On the Lagrange-Dirichlet converse in dimension three

Consider a mechanical system with a real analytic potential. We prove that in dimension three, there is an open and dense subset of the set of non strict local minimums of the potential such that every one of its points is a Lyapunov unstable equilibrium point.Comment: 44 page

State Augmented Constrained Reinforcement Learning: Overcoming the Limitations of Learning with Rewards

Constrained reinforcement learning involves multiple rewards that must individually accumulate to given thresholds. In this class of problems, we show a simple example in which the desired optimal policy cannot be induced by any linear combination of rewards. Hence, there exist constrained reinforcement learning problems for which neither regularized nor classical primal-dual methods yield optimal policies. This work addresses this shortcoming by augmenting the state with Lagrange multipliers and reinterpreting primal-dual methods as the portion of the dynamics that drives the multipliers evolution. This approach provides a systematic state augmentation procedure that is guaranteed to solve reinforcement learning problems with constraints. Thus, while primal-dual methods can fail at finding optimal policies, running the dual dynamics while executing the augmented policy yields an algorithm that provably samples actions from the optimal policy

Una Experiencia sobre la coordinación docente y los resultados de la asignatura transversal Informática en la Universidad Pública de Navarra

En este trabajo analizamos la experiencia de la asig-natura Informática en la Universidad Pública de Navarra (UPNa). Esta asignatura es obligatoria y común para los ocho grados en ingeniería que se imparten en la UPNa. Los alumnos de los diferentes grados pueden compartir grupo. En todos los grados, la asignatura está programada en el primer semestre del primer curso, aunque existe la posibilidad de cursarla también en el segundo semestre en caso de no haber superado la asignatura. Además, la asignatura se imparte en tres idiomas: castellano, euskera e inglés. Dada la envergadura de la asignatura, en este trabajo analizamos los mecanismos de coordinación que utilizamos para que, tanto la docencia como la evaluación de los diferentes grupos, sea lo más ecuánime posible. También estudiamos las estadísticas de los resultados obtenidos en los cinco cursos que se ha impartido la asignatura, centrándonos en las tasas de rendimiento, éxito y evaluación por grados y por idiomas, así como en las causas que pueden originar las diferencias encontradas.In this work we analyze the experience of the subject Introduction to Computer Science at the Public University of Navarra (UPNa). This subject is compulsory and common to the eight engineering degrees offered at the UPNa. Students from diferent degrees can share the same class group. In all the eight degrees the subject is programmed at the first semester of the first year, but students can also study it during the second semes-ter if they failed it in the first semester. Besides, the subject is taught in three different languages: Spanish, Basque and English. Due to the magnitude of the subject, in this work we analyze the coordination mechanisms we use to avoid biased teaching and evaluation methods. We also study the results obtained during the five years that the subject has been offered, focusing on performance, success and evaluation rates depending on the degree and the language used, as well as the reasons for the differences found

El Robot Moway, una herramienta para el aprendizaje basado en proyectos

En este trabajo se presenta la experiencia docente desarrollada en la asignatura ”Sistemas Inteligentes. Aplicaciones” mediante la metodología de aprendizaje basado en proyectos. Para el desarrollo del proyecto se ha utilizado el robot móvil Moway. Se describen las fases del proyecto, los resultados y las conclusiones obtenidas tras una experiencia de dos años.In this work is presented the teaching experience we have had in the subject ”Intelligent Systems. Applications” using the project-based learning methodology. The projects were developed using the Moway mobile robot. The different steps of the project, the results and the conclusions reached after a two-year experience are described