Optimistic Value Iteration

Markov decision processes are widely used for planning and verification in settings that combine controllable or adversarial choices with probabilistic behaviour. The standard analysis algorithm, value iteration, only provides lower bounds on infinite-horizon probabilities and rewards. Two “sound” variations, which also deliver an upper bound, have recently appeared. In this paper, we present a new sound approach that leverages value iteration’s ability to usually deliver good lower bounds: we obtain a lower bound via standard value iteration, use the result to “guess” an upper bound, and prove the latter’s correctness. We present this optimistic value iteration approach for computing reachability probabilities as well as expected rewards. It is easy to implement and performs well, as we show via an extensive experimental evaluation using our implementation within the mcsta model checker of the Modest Toolset

Aiming Low Is Harder -- Induction for Lower Bounds in Probabilistic Program Verification

We present a new inductive rule for verifying lower bounds on expected values of random variables after execution of probabilistic loops as well as on their expected runtimes. Our rule is simple in the sense that loop body semantics need to be applied only finitely often in order to verify that the candidates are indeed lower bounds. In particular, it is not necessary to find the limit of a sequence as in many previous rules

Relatively Complete Verification of Probabilistic Programs: An Expressive Language for Expectation-Based Reasoning

We study a syntax for specifying quantitative “assertions” - functions mapping program states to numbers - for probabilistic program verification. We prove that our syntax is expressive in the following sense: Given any probabilistic program C, if a function f is expressible in our syntax, then the function mapping each initial state σ to the expected value of f evaluated in the final states reached after termination C on σ (also called the weakest preexpectation wp[C](f)) is also expressible in our syntax. As a consequence, we obtain a relatively complete verification system for verifying expected values and probabilities in the sense of Cook: Apart from a single reasoning step about the inequality of two functions given as syntactic expressions in our language, given f, g, and C, we can check whether g ≤ wp[C](f)

Weighted programming: A programming paradigm for specifying mathematical models

We study weighted programming, a programming paradigm for specifying mathematical models. More specifically, the weighted programs we investigate are like usual imperative programs with two additional features: (1) nondeterministic branching and (2) weighting execution traces. Weights can be numbers but also other objects like words from an alphabet, polynomials, formal power series, or cardinal numbers. We argue that weighted programming as a paradigm can be used to specify mathematical models beyond probability distributions (as is done in probabilistic programming). We develop weakest-precondition- and weakest-liberal-precondition-style calculi à la Dijkstra for reasoning about mathematical models specified by weighted programs. We present several case studies. For instance, we use weighted programming to model the ski rental problem - an optimization problem. We model not only the optimization problem itself, but also the best deterministic online algorithm for solving this problem as weighted programs. By means of weakest-precondition-style reasoning, we can determine the competitive ratio of the online algorithm on source code level

Bounded Model Checking for Probabilistic Programs

In this paper we investigate the applicability of standard model checking approaches to verifying properties in probabilistic programming. As the operational model for a standard probabilistic program is a potentially infinite parametric Markov decision process, no direct adaption of existing techniques is possible. Therefore, we propose an on-the-fly approach where the operational model is successively created and verified via a step-wise execution of the program. This approach enables to take key features of many probabilistic programs into account: nondeterminism and conditioning. We discuss the restrictions and demonstrate the scalability on several benchmarks

Understanding Probabilistic Programs

We present two views of probabilistic programs and their relationship. An operational interpretation as well as a weakest pre-condition semantics are provided for an elementary probabilistic guarded command language. Our study treats important features such as sampling, conditioning, loop divergence, and non-determinism

A Pre-expectation Calculus for Probabilistic Sensitivity

Sensitivity properties describe how changes to the input of a program affect the output, typically by upper bounding the distance between the outputs of two runs by a monotone function of the distance between the corresponding inputs. When programs are probabilistic, the distance between outputs is a distance between distributions. The Kantorovich lifting provides a general way of defining a distance between distributions by lifting the distance of the underlying sample space; by choosing an appropriate distance on the base space, one can recover other usual probabilistic distances, such as the Total Variation distance. We develop a relational pre-expectation calculus to upper bound the Kantorovich distance between two executions of a probabilistic program. We illustrate our methods by proving algorithmic stability of a machine learning algorithm, convergence of a reinforcement learning algorithm, and fast mixing for card shuffling algorithms. We also consider some extensions: using our calculus to show convergence of Markov chains to the uniform distribution over states and an asynchronous extension to reason about pairs of program executions with different control flow

Finding polynomial loop invariants for probabilistic programs

Quantitative loop invariants are an essential element in the verification of probabilistic programs. Recently, multivariate Lagrange interpolation has been applied to synthesizing polynomial invariants. In this paper, we propose an alternative approach. First, we fix a polynomial template as a candidate of a loop invariant. Using Stengle's Positivstellensatz and a transformation to a sum-of-squares problem, we find sufficient conditions on the coefficients. Then, we solve a semidefinite programming feasibility problem to synthesize the loop invariants. If the semidefinite program is unfeasible, we backtrack after increasing the degree of the template. Our approach is semi-complete in the sense that it will always lead us to a feasible solution if one exists and numerical errors are small. Experimental results show the efficiency of our approach.Comment: accompanies an ATVA 2017 submissio

Ethics for civil indoor drones: a qualitative analysis

[EN] Drones face two main concerns: safety and security/privacy. Whilst safety has been broadly studied by literature, less research has been carried out into security/privacy. Moreover, current European regulations on drone flights apply to outdoor drones but not always to their indoor counterparts. However, several industrial sectors have started to use drones for indoor tasks such as surveillance, architecture, emergencies, and communication media. A qualitative study has been conducted in order to explore the concerns expressed by civil drone operators over the measures that manufacturers include in their products and information packages. Codes of conduct could also help these parties when there is no legal regulation that can be applied. We used content analysis as the method of analysis for three different sources: secondary data from a literature review and from public European documents, and primary data from focus groups. Results show that safety and security/privacy by design are seen as the best ethical measures, whilst codes of conduct could be used as complimentary information for professional users.The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this article: The project leading to this application has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 732433. Project: AiRT, Technology transfer of RPAs for the creative industry, H2020-ICT-2016-2017.De-Miguel-Molina, M.; Santamarina-Campos, V.; Carabal-Montagud, M.; De-Miguel-Molina, B. (2018). Ethics for civil indoor drones: a qualitative analysis. International Journal of Micro Air Vehicles. 10(4):340-351. https://doi.org/10.1177/1756829318794004S34035110