389 research outputs found
Exploiting Anonymity in Approximate Linear Programming: Scaling to Large Multiagent MDPs (Extended Version)
Many exact and approximate solution methods for Markov Decision Processes
(MDPs) attempt to exploit structure in the problem and are based on
factorization of the value function. Especially multiagent settings, however,
are known to suffer from an exponential increase in value component sizes as
interactions become denser, meaning that approximation architectures are
restricted in the problem sizes and types they can handle. We present an
approach to mitigate this limitation for certain types of multiagent systems,
exploiting a property that can be thought of as "anonymous influence" in the
factored MDP. Anonymous influence summarizes joint variable effects efficiently
whenever the explicit representation of variable identity in the problem can be
avoided. We show how representational benefits from anonymity translate into
computational efficiencies, both for general variable elimination in a factor
graph but in particular also for the approximate linear programming solution to
factored MDPs. The latter allows to scale linear programming to factored MDPs
that were previously unsolvable. Our results are shown for the control of a
stochastic disease process over a densely connected graph with 50 nodes and 25
agents.Comment: Extended version of AAAI 2016 pape
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
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
Decision-Making Under Uncertainty: Beyond Probabilities
This position paper reflects on the state-of-the-art in decision-making under
uncertainty. A classical assumption is that probabilities can sufficiently
capture all uncertainty in a system. In this paper, the focus is on the
uncertainty that goes beyond this classical interpretation, particularly by
employing a clear distinction between aleatoric and epistemic uncertainty. The
paper features an overview of Markov decision processes (MDPs) and extensions
to account for partial observability and adversarial behavior. These models
sufficiently capture aleatoric uncertainty but fail to account for epistemic
uncertainty robustly. Consequently, we present a thorough overview of so-called
uncertainty models that exhibit uncertainty in a more robust interpretation. We
show several solution techniques for both discrete and continuous models,
ranging from formal verification, over control-based abstractions, to
reinforcement learning. As an integral part of this paper, we list and discuss
several key challenges that arise when dealing with rich types of uncertainty
in a model-based fashion
Probabilistic Inference Techniques for Scalable Multiagent Decision Making
Decentralized POMDPs provide an expressive framework for multiagent sequential decision making. However, the complexity of these models—NEXP-Complete even for two agents—has limited their scalability. We present a promising new class of approxima-tion algorithms by developing novel connections between multiagent planning and machine learning. We show how the multiagent planning problem can be reformulated as inference in a mixture of dynamic Bayesian networks (DBNs). This planning-as-inference approach paves the way for the application of efficient inference techniques in DBNs to multiagent decision making. To further improve scalability, we identify certain conditions that are sufficient to extend the approach to multiagent systems with dozens of agents. Specifically, we show that the necessary inference within the expectation-maximization framework can be decomposed into processes that often involve a small subset of agents, thereby facilitating scalability. We further show that a number of existing multiagent planning models satisfy these conditions. Experiments on large planning benchmarks confirm the benefits of our approach in terms of runtime and scalability with respect to existing techniques
Nonapproximability Results for Partially Observable Markov Decision Processes
We show that for several variations of partially observable Markov decision
processes, polynomial-time algorithms for finding control policies are unlikely
to or simply don't have guarantees of finding policies within a constant factor
or a constant summand of optimal. Here "unlikely" means "unless some complexity
classes collapse," where the collapses considered are P=NP, P=PSPACE, or P=EXP.
Until or unless these collapses are shown to hold, any control-policy designer
must choose between such performance guarantees and efficient computation
Exploiting Anonymity in Approximate Linear Programming: Scaling to Large Multiagent MDPs
The Markov Decision Process (MDP) framework is a versatile method for addressing single and multiagent sequential decision making problems. Many exact and approximate solution methods attempt to exploit struc- ture in the problem and are based on value factoriza- tion. Especially multiagent settings (MAS), however, are known to suffer from an exponential increase in value component sizes as interactions become denser, meaning that approximation architectures are overly re- stricted in the problem sizes and types they can handle. We present an approach to mitigate this limitation for certain types of MASs, exploiting a property that can be thought of as ‘anonymous influence’ in the factored MDP. In particular, we show how anonymity can lead to representational and computational efficiencies, both for general variable elimination in a factor graph but also for the approximate linear programming solution to factored MDPs. The latter allows to scale linear pro- gramming to factored MDPs that were previously un- solvable. Our results are shown for a disease control do- main over a graph with 50 nodes that are each connected with up to 15 neighbors
- …