Dual formulations for optimizing Dec-POMDP controllers

Decentralized POMDP is an expressive model for multi-agent planning. Finite-state controllers (FSCs)---often used to represent policies for infinite-horizon problems---offer a compact, simple-to-execute policy representation. We exploit novel connections between optimizing decentralized FSCs and the dual linear program for MDPs. Consequently, we describe a dual mixed integer linear program (MIP) for optimizing deterministic FSCs. We exploit the Dec-POMDP structure to devise a compact MIP and formulate constraints that result in policies executable in partially-observable decentralized settings. We show analytically that the dual formulation can also be exploited within the expectation maximization (EM) framework to optimize stochastic FSCs. The resulting EM algorithm can be implemented by solving a sequence of linear programs, without requiring expensive message-passing over the Dec-POMDP DBN. We also present an efficient technique for policy improvement based on a weighted entropy measure. Compared with state-of-the-art FSC methods, our approach offers over an order-of-magnitude speedup, while producing similar or better solutions

Probabilistic Inference Techniques for Scalable Multiagent Decision Making

Decentralized POMDPs provide an expressive framework for multiagent sequential decision making. However, the complexity of these models—NEXP-Complete even for two agents—has limited their scalability. We present a promising new class of approxima-tion algorithms by developing novel connections between multiagent planning and machine learning. We show how the multiagent planning problem can be reformulated as inference in a mixture of dynamic Bayesian networks (DBNs). This planning-as-inference approach paves the way for the application of efficient inference techniques in DBNs to multiagent decision making. To further improve scalability, we identify certain conditions that are sufficient to extend the approach to multiagent systems with dozens of agents. Specifically, we show that the necessary inference within the expectation-maximization framework can be decomposed into processes that often involve a small subset of agents, thereby facilitating scalability. We further show that a number of existing multiagent planning models satisfy these conditions. Experiments on large planning benchmarks confirm the benefits of our approach in terms of runtime and scalability with respect to existing techniques

Agent Interactions In Decentralized Environments

The decentralized Markov decision process (Dec-POMDP) is a powerful formal model for studying multiagent problems where cooperative, coordinated action is optimal, but each agent acts based on local data alone. Unfortunately, it is known that Dec-POMDPs are fundamentally intractable: they are NEXP-complete in the worst case, and have been empirically observed to be beyond feasible optimal solution. To get around these obstacles, researchers have focused on special classes of the general Dec-POMDP problem, restricting the degree to which agent actions can interact with one another. In some cases, it has been proven that these sorts of structured forms of interaction can in fact reduce worst-case complexity. Where formal proofs have been lacking, empirical observations suggest that this may also be true for other cases, although less is known precisely. This thesis unifies a range of this existing work, extending analysis to establish novel complexity results for some popular restricted-interaction models. We also establish some new results concerning cases for which reduced complexity has been proven, showing correspondences between basic structural features and the potential for dimensionality reduction when employing mathematical programming techniques. As our new complexity results establish that worst-case intractability is more widespread than previously known, we look to new ways of analyzing the potential average-case difficulty of Dec-POMDP instances. As this would be extremely difficult using the tools of traditional complexity theory, we take a more empirical approach. In so doing, we identify new analytical measures that apply to all Dec-POMDPs, whatever their structure. These measures allow us to identify problems that are potentially easier to solve on average, and validate this claim empirically. As we show, the performance of well-known optimal dynamic programming methods correlates with our new measure of difficulty. Finally, we explore the approximate case, showing that our measure works well as a predictor of difficulty there, too, and provides a means of setting algorithm parameters to achieve far more efficient performance

Perseus: Randomized Point-based Value Iteration for POMDPs

Partially observable Markov decision processes (POMDPs) form an attractive and principled framework for agent planning under uncertainty. Point-based approximate techniques for POMDPs compute a policy based on a finite set of points collected in advance from the agents belief space. We present a randomized point-based value iteration algorithm called Perseus. The algorithm performs approximate value backup stages, ensuring that in each backup stage the value of each point in the belief set is improved; the key observation is that a single backup may improve the value of many belief points. Contrary to other point-based methods, Perseus backs up only a (randomly selected) subset of points in the belief set, sufficient for improving the value of each belief point in the set. We show how the same idea can be extended to dealing with continuous action spaces. Experimental results show the potential of Perseus in large scale POMDP problems

Optimally solving Dec-POMDPs as Continuous-State MDPs: Theory and Algorithms

Decentralized partially observable Markov decision processes (Dec-POMDPs) provide a general model for decision-making under uncertainty in cooperative decentralized settings, but are difficult to solve optimally (NEXP-Complete). As a new way of solving these problems, we introduce the idea of transforming a Dec-POMDP into a continuous-state deterministic MDP with a piecewise-linear and convex value function. This approach makes use of the fact that planning can be accomplished in a centralized offline manner, while execution can still be distributed. This new Dec-POMDP formulation, which we call an occupancy MDP, allows powerful POMDP and continuous-state MDP methods to be used for the first time. When the curse of dimensionality becomes too prohibitive, we refine this basic approach and present ways to combine heuristic search and compact representations that exploit the structure present in multi-agent domains, without losing the ability to eventually converge to an optimal solution. In particular, we introduce feature-based heuristic search that relies on feature-based compact representations, point-based updates and efficient action selection. A theoretical analysis demonstrates that our feature-based heuristic search algorithms terminate in finite time with an optimal solution. We include an extensive empirical analysis using well known benchmarks, thereby demonstrating our approach provides significant scalability improvements compared to the state of the art.Les processus de décision markoviens partiellement observables décentralisés (Dec-POMDP) fournissent un modèle général pour la prise de décision dans l'incertain dans des cadres coopératifs décentralisés. En guise de nouvelle approche de résolution de ces problèmes, nous introduisons l'idée de transformer un Dec-POMDP en un MDP déterministe à espace d'états continu dont la fonction de valeur est linéaire par morceaux et convexe. Cette approche exploite le fait que la planification peut être effectuée d'une manière centralisée hors ligne, alors que l'exécution peut toujours être distribuée. Cette nouvelle formulation des Dec-POMDP, que nous appelons un occupancy MDP, permet pour la première fois d'employer de puissantes méthodes de résolution de POMDP et MDP à états continus. La malédiction de la dimensionalité devenant prohibitive, nous raffinons cette approche basique et présentons des façons de combiner la recherche heuristique et des représentations compactes qui exploitent la structure présente dans les domaines multi-agents, sans perdre la capacité de converger à terme vers une solution optimale. En particulier, nous introduisons une recherche heuristique qui repose sur des représentations compactes fondées sur des features, sur des mises-à-jour à base de points, et une sélection d'action efficace. Une analyse théorique démontre que nos algorithmes de recherche heuristique fondés sur des features se terminent en temps fini avec une solution optimale. Nous incluons une analyse empirique extensive utilisant des bancs d'essai bien connus, démontrant ainsi que notre approche améliore significativement le passage à l'échelle en comparaison de l'état de l'art

Multiagent Planning and Learning As MILP

National audienceThe decentralized partially observable Markov decisionprocess offers a unified framework for sequential decision-making by multiple collaborating agents but remains in-tractable. Mixed-integer linear formulations proved use-ful for partially observable domains, unfortunately ex-isting applications restrict to domains with one or twoagents. In this paper, we exploit a linearization propertythat allows us to reformulate nonlinear constraints fromn-agent settings into linear ones. We further present plan-ning and learning approaches relying on MILP formula-tions for general and special cases, including network-distributed and transition-independent problems. Experi-ments on standard2-agent benchmarks as well as domainswith a large number of agents provide strong empiricalsupport to the methodology.Les processus décisionnels de Markov décentralises et partiellement observables (Dec-POMDPs) offrent un cadre unifie pour la prise de décisions séquentielles par de plusieurs agents collaboratifs—mais ils restent difficiles`a résoudre. Les reformulations en programmes linéaires mixtes (PLMs) se sont avérées utiles pour les processus décisionnels de Markov partiellement observables.Malheureusement, les applications existantes se limitent uniquement aux domaines mobilisant un ou deux agents. Dans cet article, nous exploitons une propriété de linéarisation qui nous permet de reformuler les contraintes non linéaires, omniprésentes dans les systèmes multi-agents, pour en faire des contraintes linéaires. Nous présentons en outre des approches de planification et d’apprentissage s’appuyant sur de nouvelles reformulations en PLMs des Dec-POMDPs, dans le cas général ainsi que quelques cas spécifiques. Les expérimentations sur des bancs de test standards`a deux et plus de deux agents fournissent un solide soutien`a cette méthodologie

Techniques for the allocation of resources under uncertainty

L’allocation de ressources est un problème omniprésent qui survient dès que des ressources limitées doivent être distribuées parmi de multiples agents autonomes (e.g., personnes, compagnies, robots, etc). Les approches standard pour déterminer l’allocation optimale souffrent généralement d’une très grande complexité de calcul. Le but de cette thèse est de proposer des algorithmes rapides et efficaces pour allouer des ressources consommables et non consommables à des agents autonomes dont les préférences sur ces ressources sont induites par un processus stochastique. Afin d’y parvenir, nous avons développé de nouveaux modèles pour des problèmes de planifications, basés sur le cadre des Processus Décisionnels de Markov (MDPs), où l’espace d’actions possibles est explicitement paramétrisés par les ressources disponibles. Muni de ce cadre, nous avons développé des algorithmes basés sur la programmation dynamique et la recherche heuristique en temps-réel afin de générer des allocations de ressources pour des agents qui agissent dans un environnement stochastique. En particulier, nous avons utilisé la propriété acyclique des créations de tâches pour décomposer le problème d’allocation de ressources. Nous avons aussi proposé une stratégie de décomposition approximative, où les agents considèrent des interactions positives et négatives ainsi que les actions simultanées entre les agents gérants les ressources. Cependant, la majeure contribution de cette thèse est l’adoption de la recherche heuristique en temps-réel pour l’allocation de ressources. À cet effet, nous avons développé une approche basée sur la Q-décomposition munie de bornes strictes afin de diminuer drastiquement le temps de planification pour formuler une politique optimale. Ces bornes strictes nous ont permis d’élaguer l’espace d’actions pour les agents. Nous montrons analytiquement et empiriquement que les approches proposées mènent à des diminutions de la complexité de calcul par rapport à des approches de planification standard. Finalement, nous avons testé la recherche heuristique en temps-réel dans le simulateur SADM, un simulateur d’allocation de ressource pour une frégate.Resource allocation is an ubiquitous problem that arises whenever limited resources have to be distributed among multiple autonomous entities (e.g., people, companies, robots, etc). The standard approaches to determine the optimal resource allocation are computationally prohibitive. The goal of this thesis is to propose computationally efficient algorithms for allocating consumable and non-consumable resources among autonomous agents whose preferences for these resources are induced by a stochastic process. Towards this end, we have developed new models of planning problems, based on the framework of Markov Decision Processes (MDPs), where the action sets are explicitly parameterized by the available resources. Given these models, we have designed algorithms based on dynamic programming and real-time heuristic search to formulating thus allocations of resources for agents evolving in stochastic environments. In particular, we have used the acyclic property of task creation to decompose the problem of resource allocation. We have also proposed an approximative decomposition strategy, where the agents consider positive and negative interactions as well as simultaneous actions among the agents managing the resources. However, the main contribution of this thesis is the adoption of stochastic real-time heuristic search for a resource allocation. To this end, we have developed an approach based on distributed Q-values with tight bounds to diminish drastically the planning time to formulate the optimal policy. These tight bounds enable to prune the action space for the agents. We show analytically and empirically that our proposed approaches lead to drastic (in many cases, exponential) improvements in computational efficiency over standard planning methods. Finally, we have tested real-time heuristic search in the SADM simulator, a simulator for the resource allocation of a platform

Formal Methods for Autonomous Systems

Formal methods refer to rigorous, mathematical approaches to system development and have played a key role in establishing the correctness of safety-critical systems. The main building blocks of formal methods are models and specifications, which are analogous to behaviors and requirements in system design and give us the means to verify and synthesize system behaviors with formal guarantees. This monograph provides a survey of the current state of the art on applications of formal methods in the autonomous systems domain. We consider correct-by-construction synthesis under various formulations, including closed systems, reactive, and probabilistic settings. Beyond synthesizing systems in known environments, we address the concept of uncertainty and bound the behavior of systems that employ learning using formal methods. Further, we examine the synthesis of systems with monitoring, a mitigation technique for ensuring that once a system deviates from expected behavior, it knows a way of returning to normalcy. We also show how to overcome some limitations of formal methods themselves with learning. We conclude with future directions for formal methods in reinforcement learning, uncertainty, privacy, explainability of formal methods, and regulation and certification

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