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SUMMARY:Mean Field Approaches to Two Sequential Decision Making Problems. 
 - Ramki Gummadi
DTSTART:20150608T160000Z
DTEND:20150608T170000Z
UID:TALK59759@talks.cam.ac.uk
CONTACT:12852
DESCRIPTION:In this presentation\, I will present some of my past research
  on mean field approaches to sequential decision making problems under unc
 ertainty. The talk has two parts.\n \nIn the first part\, we'll consider m
 ultiarmed bandit games\, where much of the classical work focuses on arm r
 ewards that are stationary over time. By contrast\, I will present a bandi
 t model with multiple agents where the rewards obtained by an agent can al
 so depend on how many other agents choose the same arm (as might be the ca
 se in many competitive or cooperative scenarios). Such a dynamical system 
 can be non-stationary due to the interdependent evolution of agents\, whic
 h makes an analysis using typical equilibrium concepts intractable. I will
  introduce a general model of multiarmed bandit games\, and define a notio
 n of equilibrium inspired mean field methods\, called the mean field stati
 onary state (MFSS). I will discuss three key results --  first\, we establ
 ish existence of an MFSS under quite general conditions. Second\, we show 
 under a contraction condition that the MFE is unique\, and that the popula
 tion profile converges to it from any initial state. Finally\, we show tha
 t under the contraction condition\, MFE is a good approximation to the beh
 avior of finite systems with many agents. The contraction condition requir
 es that the agent population is sufficiently mixing and that the sensitivi
 ty of the reward function to the population profile is low enough. \n\nThe
  second part is motivated by dynamic ad auction markets (e.g Facebook\, Go
 ogle\, Bing) where ad-slots are auctioned off dynamically at large scale. 
 Using a mean field approximation\, I will formulate the sequential optimiz
 ation problem facing a bidder participating in such repeated auctions in t
 he form of a very general stochastic control model\, and present an approx
 imate solution to a limiting MDP that allows for efficient computation of 
 the optimal bids. I will also discuss how the optimal bid at any given tim
 e in a dynamic setting reduces to that of an equivalent static auction wit
 h a shaded private valuation\, for a very general class of auction formats
  that includes the second price auction as a special case.\n\nThis is base
 d on joint work with Ramesh Johari (Stanford)\, Peter Key (MSR Cambridge)\
 , Jia Yuan Yu (IBM Research) and Alexandre Proutiere (KTH Stockholm) 
LOCATION:Engineering Department\, CBL Room BE-438 - Skype
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