New prioritized value iteration for Markov decision processes

The problem of solving large Markov decision processes accurately and quickly is challenging. Since the computational effort incurred is considerable, current research focuses on finding superior acceleration techniques. For instance, the convergence properties of current solution methods depend, to a great extent, on the order of backup operations. On one hand, algorithms such as topological sorting are able to find good orderings but their overhead is usually high. On the other hand, shortest path methods, such as Dijkstra's algorithm which is based on priority queues, have been applied successfully to the solution of deterministic shortest-path Markov decision processes. Here, we propose an improved value iteration algorithm based on Dijkstra's algorithm for solving shortest path Markov decision processes. 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A switching planner for combined task and observation planning

Abstract From an automated planning perspective the problem of practical mobile robot control in realistic environments poses many important and contrary challenges. On the one hand, the planning process must be lightweight, robust, and timely. Over the lifetime of the robot it must always respond quickly with new plans that accommodate exogenous events, changing objectives, and the underlying unpredictability of the environment. On the other hand, in order to promote efficient behaviours the planning process must perform computationally expensive reasoning about contingencies and possible revisions of subjective beliefs according to quantitatively modelled uncertainty in acting and sensing. Towards addressing these challenges, we develop a continual planning approach that switches between using a fast satisficing "classical" planner, to decide on the overall strategy, and decision-theoretic planning to solve small abstract subproblems where deeper consideration of the sensing model is both practical, and can significantly impact overall performance. We evaluate our approach in large problems from a realistic robot exploration domain

Optimal policies for Bayesian olfactory search in turbulent flows

In many practical scenarios, a flying insect must search for the source of an emitted cue which is advected by the atmospheric wind. On the macroscopic scales of interest, turbulence tends to mix the cue into patches of relatively high concentration over a background of very low concentration, so that the insect will only detect the cue intermittently and cannot rely on chemotactic strategies which simply climb the concentration gradient. In this work, we cast this search problem in the language of a partially observable Markov decision process (POMDP) and use the Perseus algorithm to compute strategies that are near-optimal with respect to the arrival time. We test the computed strategies on a large two-dimensional grid, present the resulting trajectories and arrival time statistics, and compare these to the corresponding results for several heuristic strategies, including (space-aware) infotaxis, Thompson sampling, and QMDP. We find that the near-optimal policy found by our implementation of Perseus outperforms all heuristics we test by several measures. We use the near-optimal policy to study how the search difficulty depends on the starting location. We discuss additionally the choice of initial belief and the robustness of the policies to changes in the environment. Finally, we present a detailed and pedagogical discussion about the implementation of the Perseus algorithm, including the benefits -- and pitfalls -- of employing a reward shaping function.Comment: 35 pages, 19 figure

Simplificación de los procesos de decisión de Markov mediante reglamentación de acciones y priorización de estados

Para que se puedan construir rumbos de acción en ambientes reales, se debe considerar que las acciones pueden tener efectos distintos en el mundo (no determinismo) y ponderar el potencial de algún plan alternativo para alcanzar las metas del problema, considerando sus costes y recompensas (metas extendidas). Al respecto, la planificación basada en teoría de decisiones ha permitido solucionar problemas estocásticos, estableciendo rumbos de acción que involucran cantidades de información difíciles de procesar por el ser humano, evaluando sus fortalezas y debilidades con base en las teorías de probabilidad y de utilidad. Esta metodología ha incrementado últimamente su investigación debido al éxito de los procesos de decisión de Markov (MDPs) en problemas de investigación de operaciones, teoría de control, economía e inteligencia artificial, entre otros. Sin embargo, el problema de resolver los MDPs de considerables dimensiones con precisión y rapidez ha conducido a un reto computacional. Dado que el esfuerzo computacional es significativo, la investigación actual se centra en la búsqueda de técnicas superiores de aceleración. Por ejemplo, las propiedades de convergencia de sus métodos de solución actuales dependen, en gran medida, del orden de las operaciones de actualización. Por un lado, algoritmos tales como el de ordenamiento topológico han sido capaces de encontrar buenos ordenamientos, pero sus costes de inicio han sido usualmente altos. Por otro lado, los métodos de ruta más corta tales como el clásico algoritmo de Dijkstra, que está basado en colas de prioridad, han sido aplicados exitosamente a la solución de procesos de decisión de Markov de ruta determinística más corta. En esta tesis se propone un nuevo algoritmo de iteración de valor basado en el algoritmo de Dijkstra para resolver MDPs de ruta estocástica más corta. A diferencia de otros enfoques priorizados tales como el barrido priorizado mejorado, el enfoque aquí propuesto es capaz de tratar con múltiples estados meta y de inicio y, puesto que sucesivamente se actualiza cada estado utilizando la ecuación de Bellman, este enfoque garantiza la convergencia a la solución óptima. Además este algoritmo utiliza la función de valor actual como métrica de prioridad, puesto que el algoritmo de Dijkstra sugiere que un orden de actualización más adecuado está dado por el valor de la programación dinámica funcional. Los resultados experimentales obtenidos en una tarea de estrategias de navegación marítima en bote de vela muestran la factibilidad del enfoque propuesto. Se comprobó que el algoritmo propuesto reduce considerablemente el tiempo de solución requerido por el algoritmo de iteración de valor, desde un crecimiento de orden cuadrático -en función del número de estados- hasta uno de orden cercano a la linealidad.García Hernández, MDG. (2013). Simplificación de los procesos de decisión de Markov mediante reglamentación de acciones y priorización de estados [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/18467Palanci

Prioritizing Point-Based POMDP Solvers ⋆

Abstract. Recent scaling up of POMDP solvers towards realistic applications is largely due to point-based methods such as PBVI, Perseus, and HSVI, which quickly converge to an approximate solution for medium-sized problems. These algorithms improve a value function by using backup operations over a single belief point. In the simpler domain of MDP solvers, prioritizing the order of equivalent backup operations on states is well known to speed up convergence. We generalize the notion of prioritized backups to the POMDP framework, and show that the ordering of backup operations on belief points is important. We also present a new algorithm, Prioritized Value Iteration (PVI), and show empirically that it outperforms current point-based algorithms. Finally, a new empirical evaluation measure, based on the number of backups and the number of belief points, is proposed, in order to provide more accurate benchmark comparisons.