Une Approche basée sur la Simulation pour l'Optimisation des Processus Décisionnels Semi-Markoviens Généralisés

Time is a crucial variable in planning and often requires special attention since it introduces a specific structure along with additional complexity, especially in the case of decision under uncertainty. In this paper, after reviewing and comparing MDP frameworks designed to deal with temporal problems, we focus on Generalized Semi-Markov Decision Processes (GSMDP) with observable time. We highlight the inherent structure and complexity of these problems and present the differences with classical reinforcement learning problems. Finally, we introduce a new simulation-based reinforcement learning method for solving GSMDP, bringing together results from simulation-based policy iteration, regression techniques and simulation theory. We illustrate our approach on a subway network control example

A Simulation-based Approach for Solving Temporal Markov Problems

Time is a crucial variable in planning and often requires special attention since it introduces a specific structure along with additional complexity, especially in the case of decision under uncertainty. In this paper, after reviewing and comparing MDP frameworks designed to deal with temporal problems, we focus on Generalized Semi-Markov Decision Processes (GSMDP) with observable time. We highlight the inherent structure and complexity of these problems and present the differences with classical reinforcement learning problems. Finally, we introduce a new simulation-based reinforcement learning method for solving GSMDP, bringing together results from simulation-based policy iteration, regression techniques and simulation theory. We illustrate our approach on a subway network control example

Numerical Methods for Convex Multistage Stochastic Optimization

Optimization problems involving sequential decisions in a stochastic environment were studied in Stochastic Programming (SP), Stochastic Optimal Control (SOC) and Markov Decision Processes (MDP). In this paper we mainly concentrate on SP and SOC modelling approaches. In these frameworks there are natural situations when the considered problems are convex. Classical approach to sequential optimization is based on dynamic programming. It has the problem of the so-called ``Curse of Dimensionality", in that its computational complexity increases exponentially with increase of dimension of state variables. Recent progress in solving convex multistage stochastic problems is based on cutting planes approximations of the cost-to-go (value) functions of dynamic programming equations. Cutting planes type algorithms in dynamical settings is one of the main topics of this paper. We also discuss Stochastic Approximation type methods applied to multistage stochastic optimization problems. From the computational complexity point of view, these two types of methods seem to be complimentary to each other. Cutting plane type methods can handle multistage problems with a large number of stages, but a relatively smaller number of state (decision) variables. On the other hand, stochastic approximation type methods can only deal with a small number of stages, but a large number of decision variables

Utility-Aware Scheduling of Stochastic Real-Time Systems

Time utility functions offer a reasonably general way to describe the complex timing constraints of real-time and cyber-physical systems. However, utility-aware scheduling policy design is an open research problem. In particular, scheduling policies that optimize expected utility accrual are needed for real-time and cyber-physical domains. This dissertation addresses the problem of utility-aware scheduling for systems with periodic real-time task sets and stochastic non-preemptive execution intervals. We model these systems as Markov Decision Processes. This model provides an evaluation framework by which different scheduling policies can be compared. By solving the Markov Decision Process we can derive value-optimal scheduling policies for moderate sized problems. However, the time and memory complexity of computing and storing value-optimal scheduling policies also necessitates the exploration of other more scalable solutions. We consider heuristic schedulers, including a generalization we have developed for the existing Utility Accrual Packet Scheduling Algorithm. We compare several heuristics under soft and hard real-time conditions, different load conditions, and different classes of time utility functions. Based on these evaluations we present guidelines for which heuristics are best suited to particular scheduling criteria. Finally, we address the memory complexity of value-optimal scheduling, and examine trade-offs between optimality and memory complexity. We show that it is possible to derive good low complexity scheduling decision functions based on a synthesis of heuristics and reduced-memory approximations of the value-optimal scheduling policy

Learning Mazes with Aliasing States: An LCS Algorithm with Associative Perception

Learning classifier systems (LCSs) belong to a class of algorithms based on the principle of self-organization and have frequently been applied to the task of solving mazes, an important type of reinforcement learning (RL) problem. Maze problems represent a simplified virtual model of real environments that can be used for developing core algorithms of many real-world applications related to the problem of navigation. However, the best achievements of LCSs in maze problems are still mostly bounded to non-aliasing environments, while LCS complexity seems to obstruct a proper analysis of the reasons of failure. We construct a new LCS agent that has a simpler and more transparent performance mechanism, but that can still solve mazes better than existing algorithms. We use the structure of a predictive LCS model, strip out the evolutionary mechanism, simplify the reinforcement learning procedure and equip the agent with the ability of associative perception, adopted from psychology. To improve our understanding of the nature and structure of maze environments, we analyze mazes used in research for the last two decades, introduce a set of maze complexity characteristics, and develop a set of new maze environments. We then run our new LCS with associative perception through the old and new aliasing mazes, which represent partially observable Markov decision problems (POMDP) and demonstrate that it performs at least as well as, and in some cases better than, other published systems