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This article deals with stochastic processes endowed with the Markov (memoryless) property and evolving over general (uncountable) state spaces. The models further depend on a non-deterministic quantity in the form of a control input, which…
This paper considers large families of Markov chains (MCs) that are defined over a set of parameters with finite discrete domains. Such families occur in software product lines, planning under partial observability, and sketching of…
We study and provide efficient algorithms for multi-objective model checking problems for Markov Decision Processes (MDPs). Given an MDP, M, and given multiple linear-time (\omega -regular or LTL) properties \varphi\_i, and probabilities…
Parametric Markov chains (pMC) are used to model probabilistic systems with unknown or partially known probabilities. Although (universal) pMC verification for reachability properties is known to be coETR-complete, there have been efforts…
We show subexponential lower bounds (i.e., $2^{\Omega (n^c)}$) on the smoothed complexity of the classical Howard's Policy Iteration algorithm for Markov Decision Processes. The bounds hold for the total reward and the average reward…
We consider a Markov control model in discrete time with countable both state space and action space. Using the value function of a suitable long-run average reward problem, we study various reachability/controllability problems. First, we…
We establish quantitative bounds for rates of convergence and asymptotic variances for iterated conditional sequential Monte Carlo (i-cSMC) Markov chains and associated particle Gibbs samplers. Our main findings are that the essential…
We present a new algorithm for the statistical model checking of Markov chains with respect to unbounded temporal properties, such as reachability and full linear temporal logic. The main idea is that we monitor each simulation run on the…
Markov decision processes model systems subject to nondeterministic and probabilistic uncertainty. A plethora of verification techniques addresses variations of reachability properties, such as: Is there a scheduler resolving the…
In this paper we study reachability verification problems of stochastic discrete-time dynamical systems over the infinite time horizon. The reachability verification of interest in this paper is to certify specified lower and upper bounds…
This report considers the problem of computing the Cramer-Rao bound for the parameters of a Markov random field. Computation of the exact bound is not feasible for most fields of interest because their likelihoods are intractable and have…
Interval Markov Decision Processes (IMDPs) are finite-state uncertain Markov models, where the transition probabilities belong to intervals. Recently, there has been a surge of research on employing IMDPs as abstractions of stochastic…
We are interested in the analysis of very large continuous-time Markov chains (CTMCs) with many distinct rates. Such models arise naturally in the context of reliability analysis, e.g., of computer network performability analysis, of power…
We present a general framework for applying learning algorithms and heuristical guidance to the verification of Markov decision processes (MDPs). The primary goal of our techniques is to improve performance by avoiding an exhaustive…
Regularization of control policies using entropy can be instrumental in adjusting predictability of real-world systems. Applications benefiting from such approaches range from, e.g., cybersecurity, which aims at maximal unpredictability, to…
Sequential decision making using Markov Decision Process underpins many realworld applications. Both model-based and model free methods have achieved strong results in these settings. However, real-world tasks must balance reward…
We introduce the notion of quantum Markov decision process (qMDP) as a semantic model of nondeterministic and concurrent quantum programs. It is shown by examples that qMDPs can be used in analysis of quantum algorithms and protocols. We…
We study the statistical limits of Imitation Learning (IL) in episodic Markov Decision Processes (MDPs) with a state space $\mathcal{S}$. We focus on the known-transition setting where the learner is provided a dataset of $N$ length-$H$…
Markov decision processes (MDPs) are standard models for probabilistic systems with non-deterministic behaviours. Long-run average rewards provide a mathematically elegant formalism for expressing long term performance. Value iteration (VI)…
In this paper, we consider multi-dimensional maximal cost-bounded reachability probability over continuous-time Markov decision processes (CTMDPs). Our major contributions are as follows. Firstly, we derive an integral characterization…