5,706 research outputs found
Verification and Control of Partially Observable Probabilistic Real-Time Systems
We propose automated techniques for the verification and control of
probabilistic real-time systems that are only partially observable. To formally
model such systems, we define an extension of probabilistic timed automata in
which local states are partially visible to an observer or controller. We give
a probabilistic temporal logic that can express a range of quantitative
properties of these models, relating to the probability of an event's
occurrence or the expected value of a reward measure. We then propose
techniques to either verify that such a property holds or to synthesise a
controller for the model which makes it true. Our approach is based on an
integer discretisation of the model's dense-time behaviour and a grid-based
abstraction of the uncountable belief space induced by partial observability.
The latter is necessarily approximate since the underlying problem is
undecidable, however we show how both lower and upper bounds on numerical
results can be generated. We illustrate the effectiveness of the approach by
implementing it in the PRISM model checker and applying it to several case
studies, from the domains of computer security and task scheduling
Verification and control of partially observable probabilistic systems
We present automated techniques for the verification and control of partially observable, probabilistic systems for both discrete and dense models of time. For the discrete-time case, we formally model these systems using partially observable Markov decision processes; for dense time, we propose an extension of probabilistic timed automata in which local states are partially visible to an observer or controller. We give probabilistic temporal logics that can express a range of quantitative properties of these models, relating to the probability of an event’s occurrence or the expected value of a reward measure. We then propose techniques to either verify that such a property holds or synthesise a controller for the model which makes it true. Our approach is based on a grid-based abstraction of the uncountable belief space induced by partial observability and, for dense-time models, an integer discretisation of real-time behaviour. The former is necessarily approximate since the underlying problem is undecidable, however we show how both lower and upper bounds on numerical results can be generated. We illustrate the effectiveness of the approach by implementing it in the PRISM model checker and applying it to several case studies from the domains of task and network scheduling, computer security and planning
Joint Design and Separation Principle for Opportunistic Spectrum Access in the Presence of Sensing Errors
We address the design of opportunistic spectrum access (OSA) strategies that
allow secondary users to independently search for and exploit instantaneous
spectrum availability. Integrated in the joint design are three basic
components: a spectrum sensor that identifies spectrum opportunities, a sensing
strategy that determines which channels in the spectrum to sense, and an access
strategy that decides whether to access based on imperfect sensing outcomes.
We formulate the joint PHY-MAC design of OSA as a constrained partially
observable Markov decision process (POMDP). Constrained POMDPs generally
require randomized policies to achieve optimality, which are often intractable.
By exploiting the rich structure of the underlying problem, we establish a
separation principle for the joint design of OSA. This separation principle
reveals the optimality of myopic policies for the design of the spectrum sensor
and the access strategy, leading to closed-form optimal solutions. Furthermore,
decoupling the design of the sensing strategy from that of the spectrum sensor
and the access strategy, the separation principle reduces the constrained POMDP
to an unconstrained one, which admits deterministic optimal policies. Numerical
examples are provided to study the design tradeoffs, the interaction between
the spectrum sensor and the sensing and access strategies, and the robustness
of the ensuing design to model mismatch.Comment: 43 pages, 10 figures, submitted to IEEE Transactions on Information
Theory in Feb. 200
Qualitative Analysis of Partially-observable Markov Decision Processes
We study observation-based strategies for partially-observable Markov
decision processes (POMDPs) with omega-regular objectives. An observation-based
strategy relies on partial information about the history of a play, namely, on
the past sequence of observations. We consider the qualitative analysis
problem: given a POMDP with an omega-regular objective, whether there is an
observation-based strategy to achieve the objective with probability~1
(almost-sure winning), or with positive probability (positive winning). Our
main results are twofold. First, we present a complete picture of the
computational complexity of the qualitative analysis of POMDP s with parity
objectives (a canonical form to express omega-regular objectives) and its
subclasses. Our contribution consists in establishing several upper and lower
bounds that were not known in literature. Second, we present optimal bounds
(matching upper and lower bounds) on the memory required by pure and randomized
observation-based strategies for the qualitative analysis of POMDP s with
parity objectives and its subclasses
Restricted Value Iteration: Theory and Algorithms
Value iteration is a popular algorithm for finding near optimal policies for
POMDPs. It is inefficient due to the need to account for the entire belief
space, which necessitates the solution of large numbers of linear programs. In
this paper, we study value iteration restricted to belief subsets. We show
that, together with properly chosen belief subsets, restricted value iteration
yields near-optimal policies and we give a condition for determining whether a
given belief subset would bring about savings in space and time. We also apply
restricted value iteration to two interesting classes of POMDPs, namely
informative POMDPs and near-discernible POMDPs
- …