Robust online planning with imperfect models

Environment models are not always known a priori, and approximating stochastic transition dynamics may introduce errors, especially if only a small amount of data is available and/or model misspecification is

Real-time dynamic programming for Markov Decision Processes with Imprecise Probabilities

Em problemas de tomada de decisão sequencial modelados como Processos de Decisão Markovianos (MDP) pode não ser possível obter uma medida exata para as probabilidades de transição de estados. Visando resolver esta situação os Processos de Decisão Markovianos com Probabilidades Imprecisas (Markov Decision Processes with Imprecise Transition Probabilities, MDP-IPs) foram introduzidos. Porém, enquanto estes MDP-IPs se mostram como um arcabouço robusto para aplicações de planejamento no mundo real, suas soluções consomem muito tempo na prática. Em trabalhos anteriores, buscando melhorar estas soluções foram propostos algoritmos de programação dinâmica síncrona eficientes para resolver MDP-IPs com uma representação fatorada para as funções de transição probabilística e recompensa, chamados de MDP-IP fatorados. Entretanto quando o estado inicial de um problema do Caminho mais Curto Estocástico (Stochastic Shortest Path MDP, SSP MDP) é dado, estas soluções não utilizam esta informação. Neste trabalho será introduzido o problema do Caminho mais Curto Estocástico com Probabilidades Imprecisas (Stochastic Shortest Path MDP-IP, SSP MDP-IP) tanto em sua forma enumerativa, quanto na fatorada. Um algoritmo de programação dinâmica assíncrona para SSP MDP-IP enumerativos com probabilidades dadas por intervalos foi proposto por Buffet e Aberdeen (2005). Entretanto, em geral um problema é dado de forma fatorada, i.e., em termos de variáveis de estado e nesse caso, mesmo se for assumida a imprecisão dada por intervalos sobre as variáveis, ele não poderá ser mais aplicado, pois as probabilidades de transição conjuntas serão multilineares. Assim, será mostrado que os SSP MDP-IPs fatorados são mais expressivos que os enumerativos e que a mudança do SSP MDP-IP enumerativo para o caso geral de um SSP MDP-IPs fatorado leva a uma mudança de resolução da função objetivo do Bellman backup de uma função linear para uma não-linear. Também serão propostos algoritmos enumerativos, chamados de RTDP-IP (Real-time Dynamic Programming with Imprecise Transition Probabilities), LRTDP-IP (Labeled Real-time Dynamic Programming with Imprecise Transition Probabilities), SSiPP-IP (Short-Sighted Probabilistic Planner with Imprecise Transition Probabilities) e LSSiPP-IP (Labeled Short-Sighted Probabilistic Planner with Imprecise Transition Probabilities) e fatorados chamados factRTDP-IP (factored RTDP-IP) e factLRTDP-IP (factored LRTDP-IP). Eles serão avaliados em relação aos algoritmos de programação dinâmica síncrona em termos de tempo de convergência da solução e de escalabilidade.In sequential decision making problems modelled as Markov Decision Processes (MDP) we may not have the state transition probabilities. To solve this issue, the framework based in Markov Decision Processes with Imprecise Transition Probabilities (MDP-IPs) is introduced. Therefore, while MDP-IPs is a robust framework to use in real world planning problems, its solutions are time-consuming in practice. In previous works, efficient algorithms based in synchronous dynamic programming to solve MDP-IPs with factored representations of the probabilistic transition function and reward function, called factored MDP-IPs. However, given a initial state of a system, modeled as a Stochastic Shortest Path MDP (SSP MDP), solutions does not use this information. In this work we introduce the Stochastic Shortest Path MDP-IPs (SSP MDP-IPs) in enumerative form and in factored form. An efficient asynchronous dynamic programming solution for SSP MDP-IPs with enumerated states has been proposed by Buffet e Aberdeen (2005) before which is restricted to interval-based imprecision. Nevertheless, in general the problem is given in a factored form, i.e., in terms of state variables and in this case even if we assume interval-based imprecision over the variables, the previous solution is no longer applicable since we have multilinear parameterized joint transition probabilities. In this work we show that the innocuous change from the enumerated SSP MDP-IP cases to the general case of factored SSP MDP-IPs leads to a switch from a linear to nonlinear objectives in the Bellman backup. Also we propose assynchronous dynamic programming enumerative algorithms, called RTDP-IP (Real-time Dynamic Programming with Imprecise Transition Probabilities), LRTDP-IP (Labeled Real-time Dynamic Programming with Imprecise Transition Probabilities), SSiPP-IP (Short-Sighted Probabilistic Planner with Imprecise Transition Probabilities) and LSSiPP-IP (Labeled Short-Sighted Probabilistic Planner with Imprecise Transition Probabilities), and factored algorithms called factRTDP-IP (factored RTDP-IP) and factLRTDP-IP (factored LRTDP-IP). There algorithms will be evaluated with the synchronous dynamic programming algorithms previously proposed in terms of convergence time and scalability

Parameter Synthesis for Markov Models

Markov chain analysis is a key technique in reliability engineering. A practical obstacle is that all probabilities in Markov models need to be known. However, system quantities such as failure rates or packet loss ratios, etc. are often not---or only partially---known. This motivates considering parametric models with transitions labeled with functions over parameters. Whereas traditional Markov chain analysis evaluates a reliability metric for a single, fixed set of probabilities, analysing parametric Markov models focuses on synthesising parameter values that establish a given reliability or performance specification $\varphi$. Examples are: what component failure rates ensure the probability of a system breakdown to be below 0.00000001?, or which failure rates maximise reliability? This paper presents various analysis algorithms for parametric Markov chains and Markov decision processes. We focus on three problems: (a) do all parameter values within a given region satisfy $\varphi$?, (b) which regions satisfy $\varphi$ and which ones do not?, and (c) an approximate version of (b) focusing on covering a large fraction of all possible parameter values. We give a detailed account of the various algorithms, present a software tool realising these techniques, and report on an extensive experimental evaluation on benchmarks that span a wide range of applications.Comment: 38 page

Operational Decision Making under Uncertainty: Inferential, Sequential, and Adversarial Approaches

Modern security threats are characterized by a stochastic, dynamic, partially observable, and ambiguous operational environment. This dissertation addresses such complex security threats using operations research techniques for decision making under uncertainty in operations planning, analysis, and assessment. First, this research develops a new method for robust queue inference with partially observable, stochastic arrival and departure times, motivated by cybersecurity and terrorism applications. In the dynamic setting, this work develops a new variant of Markov decision processes and an algorithm for robust information collection in dynamic, partially observable and ambiguous environments, with an application to a cybersecurity detection problem. In the adversarial setting, this work presents a new application of counterfactual regret minimization and robust optimization to a multi-domain cyber and air defense problem in a partially observable environment