Computational Awareness

1. Computational Awareness Lance Fortnow, Northwestern University Including Research With: Kim-Sau Chung, University of Minnesota Nikhil Devanur, Toyota Technological Institute-Chicago

2. The Big Question Where should I eat tonight? 2393 Restaurants in Boston Area (According to Yellowpages.com)

3. How Do We Choose? • Restaurants you have eaten at before • Recommendations from Friends and Others • Reviews: Zagats, Boston Globe, Google, Yahoo • Restaurants you’ve walked past • Advertisements

4. How Do We Not Choose • Carefully examine all 2393 restaurants and make choice that optimizes the expected happiness from eating there (type and quality of food, atmosphere, …) • Traditional decision making theory assumes we do make choices in this manner. • We have a lack of awareness of most restaurants.

5. How Do We Not Choose • Carefully examine all 2393 restaurants and make choice that optimizes the expected happiness from eating there (type and quality of food, atmosphere, …) • Traditional decision making theory assumes we do make choices in this manner. • We have a cost of awareness of most restaurants.

6. How Do We Not Choose • Carefully examine all 2393 restaurants and make choice that optimizes the expected happiness from eating there (type and quality of food, atmosphere, …) • Traditional decision making theory assumes we do make choices in this manner. • We have a computational cost of awareness of most restaurants.

7. Awareness • Several Proposed Definitions • φ is a logical formula in some knowledge structure • Fagin-Halpern ’88: General setup used to define explicit knowledge of φ as having implicit knowledge of φ and being aware of φ. • Modica-Rustichini ‘94: Someone is aware of φ if they either know φ or know they don’t know φ. • Modica-Rustichini ‘99/Halpern ‘01: Awareness of φ if they explicitly know φ or they explicitly know they don’t explicitly know φ.

8. Limitations • Awareness of Logical Formulas that have some truth value in an interpretation of the logical model. • What is the truth value of “Legal Sea Foods”? • Binary: Either you are aware of something or you are not aware of something. • Can we have a quantitative notion of awareness? • Consider Awareness as a process. • Can we have a computational-based definition of awareness?

9. Computational Awareness • Halpern ’01 • It is possible to consider more computationally oriented notions of awareness. The problem is then to come up with interesting notions of awareness that have enough structure to allow for interesting mathematical analysis. I believe it should also be possible to use awareness structures to allow for natural reasoning about awareness and lack of it (so that an agent can reason, for example, about the possibility that she is unaware of certain features that another may be aware of). I am currently working on modeling such reasoning.

10. Computational Awareness • Informal Definition • The amount of unawareness of an object is the time needed to enumerate that object in a certain environment and a context. • A context is a topic like “restaurant”. • The Environment would consist of ways to find restaurants including our memories, interactions with others, guidebooks, “The Internet”, etc.

11. Formal Definition • Universe is set of finite strings over some alphabet Σ. • Environment E:Σ*Σ* and a context yΣ* • Enumeration Process M, a oracle Turing machine that on input y with oracle E will enumerate strings x1, x2, … • The computational unawareness of x with respect to Environment E, context y and enumeration process M is the amount of time M uses before it enumerates x, infinity if x is never enumerated.

12. Universal Enumeration • Levin ’71: There is a universal enumeration algorithm N such that for every M there is a cM such that for all x, if ME(y) enumerates x in t steps then NE(y) will enumerate x in cMt steps. • cM does not depend on E or y. • The unawareness of x in Environment E and context y U(x|E,y) = The number of steps until NE(y) outputs x

13. Email • From: Lance • To: Scott • Subject: Referee Request • Please referee this paper. • Attachment: Paper.pdf

14. Papers to Referee High Awareness

15. Papers to Referee Low Awareness

16. Non-Monotone Awareness • As the environment changes over time, awareness of an object can drop. • Much more aware of a restaurant we ate at yesterday than one we ate at three years ago. • But we can recover awareness…

17. Email • From: Lance • To: Scott • Subject: Late Report • You still owe me a referee report.

18. Papers to Referee • High awareness arosefrom change in context • Context: Email askingabout paper. High Awareness

19. Human Memory

20. Awareness of Unawareness • You can’t be aware of what you are unaware of. • One of Fagin and Halpern’s proposed axioms. • Follow from our definition • If one can enumerate “Unawareness of x” then another enumeration process can enumerate x in about the same amount of time. • Result follows from universal enumeration.

21. Organizers • Why do we keep Calendars and Address Books? • What makes Gmail popular? • Conversations • Labels • Good search tools • Make us aware of needed information when the context arises.

22. Legal Implications of Awareness of Unawareness Joint work with Kim-Sau Chung, Minnesota

23. Simple Example Give Documentto Plaintiffs Defense Document Plaintiffs

24. Simple Example Give Documentto Plaintiffs andmake them computationallyaware of it. Defense Document Plaintiffs

25. Laws Pay $50,000

26. Loopholes • Legislature may or may not be unaware of future circumstances. • Judge is unaware whether legislature was aware of the current circumstance. • We create simple model of laws and circumstances. • We show in this model not only do loopholes occur, but legislature may purposely leave in loopholes so that more general unknown circumstances are properly handled.

27. A Computational Theory of Decision Making and Awareness Joint work with Nikhil Devanur, TTI-Chicago Very Preliminary

28. Decision Making • Lots of possible stores: • Cost • Shipping: Time and Cost • Reliability • Methods of Payment • Return Policy

29. Role of Advertising • Increases awareness of brand (store, product, service) • Changes environment so that we enumerate the brand earlier. • Intuitively makes choosing that brand more likely, if that brand fits the needs of consumer. • Sponsored Search Advertising • Increases awareness in context.

30. Models for Sponsored Search • Classic Model (Varian) • For a company C • rCi = Click-through rate when in position i in list of advertisers. • vC = Value per click • vC rCi = Value of being in position i. • vC rCi is independent of advertisers in other slots. • Sometimes assumed rCi = rCi.

31. Models for Sponsored Search • Our Model • For a company C • pC = Probability of click-through conditioned on no click-throughs in earlier slots. Independent of slot. • vC = Value per click • Click-through rate • rCi = pCj<i (1-pDj) where Dj is the company that wins bid in position j. • rCi vC is still value for being in position i. Dependent on winners in earlier slots. • Related work by Athey and Ellison.

32. Research Questions • What is the best auction mechanism for this setting? • Truthful. • Socially efficient. • Revenue Maximizing. • Easy to compute. • Compute equilibrium bids in total and partial information models. • Complexity of computing bids in various mechanisms and information settings.

33. Testing our Model • Under different orderings of same companies • Classic Model • Product of Click-Through rates is fixed (if rCi = rCi) • Our Model • Sum of Click-Through rates is fixed. • Both under ideal assumptions.

34. Conclusions • Developed new model of Computational Awareness • Computation not logic based. • Formal Process-Independent Definition. • Allows for a gradation of awareness. • Allows for losing and regaining awareness. • Seems to fit many intuitive uses of awareness. • Applications • Legal: Possible explanation for loopholes. • E-Commerce: Leads to new models of sponsored search.