Related papers: Approximating a Behavioural Pseudometric without D…
Behaviour distances to measure the resemblance of two states in a (nondeterministic) fuzzy transition system have been proposed recently in the literature. Such a distance, defined as a pseudo-ultrametric over the state space of the model,…
Bisimulation metrics provide a robust and accurate approach to study the behavior of nondeterministic probabilistic processes. In this paper, we propose a logical characterization of bisimulation metrics based on a simple probabilistic…
We develop a pseudo-metric analogue of bisimulation for generalized semi-Markov processes. The kernel of this pseudo-metric corresponds to bisimulation; thus we have extended bisimulation for continuous-time probabilistic processes to a…
Behavioural distances generally offer more fine-grained means of comparing quantitative systems than two-valued behavioural equivalences. They often relate to quantitative modalities, which generate quantitative modal logics that…
In probabilistic transition systems, behavioural metrics provide a more fine-grained and stable measure of system equivalence than crisp notions of bisimilarity. They correlate strongly to quantitative probabilistic logics, and in fact the…
Behavioural distances provide a robust alternative to notions of equivalence such as bisimilarity in the context of probabilistic transition systems. They can be defined as least fixed points, whose universal property allows us to exhibit…
A subalgebraic approximation algorithm is proposed to estimate from a set of time series the parameters of the observer representation of a discrete-time polynomial system without inputs which can generate an approximation of the observed…
We present new algorithms for computing and approximating bisimulation metrics in Markov Decision Processes (MDPs). Bisimulation metrics are an elegant formalism that capture behavioral equivalence between states and provide strong…
Dempster-Shafer theory is widely applied in uncertainty modelling and knowledge reasoning due to its ability of expressing uncertain information. A distance between two basic probability assignments(BPAs) presents a measure of performance…
In contrast to the existing approaches to bisimulation for fuzzy systems, we introduce a behavioral distance to measure the behavioral similarity of states in a nondeterministic fuzzy-transition system. This behavioral distance is defined…
In many real-world reinforcement learning applications, access to the environment is limited to a fixed dataset, instead of direct (online) interaction with the environment. When using this data for either evaluation or training of a new…
Many popular policy gradient methods for reinforcement learning follow a biased approximation of the policy gradient known as the discounted approximation. While it has been shown that the discounted approximation of the policy gradient is…
The probabilistic bisimilarity distance of Deng et al. has been proposed as a robust quantitative generalization of Segala and Lynch's probabilistic bisimilarity for probabilistic automata. In this paper, we present a characterization of…
The fuzzy modality `probably` is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is…
The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…
We study behavioral metrics in an abstract coalgebraic setting. Given a coalgebra alpha: X -> FX in Set, where the functor F specifies the branching type, we define a framework for deriving pseudometrics on X which measure the behavioral…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
Results on approximate deduction in the context of the calculus of evidence of Dempster-Shafer and the theory of interval probabilities are reported. Approximate conditional knowledge about the truth of conditional propositions was assumed…
The most studied and accepted pseudometric for probabilistic processes is one based on the Kantorovich distance between distributions. It comes with many theoretical and motivating results, in particular it is the fixpoint of a given…
We study different behavioral metrics, such as those arising from both branching and linear-time semantics, in a coalgebraic setting. Given a coalgebra $\alpha\colon X \to HX$ for a functor $H \colon \mathrm{Set}\to \mathrm{Set}$, we define…