of 7 10/01/2013LIDS Lunch: Communication Amid Uncertainty1 Communication Amid Uncertainty Madhu Sudan Microsoft Research

of 7 Uncertainty in Communication? Always an issue … but usually uncertainty in channel of communication. Always an issue … but usually uncertainty in channel of communication. Lately, however … Also have to worry about uncertainty of communicating “agents” about each other. Lately, however … Also have to worry about uncertainty of communicating “agents” about each other. E.g.: How would you like to archive your family photographs “digitally” when you are uncertain which format will be viewable? Would you compress? E.g.: How would you like to archive your family photographs “digitally” when you are uncertain which format will be viewable? Would you compress? New class of questions … new solutions needed. New class of questions … new solutions needed. First, a new model. First, a new model. 10/01/2013LIDS Lunch: Communication Amid Uncertainty2

of 7 Modelling uncertainty Classical Shannon Model 10/01/2013LIDS Lunch: Communication Amid Uncertainty3 A B Channel B2B2B2B2 AkAkAkAk A3A3A3A3 A2A2A2A2 A1A1A1A1 B1B1B1B1 B3B3B3B3 BjBjBjBj Uncertain Communication Model New Class of Problems New challenges Needs more attention!

of 7 Example: Compression 10/01/2013LIDS Lunch: Communication Amid Uncertainty4

of 7 Misunderstanding and Meaning Bits lead to action Bits lead to action How can sender ensure receiver understands instruction and acts accordingly? How can sender ensure receiver understands instruction and acts accordingly? Incentive? Incentive? Receiver may not want to follow sender’s instructions. Receiver may not want to follow sender’s instructions. Or receiver may not understand … Or receiver may not understand … Goal-oriented comm. [GoldreichJubaS.12] Goal-oriented comm. [GoldreichJubaS.12] Sender must have goal + sense progress. Sender must have goal + sense progress. Achievement of goal is “functional” defn. of communicating meaningfully. Achievement of goal is “functional” defn. of communicating meaningfully. Sufficient conditions for comm. meaningfully. Sufficient conditions for comm. meaningfully. 10/01/2013LIDS Lunch: Communication Amid Uncertainty5

of 7 Communication as Coordination Game [Leshno,S.’13] Two players playing series of coordination games Two players playing series of coordination games Coordination? Coordination? Two players simultaneously choose 0/1 actions. Two players simultaneously choose 0/1 actions. “Win” if both agree : “Win” if both agree : Alice’s payoff: not less if they agree Alice’s payoff: not less if they agree Bob’s payoff: strictly higher if they agree. Bob’s payoff: strictly higher if they agree. How should Bob play? How should Bob play? Doesn’t know what Alice will do. But can hope to learn. Doesn’t know what Alice will do. But can hope to learn. Can he hope to eventually learn her behavior and (after finite # of miscoordinations) always coordinate? Can he hope to eventually learn her behavior and (after finite # of miscoordinations) always coordinate? Theorem: Theorem: Not Deterministically (under mild “general” assumptions) Not Deterministically (under mild “general” assumptions) Yes, with randomness (under mild restrictions) Yes, with randomness (under mild restrictions) 10/01/2013LIDS Lunch: Communication Amid Uncertainty6

of 7 Thank You! 10/01/2013LIDS Lunch: Communication Amid Uncertainty7