Multi-objective Robust Strategy Synthesis for Interval Markov Decision Processes

Interval Markov decision processes (IMDPs) generalise classical MDPs by having interval-valued transition probabilities. They provide a powerful modelling tool for probabilistic systems with an additional variation or uncertainty that prevents the knowledge of the exact transition probabilities. In this paper, we consider the problem of multi-objective robust strategy synthesis for interval MDPs, where the aim is to find a robust strategy that guarantees the satisfaction of multiple properties at the same time in face of the transition probability uncertainty. We first show that this problem is PSPACE-hard. Then, we provide a value iteration-based decision algorithm to approximate the Pareto set of achievable points. We finally demonstrate the practical effectiveness of our proposed approaches by applying them on several case studies using a prototypical tool.Comment: This article is a full version of a paper accepted to the Conference on Quantitative Evaluation of SysTems (QEST) 201

Multi-Objective Approaches to Markov Decision Processes with Uncertain Transition Parameters

Markov decision processes (MDPs) are a popular model for performance analysis and optimization of stochastic systems. The parameters of stochastic behavior of MDPs are estimates from empirical observations of a system; their values are not known precisely. Different types of MDPs with uncertain, imprecise or bounded transition rates or probabilities and rewards exist in the literature. Commonly, analysis of models with uncertainties amounts to searching for the most robust policy which means that the goal is to generate a policy with the greatest lower bound on performance (or, symmetrically, the lowest upper bound on costs). However, hedging against an unlikely worst case may lead to losses in other situations. In general, one is interested in policies that behave well in all situations which results in a multi-objective view on decision making. In this paper, we consider policies for the expected discounted reward measure of MDPs with uncertain parameters. In particular, the approach is defined for bounded-parameter MDPs (BMDPs) [8]. In this setting the worst, best and average case performances of a policy are analyzed simultaneously, which yields a multi-scenario multi-objective optimization problem. The paper presents and evaluates approaches to compute the pure Pareto optimal policies in the value vector space.Comment: 9 pages, 5 figures, preprint for VALUETOOLS 201

HMM based scenario generation for an investment optimisation problem

This is the post-print version of the article. The official published version can be accessed from the link below - Copyright @ 2012 Springer-Verlag.The Geometric Brownian motion (GBM) is a standard method for modelling financial time series. An important criticism of this method is that the parameters of the GBM are assumed to be constants; due to this fact, important features of the time series, like extreme behaviour or volatility clustering cannot be captured. We propose an approach by which the parameters of the GBM are able to switch between regimes, more precisely they are governed by a hidden Markov chain. Thus, we model the financial time series via a hidden Markov model (HMM) with a GBM in each state. Using this approach, we generate scenarios for a financial portfolio optimisation problem in which the portfolio CVaR is minimised. Numerical results are presented.This study was funded by NET ACE at OptiRisk Systems

Stochastic Shortest Path with Energy Constraints in POMDPs

We consider partially observable Markov decision processes (POMDPs) with a set of target states and positive integer costs associated with every transition. The traditional optimization objective (stochastic shortest path) asks to minimize the expected total cost until the target set is reached. We extend the traditional framework of POMDPs to model energy consumption, which represents a hard constraint. The energy levels may increase and decrease with transitions, and the hard constraint requires that the energy level must remain positive in all steps till the target is reached. First, we present a novel algorithm for solving POMDPs with energy levels, developing on existing POMDP solvers and using RTDP as its main method. Our second contribution is related to policy representation. For larger POMDP instances the policies computed by existing solvers are too large to be understandable. We present an automated procedure based on machine learning techniques that automatically extracts important decisions of the policy allowing us to compute succinct human readable policies. Finally, we show experimentally that our algorithm performs well and computes succinct policies on a number of POMDP instances from the literature that were naturally enhanced with energy levels.Comment: Technical report accompanying a paper published in proceedings of AAMAS 201

Computational Approaches for Stochastic Shortest Path on Succinct MDPs

We consider the stochastic shortest path (SSP) problem for succinct Markov decision processes (MDPs), where the MDP consists of a set of variables, and a set of nondeterministic rules that update the variables. First, we show that several examples from the AI literature can be modeled as succinct MDPs. Then we present computational approaches for upper and lower bounds for the SSP problem: (a)~for computing upper bounds, our method is polynomial-time in the implicit description of the MDP; (b)~for lower bounds, we present a polynomial-time (in the size of the implicit description) reduction to quadratic programming. Our approach is applicable even to infinite-state MDPs. Finally, we present experimental results to demonstrate the effectiveness of our approach on several classical examples from the AI literature

Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks