6,266 research outputs found
A Model Approximation Scheme for Planning in Partially Observable Stochastic Domains
Partially observable Markov decision processes (POMDPs) are a natural model
for planning problems where effects of actions are nondeterministic and the
state of the world is not completely observable. It is difficult to solve
POMDPs exactly. This paper proposes a new approximation scheme. The basic idea
is to transform a POMDP into another one where additional information is
provided by an oracle. The oracle informs the planning agent that the current
state of the world is in a certain region. The transformed POMDP is
consequently said to be region observable. It is easier to solve than the
original POMDP. We propose to solve the transformed POMDP and use its optimal
policy to construct an approximate policy for the original POMDP. By
controlling the amount of additional information that the oracle provides, it
is possible to find a proper tradeoff between computational time and
approximation quality. In terms of algorithmic contributions, we study in
details how to exploit region observability in solving the transformed POMDP.
To facilitate the study, we also propose a new exact algorithm for general
POMDPs. The algorithm is conceptually simple and yet is significantly more
efficient than all previous exact algorithms.Comment: See http://www.jair.org/ for any accompanying file
Perseus: Randomized Point-based Value Iteration for POMDPs
Partially observable Markov decision processes (POMDPs) form an attractive
and principled framework for agent planning under uncertainty. Point-based
approximate techniques for POMDPs compute a policy based on a finite set of
points collected in advance from the agents belief space. We present a
randomized point-based value iteration algorithm called Perseus. The algorithm
performs approximate value backup stages, ensuring that in each backup stage
the value of each point in the belief set is improved; the key observation is
that a single backup may improve the value of many belief points. Contrary to
other point-based methods, Perseus backs up only a (randomly selected) subset
of points in the belief set, sufficient for improving the value of each belief
point in the set. We show how the same idea can be extended to dealing with
continuous action spaces. Experimental results show the potential of Perseus in
large scale POMDP problems
Anytime Point-Based Approximations for Large POMDPs
The Partially Observable Markov Decision Process has long been recognized as
a rich framework for real-world planning and control problems, especially in
robotics. However exact solutions in this framework are typically
computationally intractable for all but the smallest problems. A well-known
technique for speeding up POMDP solving involves performing value backups at
specific belief points, rather than over the entire belief simplex. The
efficiency of this approach, however, depends greatly on the selection of
points. This paper presents a set of novel techniques for selecting informative
belief points which work well in practice. The point selection procedure is
combined with point-based value backups to form an effective anytime POMDP
algorithm called Point-Based Value Iteration (PBVI). The first aim of this
paper is to introduce this algorithm and present a theoretical analysis
justifying the choice of belief selection technique. The second aim of this
paper is to provide a thorough empirical comparison between PBVI and other
state-of-the-art POMDP methods, in particular the Perseus algorithm, in an
effort to highlight their similarities and differences. Evaluation is performed
using both standard POMDP domains and realistic robotic tasks
Influence-Optimistic Local Values for Multiagent Planning --- Extended Version
Recent years have seen the development of methods for multiagent planning
under uncertainty that scale to tens or even hundreds of agents. However, most
of these methods either make restrictive assumptions on the problem domain, or
provide approximate solutions without any guarantees on quality. Methods in the
former category typically build on heuristic search using upper bounds on the
value function. Unfortunately, no techniques exist to compute such upper bounds
for problems with non-factored value functions. To allow for meaningful
benchmarking through measurable quality guarantees on a very general class of
problems, this paper introduces a family of influence-optimistic upper bounds
for factored decentralized partially observable Markov decision processes
(Dec-POMDPs) that do not have factored value functions. Intuitively, we derive
bounds on very large multiagent planning problems by subdividing them in
sub-problems, and at each of these sub-problems making optimistic assumptions
with respect to the influence that will be exerted by the rest of the system.
We numerically compare the different upper bounds and demonstrate how we can
achieve a non-trivial guarantee that a heuristic solution for problems with
hundreds of agents is close to optimal. Furthermore, we provide evidence that
the upper bounds may improve the effectiveness of heuristic influence search,
and discuss further potential applications to multiagent planning.Comment: Long version of IJCAI 2015 paper (and extended abstract at AAMAS
2015
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