition models • Contract symmetric states [Dean+Givan AAAI’97] b b a a a b a a b ½ b b a 1 1 ½ ½ 1 ½ a a a b b b b b b ½ a a a a b a b a b b a b ½ a b a 1 1 ½ ½ ½ b a a a b b a b b ½ b a a

30. Social Choice Constraints • Second obstacle: constraints • Literature falls short • Theorem: Assume a constant m and constant #transition models. Can compute an optimal policy subject to axiom in poly time in n • axiom  {majority consistency, ontoness,...} • Example: Ontoness

31. Algorithm by Animation a a a b a b b b a a a a a b a b a a b a c c b b b b b b b

32. Implementation • Challenges • Developing transition models • Practical heuristics • Extend to dynamic voters and alternatives

33. CS and SC: Yin and Yang

34. A New Hope • Classic SC is rife with impossibilities • Computational social choice is constructive and positive • AI is a testbed for principles of SC • Via MAS • Via human computation • Does classic SC literature have “operational value”?

35. back to theme The interaction between AI and economics leads to new paradigms that can change the way we think about fundamental issues in AI and in economics

36. Research Overview • AI + Computational GT and SC • Fair division • Combinatorial optimization and approximation algorithms • Crowdsourcing and human computation

37. The End Thank You!