Sampling-Based Approximation Algorithms for Reachability Analysis with Provable Guarantees

The successful deployment of many autonomous systems in part hinges on providing rigorous guarantees on their performance and safety through a formal verification method, such as reachability analysis. In this work, we present a simple-to-implement, sampling-based algorithm for reachability analysis that is provably optimal up to any desired approximation accuracy. Our method achieves computational efficiency by judiciously sampling a finite subset of the state space and generating an approximate reachable set by conducting reachability analysis on this finite set of states. We prove that the reachable set generated by our algorithm approximates the ground-truth reachable set for any user-specified approximation accuracy. As a corollary to our main method, we introduce an asymptoticallyoptimal, anytime algorithm for reachability analysis. We present simulation results that reaffirm the theoretical properties of our algorithm and demonstrate its effectiveness in real-world inspired scenariosNational Science Foundation (U.S.

Multi-robot task allocation for safe planning under dynamic uncertainties

This paper considers the problem of multi-robot safe mission planning in uncertain dynamic environments. This problem arises in several applications including safety-critical exploration, surveillance, and emergency rescue missions. Computation of a multi-robot optimal control policy is challenging not only because of the complexity of incorporating dynamic uncertainties while planning, but also because of the exponential growth in problem size as a function of the number of robots. Leveraging recent works obtaining a tractable safety maximizing plan for a single robot, we propose a scalable two-stage framework to solve the problem at hand. Specifically, the problem is split into a low-level single-agent planning problem and a high-level task allocation problem. The low-level problem uses an efficient approximation of stochastic reachability for a Markov decision process to handle the dynamic uncertainty. The task allocation, on the other hand, is solved using polynomial-time forward and reverse greedy heuristics. The safety objective of our multi-robot safe planning problem allows an implementation of the greedy heuristics through a distributed auction-based approach. Moreover, by leveraging the properties of the safety objective function, we ensure provable performance bounds on the safety of the approximate solutions proposed by these two heuristics. Our result is illustrated through case studies

Importance Sketching of Influence Dynamics in Billion-scale Networks

The blooming availability of traces for social, biological, and communication networks opens up unprecedented opportunities in analyzing diffusion processes in networks. However, the sheer sizes of the nowadays networks raise serious challenges in computational efficiency and scalability. In this paper, we propose a new hyper-graph sketching framework for inflence dynamics in networks. The central of our sketching framework, called SKIS, is an efficient importance sampling algorithm that returns only non-singular reverse cascades in the network. Comparing to previously developed sketches like RIS and SKIM, our sketch significantly enhances estimation quality while substantially reducing processing time and memory-footprint. Further, we present general strategies of using SKIS to enhance existing algorithms for influence estimation and influence maximization which are motivated by practical applications like viral marketing. Using SKIS, we design high-quality influence oracle for seed sets with average estimation error up to 10x times smaller than those using RIS and 6x times smaller than SKIM. In addition, our influence maximization using SKIS substantially improves the quality of solutions for greedy algorithms. It achieves up to 10x times speed-up and 4x memory reduction for the fastest RIS-based DSSA algorithm, while maintaining the same theoretical guarantees.Comment: 12 pages, to appear in ICDM 2017 as a regular pape

Scalable Synthesis and Verification: Towards Reliable Autonomy

We have seen the growing deployment of autonomous systems in our daily life, ranging from safety-critical self-driving cars to dialogue agents. While impactful and impressive, these systems do not often come with guarantees and are not rigorously evaluated for failure cases. This is in part due to the limited scalability of tools available for designing correct-by-construction systems, or verifying them posthoc. Another key limitation is the lack of availability of models for the complex environments with which autonomous systems often have to interact with. In the direction of overcoming these above mentioned bottlenecks to designing reliable autonomous systems, this thesis makes contributions along three fronts. First, we develop an approach for parallelized synthesis from linear-time temporal logic Specifications corresponding to the generalized reactivity (1) fragment. We begin by identifying a special case corresponding to singleton liveness goals that allows for a decomposition of the synthesis problem, which facilitates parallelized synthesis. Based on the intuition from this special case, we propose a more generalized approach for parallelized synthesis that relies on identifying equicontrollable states. Second, we consider learning-based approaches to enable verification at scale for complex systems, and for autonomous systems that interact with black-box environments. For the former, we propose a new abstraction refinement procedure based on machine learning to improve the performance of nonlinear constraint solving algorithms on large-scale problems. For the latter, we present a data-driven approach based on chance-constrained optimization that allows for a system to be evaluated for specification conformance without an accurate model of the environment. We demonstrate this approach on several tasks, including a lane-change scenario with real-world driving data. Lastly, we consider the problem of interpreting and verifying learning-based components such as neural networks. We introduce a new method based on Craig's interpolants for computing compact symbolic abstractions of pre-images for neural networks. Our approach relies on iteratively computing approximations that provably overapproximate and underapproximate the pre-images at all layers. Further, building on existing work for training neural networks for verifiability in the classification setting, we propose extensions that allow us to generalize the approach to more general architectures and temporal specifications.</p

Anytime Guarantees for Reachability in Uncountable Markov Decision Processes

We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a sequence of approximations converging to the true value in the limit, our aim is to obtain an algorithm with guarantees on the precision of the approximation. As this problem is undecidable in general, assumptions on the MDP are necessary. Our main contribution is to identify sufficient assumptions that are as weak as possible, thus approaching the "boundary" of which systems can be correctly and reliably analyzed. To this end, we also argue why each of our assumptions is necessary for algorithms based on processing finitely many observations. We present two solution variants. The first one provides converging lower bounds under weaker assumptions than typical ones from previous works concerned with guarantees. The second one then utilizes stronger assumptions to additionally provide converging upper bounds. Altogether, we obtain an anytime algorithm, i.e. yielding a sequence of approximants with known and iteratively improving precision, converging to the true value in the limit. Besides, due to the generality of our assumptions, our algorithms are very general templates, readily allowing for various heuristics from literature in contrast to, e.g., a specific discretization algorithm. Our theoretical contribution thus paves the way for future practical improvements without sacrificing correctness guarantees