4 research outputs found
Dual formulations for optimizing Dec-POMDP controllers
Decentralized POMDP is an expressive model for multi-agent planning. Finite-state controllers (FSCs)---often used to represent policies for infinite-horizon problems---offer a compact, simple-to-execute policy representation. We exploit novel connections between optimizing decentralized FSCs and the dual linear program for MDPs. Consequently, we describe a dual mixed integer linear program (MIP) for optimizing deterministic FSCs. We exploit the Dec-POMDP structure to devise a compact MIP and formulate constraints that result in policies executable in partially-observable decentralized settings. We show analytically that the dual formulation can also be exploited within the expectation maximization (EM) framework to optimize stochastic FSCs. The resulting EM algorithm can be implemented by solving a sequence of linear programs, without requiring expensive message-passing over the Dec-POMDP DBN. We also present an efficient technique for policy improvement based on a weighted entropy measure. Compared with state-of-the-art FSC methods, our approach offers over an order-of-magnitude speedup, while producing similar or better solutions
Strengthening Deterministic Policies for POMDPs
The synthesis problem for partially observable Markov decision processes
(POMDPs) is to compute a policy that satisfies a given specification. Such
policies have to take the full execution history of a POMDP into account,
rendering the problem undecidable in general. A common approach is to use a
limited amount of memory and randomize over potential choices. Yet, this
problem is still NP-hard and often computationally intractable in practice. A
restricted problem is to use neither history nor randomization, yielding
policies that are called stationary and deterministic. Previous approaches to
compute such policies employ mixed-integer linear programming (MILP). We
provide a novel MILP encoding that supports sophisticated specifications in the
form of temporal logic constraints. It is able to handle an arbitrary number of
such specifications. Yet, randomization and memory are often mandatory to
achieve satisfactory policies. First, we extend our encoding to deliver a
restricted class of randomized policies. Second, based on the results of the
original MILP, we employ a preprocessing of the POMDP to encompass memory-based
decisions. The advantages of our approach over state-of-the-art POMDP solvers
lie (1) in the flexibility to strengthen simple deterministic policies without
losing computational tractability and (2) in the ability to enforce the
provable satisfaction of arbitrarily many specifications. The latter point
allows taking trade-offs between performance and safety aspects of typical
POMDP examples into account. We show the effectiveness of our method on a broad
range of benchmarks