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In stochastic sequential decision problems, such as Stochastic Shortest Path Problems, the GUBS (Goal with UtilityBased Semantics) criterion considers a trade-off between probability-to-goal and cost-to-goal using a goal semantics based on Expected Utility Theory (EUT); in such a semantics, goal paths have priority over non-goal paths, but it implies neither the MAXPROB criterion nor the dual optimization criterion that finds the cheapest policy among the policies that maximize goal probability. Whereas evaluation criteria based on a sound theory such as EUT are desirable, optimal policies under GUBS are non-markovian. Non-markovian solutions are undesirable because there is not always a finite representation and even if it can be represented in a finite way, the representation may be too large to be stored. Here we define a special case of GUBS criterion that allows a finite representation to the optimal policy, the eGUBS criterion, where the cost utility function is exponencial. Considering this special case, we contribute with: (i) the proof that the eGUBSoptimal policy has a finite representation; (ii) the first exact algorithm to obtain finite optimal policies for the eGUBS criterion, and (iii) four strategies to find sub-optimal policies. We conduct experiments on one synthetic problem to evaluate each strategy. Although optimal solutions have a high memory cost, sub-optimal policies can save memory space with a small decrease in performance.

Um Processo de Decisão Markoviano (MDP) pode ser usado para modelar problemas de decisão sequencial. No entanto, podem existir limitações na obtenção de probabilidades para modelagem da transição de estados ou falta de confiabilidade nas informações existentes sobre estas probabilidades. Um modelo menos restritivo e que pode resolver este problema é o Processo de Decisão Markoviano com Probabilidades Intervalares (BMDP), que permite a representação imprecisa das probabilidades de transição de estados e raciocínio sobre uma solução robusta. Para resolver BMDPs de horizonte infinito, existem os algoritmos síncronos de Iteração de Valor Intervalar e Iteração de Política Robusto, que são ineficientes quando o tamanho do espaço de estados é grande. Neste trabalho são propostos algoritmos assíncronos de Iteração de Política baseados no particionamento do espaço de estados em subconjuntos aleatórios (Robust Asynchronous Policy Iteration - RAPI) ou em componentes fortemente conexos (Robust Topological Policy Iteration - RTPI). Também são propostas formas de inicializar a função valor e a política dos algoritmos, de forma a melhorar a convergência destes. O desempenho dos algoritmos propostos é avaliado em comparação com o algoritmo de Iteração de Política Robusto para BMDPs para domínios de planejamento existentes e um novo domínio proposto. Os resultados dos experimentos realizados mostram que (i) quanto mais estruturado é o domínio, melhor é o desempenho do algoritmo RTPI; (ii) o uso de computação paralela no algoritmo RAPI possui um pequeno ganho computacional em relação à sua versão sequencial; e (iii) uma boa inicialização da função valor e política pode impactar positivamente o tempo de convergência dos algoritmos. A Markov Decision Process (MDP) can be used to model sequential decision problems. However, there may be limitations in obtaining probabilities for state transition modeling or lack of reliability in existing information on these probabilities. A less restrictive model that can solve this problem is the Bounded-parameter Markov Decision Process (BMDP), which allows the imprecise representation of the transition probabilities and reasoning about a robust solution. To solve infinite horizon BMDPs, there are synchronous algorithms such as Interval Value Iteration and Robust Policy Iteration, which are inefficient for large state spaces. In this work, we propose new asynchronous Policy Iteration algorithms based on state space partitioning in random subsets (Robust Asynchronous Policy Iteration - RAPI) or in strongly connected components (Robust Topological Policy Iteration - RTPI). We also propose ways to initialize the value function and policy of the algorithms, in order to improve their convergence. The performance of the proposed algorithms is evaluated in comparison with the Robust Policy Iteration algorithm for BMDPs for existing planning domains and a proposed new domain. The results of the experiments show that (i) the more structured the domain, the better is the performance of the RTPI algorithm; (ii) the use of parallel computing in the RAPI algorithm has a small computational gain compared to its sequential version; and (iii) a good initialization of the value function and policy can positively impact the convergence time of the algorithms.

Markov Decision Processes ( mdp s) are commonly used to solve sequential decision problems. A less restrictive model is the Bounded-parameter mdp ( bmdp ) that allows: (i) the transition function to be expressed in terms of probability intervals and (ii) reasoning about a robust solution, i.e., the best solution under the worst model. In this paper, we propose the Robust Topological Policy Iteration ( rtpi ) algorithm which is a new policy iteration algorithm for infinite horizon bmdp s based on a partition of the state space. The empirical results show that the more structured the domain, the better is the performance of rtpi .