Policy learning in continuous-time Markov decision processes using Gaussian Processes

Abstract

Continuous-time Markov decision processes provide a very powerful mathematical framework to solve policy-making problems in a wide range of applications, ranging from the control of populations to cyber–physical systems. The key problem to solve for these models is to efficiently compute an optimal policy to control the system in order to maximise the probability of satisfying a set of temporal logic specifications. Here we introduce a novel method based on statistical model checking and an unbiased estimation of a functional gradient in the space of possible policies. Our approach presents several advantages over the classical methods based on discretisation techniques, as it does not assume the a-priori knowledge of a model that can be replaced by a black-box, and does not suffer from state-space explosion. The use of a stochastic moment-based gradient ascent algorithm to guide our search considerably improves the efficiency of learning policies and accelerates the convergence using the momentum term. We demonstrate the strong performance of our approach on two examples of non-linear population models: an epidemiology model with no permanent recovery and a queuing system with non-deterministic choice

Policy Synthesis for Collective Dynamics

“…, using the Gillespie algorithm. This is done in the context of statistical model checking [11] and has recently been applied to learning effective time-dependent policies for CT-MDPs [12]. Here, we argue that in the case of some reward functionals a good estimate can be achieved via fluid approximation.…”

Reliability Analysis of Dynamic Fault Tree Based on Binary Decision Diagrams for Explosive Vehicle

“…Obtain the probability of M1, M2, and A, and the probability of M3 can be calculated as 0.657. Continuous-time Markov decision processes provide a very powerful mathematical framework to solve widely used decision problems, as discussed by Bartocci [31]. e process can be defined as the following random process:…”

Towards a framework for certification of reliable autonomous systems

“…RV of multiagent systems using trace expressions [9,88] is also a viable approach to cope with the RuLes LayeR. RV has been used for the Reactions LayeR, for example in [19]. LayeR and RuLes LayeR, and is applied for testing features at both levels in autonomous [105,227] and multiagent systems [192], we are not aware of proposals for testing the PRinciPLes LayeR of an autonomous system.…”