This paper studies the synthesis of control policies for an agent that has to satisfy a temporal logic specification in a partially observable environment, in the presence of an adversary. The interaction of the agent (defender) with the adversary is modeled as a partially observable stochastic game. The search for policies is limited to over the space of finite state controllers, which leads to a tractable approach to determine policies. The goal is to generate a defender policy to maximize satisfaction of a given temporal logic specification under any adversary policy. We relate the satisfaction of the specification in terms of reaching (a subset of) recurrent states of a Markov chain. We then present a procedure to determine a set of defender and adversary finite state controllers of given sizes that will satisfy the temporal logic specification. We illustrate our approach with an example.
Dynamic programming (DP) for POSGs has been studied in @cite_15 , resulting in an algorithm that generalizes both DP for POMDPs and iterated elimination of dominated strategies for normal form games. This work, however, considered the finite horizon case, and all agents had to maximize their own expected rewards. When agents cooperate to earn rewards, the framework is called a decentralized-POMDP (Dec-POMDP). The infinite horizon case for Dec-POMDPs was studied in @cite_42 , where the authors proposed a bounded policy iteration algorithm for policies represented as joint FSCs. A complete and optimal algorithm for deterministic FSC policies for DecPOMDPs was presented in @cite_14 . Optimization techniques for fixed-size controllers' to solve Dec-POMDPs were investigated in @cite_38 . A survey of recent research in Dec- POMDPs is presented in @cite_39 .
@cite_38 @cite_14 @cite_42 @cite_39 @cite_15
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POMDPs and their decentralized multiagent counterparts, DEC-POMDPs, offer a rich framework for sequential decision making under uncertainty. Their high computational complexity, however, presents an important research challenge. One way to address the intractable memory requirements of current algorithms is based on representing agent policies as finite-state controllers. Using this representation, we propose a new approach that formulates the problem as a nonlinear program, which defines an optimal policy of a desired size for each agent. This new formulation allows a wide range of powerful nonlinear programming algorithms to be used to solve POMDPs and DEC-POMDPs. Although solving the NLP optimally is often intractable, the results we obtain using an off-the-shelf optimization method are competitive with state-of-the-art POMDP algorithms and outperform state-of-the-art DEC-POMDP algorithms. Our approach is easy to implement and it opens up promising research directions for solving POMDPs and DEC-POMDPs using nonlinear programming methods. We develop an exact dynamic programming algorithm for partially observable stochastic games (POSGs). The algorithm is a synthesis of dynamic programming for partially observable Markov decision processes (POMDPs) and iterated elimination or dominated strategies in normal form games. We prove that when applied to finite-horizon POSGs, the algorithm iteratively eliminates very weakly dominated strategies without first forming a normal form representation of the game. For the special case in which agents share the same payoffs, the algorithm can be used to find an optimal solution. We present preliminary empirical results and discuss ways to further exploit POMDP theory in solving POSGs. There has been substantial progress on algorithms for single-agent sequential decision making using partially observable Markov decision processes (POMDPs). A number of efficient algorithms for solving POMDPs share two desirable properties: error-bounds and fast convergence rates. Despite significant efforts, no algorithms for solving decentralized POMDPs benefit from these properties, leading to either poor solution quality or limited scalability. This paper presents the first approach for solving transition independent decentralized Markov decision processes (Dec-MDPs), that inherits these properties. Two related algorithms illustrate this approach. The first recasts the original problem as a deterministic and completely observable Markov decision process. In this form, the original problem is solved by combining heuristic search with constraint optimization to quickly converge into a near-optimal policy. This algorithm also provides the foundation for the first algorithm for solving infinite-horizon transition independent decentralized MDPs. We demonstrate that both methods outperform state-of-the-art algorithms by multiple orders of magnitude, and for infinite-horizon decentralized MDPs, the algorithm is able to construct more concise policies by searching cyclic policy graphs. Decentralized partially observable Markov decision processes (DEC-POMDPs) form a general framework for planning for groups of cooperating agents that inhabit a stochastic and partially observable environment. Unfortunately, computing optimal plans in a DEC-POMDP has been shown to be intractable (NEXP-complete), and approximate algorithms for specific subclasses have been proposed. Many of these algorithms rely on an (approximate) solution of the centralized planning problem (i.e., treating the whole team as a single agent). We take a more decentralized approach, in which each agent only reasons over its own local state and some uncontrollable state features, which are shared by all team members. In contrast to other approaches, we model communication as an integral part of the agent's reasoning, in which the meaning of a message is directly encoded in the policy of the communicating agent. We explore iterative methods for approximately solving such models, and we conclude with some encouraging preliminary experimental results. We present a bounded policy iteration algorithm for infinite-horizon decentralized POMDPs. Policies are represented as joint stochastic finite-state controllers, which consist of a local controller for each agent. We also let a joint controller include a correlation device that allows the agents to correlate their behavior without exchanging information during execution, and show that this leads to improved performance. The algorithm uses a fixed amount of memory, and each iteration is guaranteed to produce a controller with value at least as high as the previous one for all possible initial state distributions. For the case of a single agent, the algorithm reduces to Poupart and Boutilier's bounded policy iteration for POMDPs. Decentralized partially observable Markov decision processes (Dec-POMDPs) constitute an expressive framework for multiagent planning under uncertainty, but solving them is provably intractable. We demonstrate how their scalability can be improved by exploiting locality of interaction between agents in a factored representation. Factored Dec-POMDP representations have been proposed before, but only for Dec-POMDPs whose transition and observation models are fully independent. Such strong assumptions simplify the planning problem, but result in models with limited applicability. By contrast, we consider general factored Dec-POMDPs for which we analyze the model dependencies over space (locality of interaction) and time (horizon of the problem). We also present a formulation of decomposable value functions. Together, our results allow us to exploit the problem structure as well as heuristics in a single framework that is based on collaborative graphical Bayesian games (CGBGs). A preliminary experiment shows a speedup of two orders of magnitude. Decentralized POMDPs are powerful theoretical models for coordinating agents' decisions in uncertain environments, but the generally-intractable complexity of optimal joint policy construction presents a significant obstacle in applying Dec-POMDPs to problems where many agents face many policy choices. Here, we argue that when most agent choices are independent of other agents' choices, much of this complexity can be avoided: instead of coordinating full policies, agents need only coordinate policy abstractions that explicitly convey the essential interaction influences. To this end, we develop a novel framework for influence-based policy abstraction for weakly-coupled transition-dependent Dec-POMDP problems that subsumes several existing approaches. In addition to formally characterizing the space of transition-dependent influences, we provide a method for computing optimal and approximately-optimal joint policies. We present an initial empirical analysis, over problems with commonly-studied flavors of transition-dependent influences, that demonstrates the potential computational benefits of influence-based abstraction over state-of-the-art optimal policy search methods. Dec-POMDPs are a powerful framework for planning in multiagent systems, but are provably intractable to solve. Despite recent work on scaling to more agents by exploiting weak couplings in factored models, scalability for unrestricted subclasses remains limited. This paper proposes a factored forward-sweep policy computation method that tackles the stages of the problem one by one, exploiting weakly coupled structure at each of these stages. To enable the method to scale to many agents, we propose a set of approximations: approximation of stages using a sparse interaction structure, bootstrapping off smaller tasks to compute heuristic payoff functions, and employing approximate inference to estimate required probabilities at each stage and to compute the best decision rules. An empirical evaluation shows that the loss in solution quality due to these approximations is small and that the proposed method achieves unprecedented scalability, solving Dec-POMDPs with hundreds of agents. Autonomous agents operating in partially observable stochastic environments often face the problem of optimizing expected performance while bounding the risk of violating safety constraints. Such problems can be modeled as chance-constrained POMDP's (CC-POMDP's). Our first contribution is a systematic derivation of execution risk in POMDP domains, which improves upon how chance constraints are handled in the constrained POMDP literature. Second, we present RAO*, a heuristic forward search algorithm producing optimal, deterministic, finite-horizon policies for CC-POMDP's. In addition to the utility heuristic, RAO* leverages an admissible execution risk heuristic to quickly detect and prune overly-risky policy branches. Third, we demonstrate the usefulness of RAO* in two challenging domains of practical interest: power supply restoration and autonomous science agents. Partially observable Markov decision processes (POMDPs) provide a principled framework for modeling an agent's decision-making problem when the agent needs to consider noisy state estimates. POMDP policies take into account an action's influence on the environment as well as the potential information gain. This is a crucial feature for robotic agents which generally have to consider the effect of actions on sensing. However, building POMDP models which reward information gain directly is not straightforward, but is important in domains such as robot-assisted surveillance in which the value of information is hard to quantify. Common techniques for uncertainty reduction such as expected entropy minimization lead to non-standard POMDPs that are hard to solve. We present the POMDP with Information Rewards (POMDP-IR) modeling framework, which rewards an agent for reaching a certain level of belief regarding a state feature. By remaining in the standard POMDP setting we can exploit many known results as well as successful approximate algorithms. We demonstrate our ideas in a toy problem as well as in real robot-assisted surveillance, showcasing their use for active cooperative perception scenarios. Finally, our experiments show that the POMDP-IR framework compares favorably with a related approach on benchmark domains. Most algorithms for solving POMDPs iteratively improve a value function that implicitly represents a policy and are said to search in value function space. This paper presents an approach to solving POMDPs that represents a policy explicitly as a finite-state controller and iteratively improves the controller by search in policy space. Two related algorithms illustrate this approach. The first is a policy iteration algorithm that can outperform value iteration in solving infinitehorizon POMDPs. It provides the foundation for a new heuristic search algorithm that promises further speedup by focusing computational effort on regions of the problem space that are reachable, or likely to be reached, from a start state. We introduce a principled method for multi-robot coordination based on a general model termed a MacDec-POMDP of multi-robot cooperative planning in the presence of stochasticity, uncertain sensing, and communication limitations. A new MacDec-POMDP planning algorithm is presented that searches over policies represented as finite-state controllers, rather than the previous policy tree representation. Finite-state controllers can be much more concise than trees, are much easier to interpret, and can operate over an infinite horizon. The resulting policy search algorithm requires a substantially simpler simulator that models only the outcomes of executing a given set of motor controllers, not the details of the executions themselves and can solve significantly larger problems than existing MacDec-POMDP planners. We demonstrate significant performance improvements over previous methods and show that our method can be used for actual multi-robot systems through experiments on a cooperative multi-robot bartending domain. This book introduces multiagent planning under uncertainty as formalized by decentralized partially observable Markov decision processes (Dec-POMDPs). The intended audience is researchers and graduate students working in the fields of artificial intelligence related to sequential decision making: reinforcement learning, decision-theoretic planning for single agents, classical multiagent planning, decentralized control, and operations research. In many real-world multiagent applications such as distributed sensor nets, a network of agents is formed based on each agent's limited interactions with a small number of neighbors. While distributed POMDPs capture the real-world uncertainty in multiagent domains, they fail to exploit such locality of interaction. Distributed constraint optimization (DCOP) captures the locality of interaction but fails to capture planning under uncertainty. This paper present a new model synthesized from distributed POMDPs and DCOPs, called Networked Distributed POMDPs (ND-POMDPs). Exploiting network structure enables us to present two novel algorithms for ND-POMDPs: a distributed policy generation algorithm that performs local search and a systematic policy search that is guaranteed to reach the global optimal. We propose a new approach to the problem of searching a space of policies for a Markov decision process (MDP) or a partially observable Markov decision process (POMDP), given a model. Our approach is based on the following observation: Any (PO)MDP can be transformed into an "equivalent" POMDP in which all state transitions (given the current state and action) are deterministic. This reduces the general problem of policy search to one in which we need only consider POMDPs with deterministic transitions. We give a natural way of estimating the value of all policies in these transformed POMDPs. Policy search is then simply performed by searching for a policy with high estimated value. We also establish conditions under which our value estimates will be good, recovering theoretical results similar to those of Kearns, Mansour and Ng (1999), but with "sample complexity" bounds that have only a polynomial rather than exponential dependence on the horizon time. Our method applies to arbitrary POMDPs, including ones with infinite state and action spaces. We also present empirical results for our approach on a small discrete problem, and on a complex continuous state continuous action problem involving learning to ride a bicycle. Just as POMDPs have been used to reason explicitly about uncertainty in single-agent systems, there has been recent interest in using multi-agent POMDPs to coordinate teams of agents in the presence of uncertainty. Although multi-agent POMDPs are known to be highly intractable, communication at every time step transforms a multi-agent POMDP into a more tractable single-agent POMDP. In this paper, we present an approach that generates "centralized" policies for multi-agent POMDPs at plan-time by assuming the presence of free communication, and at run-time, handles the problem of limited communication resources by reasoning about the use of communication as needed for effective execution. This approach trades off the need to do some computation at execution-time for the ability to generate policies more tractably at plan-time. In our algorithm, each agent, at run-time, models the distribution of possible joint beliefs. Joint actions are selected over this distribution, ensuring that agents remain synchronized. Communication is used to integrate local observations into the team belief only when those observations would improve team performance. We show, both through a detailed example and with experimental results, that our approach allows for effective decentralized execution while avoiding unnecessary instances of communication. Decentralized Partially Observable Markov Decision Processes (Dec-POMDPs) provide powerful modeling tools for multiagent decision-making in the face of uncertainty, but solving these models comes at a very high computational cost. Two avenues for side-stepping the computational burden can be identified: structured interactions between agents and intra-agent communication. In this paper, we focus on the interplay between these concepts, namely how sparse interactions impact the communication needs. A key insight is that in domains with local interactions the amount of communication necessary for successful joint behavior can be heavily reduced, due to the limited influence between agents. We exploit this insight by deriving local POMDP models that optimize each agent's communication behavior. Our experimental results show that our approach successfully exploits sparse interactions: we can effectively identify the situations in which it is beneficial to communicate, as well as trade off the cost of communication with overall task performance. Despite the significant progress to extend Markov Decision Processes (MDP) to cooperative multi-agent systems, developing approaches that can deal with realistic problems remains a serious challenge. Existing approaches that solve Decentralized Markov Decision Processes (DEC-MDPs) suffer from the fact that they can only solve relatively small problems without complex constraints on task execution. OC-DEC-MDP has been introduced to deal with large DEC-MDPs under resource and temporal constraints. However, the proposed algorithm to solve this class of DEC-MDPs has some limits: it suffers from overestimation of opportunity cost and restricts policy improvement to one sweep (or iteration). In this paper, we propose to overcome these limits by first introducing the notion of Expected Opportunity Cost to better assess the influence of a local decision of an agent on the others. We then describe an iterative version of the algorithm to incrementally improve the policies of agents leading to higher quality solutions in some settings. Experimental results are shown to support our claims. In this paper, we address the problem of suboptimal behavior during online partially observable Markov decision process (POMDP) planning caused by time constraints on planning. Taking inspiration from the related field of reinforcement learning (RL), our solution is to shape the agent's reward function in order to lead the agent to large future rewards without having to spend as much time explicitly estimating cumulative future rewards, enabling the agent to save time to improve the breadth planning and build higher quality plans. Specifically, we extend potential-based reward shaping (PBRS) from RL to online POMDP planning. In our extension, information about belief states is added to the function optimized by the agent during planning. This information provides hints of where the agent might find high future rewards beyond its planning horizon, and thus achieve greater cumulative rewards. We develop novel potential functions measuring information useful to agent metareasoning in POMDPs (reflecting on agent knowledge and or histories of experience with the environment), theoretically prove several important properties and benefits of using PBRS for online POMDP planning, and empirically demonstrate these results in a range of classic benchmark POMDP planning problems. Automated sequential decision making is crucial in many contexts. In the face of uncertainty, this task becomes even more important, though at the same time, computing optimal decision policies becomes more complex. The more sources of uncertainty there are, the harder the problem becomes to solve. In this work, we look at sequential decision making in environments where the actions have probabilistic outcomes and in which the system state is only partially observable. We focus on using a model called a partially observable Markov decision process (POMDP) and explore algorithms which address computing both optimal and approximate policies for use in controlling processes that are modeled using POMDPs. Although solving for the optimal policy is PSPACE-complete (or worse), the study and improvements of exact algorithms lends insight into the optimal solution structure as well as providing a basis for approximate solutions. We present some improvements, analysis and empirical comparisons for some existing and some novel approaches for computing the optimal POMDP policy exactly. Since it is also hard (NP-complete or worse) to derive close approximations to the optimal solution for POMDPs, we consider a number of approaches for deriving policies that yield sub-optimal control and empirically explore their performance on a range of problems. These approaches borrow and extend ideas from a number of areas; from the more mathematically motivated techniques in reinforcement learning and control theory to entirely heuristic control rules.