Abstracting Influences for Efficient Multiagent Coordination Under Uncertainty.

Publication Info

Stefan J. Witwicki. Ph.D. thesis, University of Michigan, Ann Arbor, Michigan, USA. January 2011.


When planning optimal decisions for teams of agents acting in uncertain domains, conventional methods explicitly coordinate all joint policy decisions and, in doing so, are inherently susceptible to the curse of dimensionality, as state, action, and observation spaces grow exponentially with the number of agents. With the goal of extending the scalability of optimal team coordination, the research presented in this dissertation examines how agents can reduce the amount of information they need to coordinate. Intuitively, to the extent that agents are weakly coupled, they can avoid the complexity of coordinating all decisions; they need instead only coordinate abstractions of their policies that convey their essential influences on each other.

In formalizing this intuition, I consider several complementary aspects of weakly-coupled problem structure, including agent scope size, corresponding to the number of an agent's peers whose decisions influence the agent's decisions, and degree of influence, corresponding to the proportion of unique influences that peers can feasibly exert. To exploit this structure, I introduce a (transition-dependent decentralized POMDP) model that efficiently decomposes into local decision models with shared state features. This context yields a novel characterization of influences as transition probabilities (compactly encoded using a dynamic Bayesian network). Not only is this influence representation provably sufficient for optimal coordination, but it also allows me to frame the subproblems of (1) proposing influences, (2) evaluating influences, and (3) computing optimal policies around influences as mixed-integer linear programs.

The primary advantage of working in the influence space is that there are potentially significantly fewer feasible influences than there are policies. Blending prior work on decoupled joint policy search and constraint optimization, I develop influence-space search algorithms that, for problems with a low degree of influence, compute optimal solutions orders of magnitude faster than policy-space search. When agents' influences are constrained, influence-space search also outperforms other state-of-the-art optimal solution algorithms. Moreover, by exploiting both degree of influence and agent scope size, I demonstrate scalability, substantially beyond the reach of prior optimal methods, to teams of 50 weakly-coupled transition-dependent agents.

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  author = 	 {Stefan J. Witwicki},
  title = 	 {Abstracting Influences for Efficient Multiagent Coordination 
                Under Uncertainty},
  school = 	 {University of Michigan},
  year = 	 {2011},
  month =    {January},
  address =  {Ann Arbor, Michigan, USA}