Multiscale Markov Decision Problems: Compression, Solution, and Transfer Learning

Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure, particularly beyond a single level of abstraction, has remained a longstanding challenge. We describe a fast multiscale procedure for repeatedly compressing, or homogenizing, Markov decision processes (MDPs), wherein a hierarchy of sub-problems at different scales is automatically determined. Coarsened MDPs are themselves independent, deterministic MDPs, and may be solved using existing algorithms. The multiscale representation delivered by this procedure decouples sub-tasks from each other and can lead to substantial improvements in convergence rates both locally within sub-problems and globally across sub-problems, yielding significant computational savings. A second fundamental aspect of this work is that these multiscale decompositions yield new transfer opportunities across different problems, where solutions of sub-tasks at different levels of the hierarchy may be amenable to transfer to new problems. Localized transfer of policies and potential operators at arbitrary scales is emphasized. Finally, we demonstrate compression and transfer in a collection of illustrative domains, including examples involving discrete and continuous statespaces.Comment: 86 pages, 15 figure

Solving MDPs with thresholded lexicographic ordering using reinforcement learning

Includes bibliographical references.2022 Fall.Multiobjective problems with a strict importance order over the objectives occur in many real-life scenarios. While Reinforcement Learning (RL) is a promising approach with a great potential to solve many real-life problems, the RL literature focuses primarily on single-objective tasks, and approaches that can directly address multiobjective with importance order have been scarce. The few proposed approach were noted to be heuristics without theoretical guarantees. However, we found that their practical applicability is very limited as they fail to find a good solution even in very common scenarios. In this work, we first investigate these shortcomings of the existing approaches and propose some solutions that could improve their practical performance. Finally, we propose a completely different approach based on policy optimization using our Lexicographic Projection Optimization (LPO) algorithm and show its performance on some benchmark problems

Utilising Assured Multi-Agent Reinforcement Learning within safety-critical scenarios

Multi-agent reinforcement learning allows a team of agents to learn how to work together to solve complex decision-making problems in a shared environment. However, this learning process utilises stochastic mechanisms, meaning that its use in safety-critical domains can be problematic. To overcome this issue, we propose an Assured Multi-Agent Reinforcement Learning (AMARL) approach that uses a model checking technique called quantitative verification to provide formal guarantees of agent compliance with safety, performance, and other non-functional requirements during and after the reinforcement learning process. We demonstrate the applicability of our AMARL approach in three different patrolling navigation domains in which multi-agent systems must learn to visit key areas by using different types of reinforcement learning algorithms (temporal difference learning, game theory, and direct policy search). Furthermore, we compare the effectiveness of these algorithms when used in combination with and without our approach. Our extensive experiments with both homogeneous and heterogeneous multi-agent systems of different sizes show that the use of AMARL leads to safety requirements being consistently satisfied and to better overall results than standard reinforcement learning

Abstractions in Reasoning for Long-Term Autonomy

The path to building adaptive, robust, intelligent agents has led researchers to develop a suite of powerful models and algorithms for agents with a single objective. However, in recent years, attempts to use this monolithic approach to solve an ever-expanding set of complex real-world problems, which increasingly include long-term autonomous deployments, have illuminated challenges in its ability to scale. Consequently, a fragmented collection of hierarchical and multi-objective models were developed. This trend continues into the algorithms as well, as each approximates an optimal solution in a different manner for scalability. These models and algorithms represent an attempt to solve pieces of an overarching problem: how can an agent explicitly model and integrate the necessary aspects of reasoning required to achieve long-term autonomy? This thesis presents a general hierarchical and multi-objective model called a policy network that unifies prior fragmented solutions into a single graphical decision-making structure. Policy networks are broadly useful to solve numerous real-world problems. This thesis focuses on autonomous vehicle (AV) problems: (1) route-planning with multiple objectives; (2) semi-autonomy with proactive transfer of control; and (3) intersection decision-making for reasoning online about any number of other vehicles and pedestrians. Formal models are presented for each of the distinct problems. Solutions are evaluated using real-world map data in simulation and demonstrated on a fully operational AV prototype driving on real public roads. Policy networks serve as a shared underlying framework for all three, enabling their seamless integration as parts of an overall solution for rich, real-world, scalable decision-making in agents with long-term autonomy