1. of 22 10/30/2015WUSTL: Uncertain Communication1 Communication Amid Uncertainty Madhu Sudan Harvard Based on Juba, S. (STOC 2008, ITCS 2011) Juba, S. (STOC 2008, ITCS 2011) Goldreich, Juba, S. (JACM 2011) Goldreich, Juba, S. (JACM 2011) Juba, Kalai, Khanna, S. (ITCS 2011) Juba, Kalai, Khanna, S. (ITCS 2011) Haramaty, S. (ITCS 2014) Haramaty, S. (ITCS 2014) Canonne, Guruswami, Meka, S. (ITCS 2015) Canonne, Guruswami, Meka, S. (ITCS 2015) Ghazi, Kamath, S. (SODA 2016) Ghazi, Kamath, S. (SODA 2016) Ghazi, Komargodski, Kothari, S. (SODA 2016) Ghazi, Komargodski, Kothari, S. (SODA 2016) Leshno, S. (manuscript) Leshno, S. (manuscript)

2. of 22 Communication vs. Computation Communication vs. Computation Interdependent technologies: Neither can exist without other Interdependent technologies: Neither can exist without other Technologies/Products/Commerce developed (mostly) independently. Technologies/Products/Commerce developed (mostly) independently. Early products based on clean abstractions of the other. Early products based on clean abstractions of the other. Later versions added other capability as afterthought. Later versions added other capability as afterthought. Today products … deeply integrated. Today products … deeply integrated. Deep theories: Deep theories: 10/30/2015WUSTL: Uncertain Communication2 Well separated … and have stayed that way Turing ‘36 Shannon ‘48

3. of 22 Consequences of the wall 10/30/2015WUSTL: Uncertain Communication3

4. of 22 Sample problems: Universal printing: Universal printing: You are visiting a friend. You can use their Wifi network, but not their printer. Why? You are visiting a friend. You can use their Wifi network, but not their printer. Why? Projecting from your laptop: Projecting from your laptop: Machines that learn to communicate, and learn to understand each other. Machines that learn to communicate, and learn to understand each other. Digital libraries: Digital libraries: Data that lives forever (communication across time), while devices change. Data that lives forever (communication across time), while devices change. 10/30/2015WUSTL: Uncertain Communication4

5. of 22 Essence of “semantics”: Uncertainty Shannon: Shannon: “The significant aspect is that the actual message is one selected from a set of possible messages” “The significant aspect is that the actual message is one selected from a set of possible messages” Essence of unreliability today: Essence of unreliability today: Context: Determines set of possible messages. Context: Determines set of possible messages. dictionary, grammar, general knowledge dictionary, grammar, general knowledge coding scheme, prior distribution, communication protocols … coding scheme, prior distribution, communication protocols … Context is HUGE; and not shared perfectly; Context is HUGE; and not shared perfectly; 10/30/2015WUSTL: Uncertain Communication5

6. of 22 Modelling uncertainty Classical Shannon Model 10/30/2015WUSTL: Uncertain Communication6 A B Channel B2B2B2B2 AkAkAkAk A3A3A3A3 A2A2A2A2 A1A1A1A1 B1B1B1B1 B3B3B3B3 BjBjBjBj Uncertain Communication Model New Class of Problems New challenges Needs more attention!

7. of 22 Hope Better understanding of existing mechanisms Better understanding of existing mechanisms In natural communication In natural communication In “ad-hoc” (but “creative”) designs In “ad-hoc” (but “creative”) designs What problems are they solving? What problems are they solving? Better solutions? Better solutions? Or at least understand how to measure the quality of a solution. Or at least understand how to measure the quality of a solution. 10/30/2015WUSTL: Uncertain Communication7

8. of 22 10/30/2015WUSTL: Uncertain Communication8 II: Uncertain Compression

9. of 22 Human-Human Communication 10/30/2015WUSTL: Uncertain Communication9 Prob. distribution on messages

10. of 22 Human Communication - 2 10/30/2015WUSTL: Uncertain Communication10ReceivercontextSendercontext

11. of 22 Implications 10/30/2015WUSTL: Uncertain Communication11

12. of 22 10/30/2015WUSTL: Uncertain Communication12 III: Imperfectly Shared Randomness

13. of 22 Communication (Complexity) 10/30/2015WUSTL: Uncertain Communication13 AliceAlice BobBob CompressDecompress

14. of 22 (Recall) Communication Complexity (Recall) Communication Complexity The model The model 10/30/2015WUSTL: Uncertain Communication14 (with shared randomness) AliceAlice BobBob w.p. 2/3 Usually studied for lower bounds. This talk: CC as +ve model.

15. of 22 Brief history 10/30/2015WUSTL: Uncertain Communication15 [Ghazi, Kamath, S., SODA 2016]:Taxonomy of simple problems; Many interesting problems and protocols!

16. of 22 Results 10/30/2015WUSTL: Uncertain Communication16

17. of 22 Some General Lessons Compression Protocol: Compression Protocol: Adds “error-correction” to [JKKS] protocol. Adds “error-correction” to [JKKS] protocol. Send shortest word that is far from words of other high probability messages. Send shortest word that is far from words of other high probability messages. Another natural protocol. Another natural protocol. General Protocol: General Protocol: Much more “statistical” Much more “statistical” Classical protocol for Equality: Classical protocol for Equality: Alice sends random coordinate of ECC(x) Alice sends random coordinate of ECC(x) New Protocol New Protocol ~ Alice send # 1’s in random subset of coordinates. ~ Alice send # 1’s in random subset of coordinates. 10/30/2015WUSTL: Uncertain Communication17

18. of 22 10/30/2015WUSTL: Uncertain Communication18 IV: Focussed Communication

19. of 22 Model 10/30/2015WUSTL: Uncertain Communication19

20. of 22 Results 10/30/2015WUSTL: Uncertain Communication20

21. of 22 Conclusions 10/30/2015WUSTL: Uncertain Communication21 (which is a good thing)

22. of 22 Thank You! 10/30/2015WUSTL: Uncertain Communication22

23. of 22 10/30/2015WUSTL: Uncertain Communication23 IV: Coordination

24. of 22 Communicate meaning? 10/30/2015WUSTL: Uncertain Communication24

25. of 22 (Mis) Understanding? Uncertainty problem: Uncertainty problem: Sender/receiver disagree on meaning of bits Sender/receiver disagree on meaning of bits Definition of Understanding? Definition of Understanding? Sender sends instructions; Receiver follows? Sender sends instructions; Receiver follows? Errors undetectable (by receiver) Errors undetectable (by receiver) Not the right definition anyway: Not the right definition anyway: Does receiver want to follow instructions Does receiver want to follow instructions What does receiver gain by following instructions? Must have its own “Goal”/”Incentives”. What does receiver gain by following instructions? Must have its own “Goal”/”Incentives”. [ Goldreich,Juba,S. 2012 ]: Goal-oriented communication: [ Goldreich,Juba,S. 2012 ]: Goal-oriented communication: 10/30/2015WUSTL: Uncertain Communication25ReceiverdictionarySenderdictionary

26. of 22 (Mis) Understanding? Uncertainty problem: Uncertainty problem: Sender/receiver disagree on meaning of bits Sender/receiver disagree on meaning of bits Definition of Understanding? Definition of Understanding? Receiver has goals/incentives. Receiver has goals/incentives. [ Goldreich,Juba,S. 2012 ]: Goal-oriented communication: [ Goldreich,Juba,S. 2012 ]: Goal-oriented communication: Define general communication problems (and goals) Define general communication problems (and goals) Show that if Show that if Sender can help receiver achieve goal (from any state) Sender can help receiver achieve goal (from any state) Receiver can sense progress towards goal Receiver can sense progress towards goal then then Receiver can achieve goal. Receiver can achieve goal. Functional definition of understanding. Functional definition of understanding. 10/30/2015WUSTL: Uncertain Communication26ReceiverdictionarySenderdictionary

27. of 22 Illustration: (Repeated) Coordination 10/30/2015WUSTL: Uncertain Communication27

28. of 22 Our setting 10/30/2015WUSTL: Uncertain Communication28

29. of 22 Coordination with Uncertainty 10/30/2015WUSTL: Uncertain Communication29

30. of 22 Lessons Coordination is possible: Coordination is possible: Even in extreme settings where Even in extreme settings where Alice has almost no idea of Bob Alice has almost no idea of Bob Bob has almost no idea of Alice Bob has almost no idea of Alice Alice is trying to learn Bob Alice is trying to learn Bob Bob is trying to learn Alice Bob is trying to learn Alice Learning is slow … Learning is slow … Need to incorporate beliefs to measure efficiency. [Juba, S. 2011] Need to incorporate beliefs to measure efficiency. [Juba, S. 2011] Does process become more efficient when languages have structure? [Open] Does process become more efficient when languages have structure? [Open] 10/30/2015WUSTL: Uncertain Communication30