Decentralized Partially Observable Markov Decision Processes Research Articles

Informed Initial Policies for Learning in Dec-POMDPs

Decentralized partially observable Markov decision processes (Dec-POMDPs) offer a formal model for planning in cooperative multiagent systems where agents operate with noisy sensors and actuators, and local information. Prevalent Dec-POMDP solution techniques have mostly been centralized and have assumed knowledge of the model. In real world scenarios, however, solving centrally may not be an option and model parameters maybe unknown. To address this, we propose a distributed, model-free algorithm for learning Dec-POMDP policies, in which agents take turns learning, with each agent not currently learning following a static policy. For agents that have not yet learned a policy, this static policy must be initialized. We propose a principled method for learning such initial policies through interaction with the environment. We show that by using such informed initial policies, our alternate learning algorithm can find near-optimal policies for two benchmark problems.

Sample Bounded Distributed Reinforcement Learning for Decentralized POMDPs

Decentralized partially observable Markov decision processes (Dec-POMDPs) offer a powerful modeling technique for realistic multi-agent coordination problems under uncertainty. Prevalent solution techniques are centralized and assume prior knowledge of the model. We propose a distributed reinforcement learning approach, where agents take turns to learn best responses to each other’s policies. This promotes decentralization of the policy computation problem, and relaxes reliance on the full knowledge of the problem parameters. We derive the relation between the sample complexity of best response learning and error tolerance. Our key contribution is to show that sample complexity could grow exponentially with the problem horizon. We show empirically that even if the sample requirement is set lower than what theory demands, our learning approach can produce (near) optimal policies in some benchmark Dec-POMDP problems.

Dependency Stochastic Boolean Satisfiability: A Logical Formalism for NEXPTIME Decision Problems with Uncertainty

Stochastic Boolean Satisfiability (SSAT) is a logical formalism to model decision problems with uncertainty, such as Partially Observable Markov Decision Process (POMDP) for verification of probabilistic systems. SSAT, however, is limited by its descriptive power within the PSPACE complexity class. More complex problems, such as the NEXPTIME-complete Decentralized POMDP (Dec-POMDP), cannot be succinctly encoded with SSAT. To provide a logical formalism of such problems, we generalize the Dependency Quantified Boolean Formula (DQBF), a representative problem in the NEXPTIME-complete class, to its stochastic variant, named Dependency SSAT (DSSAT), and show that DSSAT is also NEXPTIME-complete. We demonstrate the potential applications of DSSAT to circuit synthesis of probabilistic and approximate design. Furthermore, to study the descriptive power of DSSAT, we establish a polynomial-time reduction from Dec-POMDP to DSSAT. With the theoretical foundations paved in this work, we hope to encourage the development of DSSAT solvers for potential broad applications.

Forward and Backward Bellman Equations Improve the Efficiency of the EM Algorithm for DEC-POMDP.

Decentralized partially observable Markov decision process (DEC-POMDP) models sequential decision making problems by a team of agents. Since the planning of DEC-POMDP can be interpreted as the maximum likelihood estimation for the latent variable model, DEC-POMDP can be solved by the EM algorithm. However, in EM for DEC-POMDP, the forward–backward algorithm needs to be calculated up to the infinite horizon, which impairs the computational efficiency. In this paper, we propose the Bellman EM algorithm (BEM) and the modified Bellman EM algorithm (MBEM) by introducing the forward and backward Bellman equations into EM. BEM can be more efficient than EM because BEM calculates the forward and backward Bellman equations instead of the forward–backward algorithm up to the infinite horizon. However, BEM cannot always be more efficient than EM when the size of problems is large because BEM calculates an inverse matrix. We circumvent this shortcoming in MBEM by calculating the forward and backward Bellman equations without the inverse matrix. Our numerical experiments demonstrate that the convergence of MBEM is faster than that of EM.

Hybrid Dec-POMDP/PID Guidance System for Formation Flight of Multiple UAVs

This paper proposes a guidance system with a new hybrid architecture for multiple fixed-wing unmanned aerial vehicles (UAVs) formation flight. The proposed architecture is hybrid in the sense of combining two control policies found in guidance systems: the Decentralized Partially Observable Markov Decision Process (Dec-POMDP) policy and the well-known PID controller. The Dec-POMDP policy part enables every UAV to avoid collision with any other UAV from the formation. The PID part is activated for regions far from the collision risk zone and is implemented in such a way that each UAV is completely controlled by only its own data, independent of its neighbors. The major novelty of the proposed system, compared to other hybrid approaches, is its decentralized nature which favors overcoming the usual problems that come with centralization such as the high dependence on a central decision node, a leader, or a ground station. Inherited from both parts, the overall system performance is robust in noisy and uncertain environments. Simulations were extensively performed to show the effectiveness of the proposed guidance system in distinct scenarios.

Multi-UAV Path Planning for Wireless Data Harvesting With Deep Reinforcement Learning

Harvesting data from distributed Internet of Things (IoT) devices with multiple autonomous unmanned aerial vehicles (UAVs) is a challenging problem requiring flexible path planning methods. We propose a multi-agent reinforcement learning (MARL) approach that, in contrast to previous work, can adapt to profound changes in the scenario parameters defining the data harvesting mission, such as the number of deployed UAVs, number, position and data amount of IoT devices, or the maximum flying time, without the need to perform expensive recomputations or relearn control policies. We formulate the path planning problem for a cooperative, non-communicating, and homogeneous team of UAVs tasked with maximizing collected data from distributed IoT sensor nodes subject to flying time and collision avoidance constraints. The path planning problem is translated into a decentralized partially observable Markov decision process (Dec-POMDP), which we solve through a deep reinforcement learning (DRL) approach, approximating the optimal UAV control policy without prior knowledge of the challenging wireless channel characteristics in dense urban environments. By exploiting a combination of centered global and local map representations of the environment that are fed into convolutional layers of the agents, we show that our proposed network architecture enables the agents to cooperate effectively by carefully dividing the data collection task among themselves, adapt to large complex environments and state spaces, and make movement decisions that balance data collection goals, flight-time efficiency, and navigation constraints. Finally, learning a control policy that generalizes over the scenario parameter space enables us to analyze the influence of individual parameters on collection performance and provide some intuition about system-level benefits.

Multi-agent active information gathering in discrete and continuous-state decentralized POMDPs by policy graph improvement

Decentralized policies for information gathering are required when multiple autonomous agents are deployed to collect data about a phenomenon of interest when constant communication cannot be assumed. This is common in tasks involving information gathering with multiple independently operating sensor devices that may operate over large physical distances, such as unmanned aerial vehicles, or in communication limited environments such as in the case of autonomous underwater vehicles. In this paper, we frame the information gathering task as a general decentralized partially observable Markov decision process (Dec-POMDP). The Dec-POMDP is a principled model for co-operative decentralized multi-agent decision-making. An optimal solution of a Dec-POMDP is a set of local policies, one for each agent, which maximizes the expected sum of rewards over time. In contrast to most prior work on Dec-POMDPs, we set the reward as a non-linear function of the agents’ state information, for example the negative Shannon entropy. We argue that such reward functions are well-suited for decentralized information gathering problems. We prove that if the reward function is convex, then the finite-horizon value function of the Dec-POMDP is also convex. We propose the first heuristic anytime algorithm for information gathering Dec-POMDPs, and empirically prove its effectiveness by solving discrete problems an order of magnitude larger than previous state-of-the-art. We also propose an extension to continuous-state problems with finite action and observation spaces by employing particle filtering. The effectiveness of the proposed algorithms is verified in domains such as decentralized target tracking, scientific survey planning, and signal source localization.

Decentralized Computation Offloading in IoT Fog Computing System With Energy Harvesting: A Dec-POMDP Approach

Recently, fog computing has emerged as a prospective technique to provide pervasive and agile computation services for Internet-of-Things (IoT) devices and support advanced applications. Introducing the energy harvesting (EH) technique into the fog computing system can extend the battery lifetime and provide a higher quality of experiences (QoE) for IoT devices. In the EH-enabled IoT fog system, computation offloading is an important issue and has attracted much attention. In most existing works, it is assumed that the IoT device is fully aware of the system state. However, in practical offloading problems, the IoT device may not be able to obtain accurate system state information, and only have a partial observation of the environment. Therefore, in this article, we investigate the decentralized partially observable offloading problem in the EH-enabled IoT fog system, in which multiple IoT devices cooperate to maximize the network performance while meeting their QoE requirements. We formulate the optimization problem as a decentralized partially observable Markov decision process (Dec-POMDP) in which each IoT device makes the task offloading decisions according to its local observation of the environment. The Lagrangian approach and the policy gradient method are adopted to find the optimal solution for the proposed problem. Due to the high complexity of solving the Dec-POMDP, a learning-based decentralized offloading algorithm with low complexity is presented to find the approximate optimal solution. Finally, extensive experimental evaluation and comparison are carried out to show the effectiveness of the proposed scheme.

Decentralized Incremental Fuzzy Reinforcement Learning for Multi-Agent Systems

We present a new incremental fuzzy reinforcement learning algorithm to find a sub-optimal policy for infinite-horizon Decentralized Partially Observable Markov Decision Processes (Dec-POMDPs). The algorithm addresses the high computational complexity of solving large Dec-POMDPs by generating a compact fuzzy rule-base for each agent. In our method, each agent uses its own fuzzy rule-base to make the decisions. The fuzzy rules in these rule-bases are incrementally created and tuned according to experiences of the agents. Reinforcement learning is used to tune the behavior of each agent in such a way that maximum global reward is achieved. In addition, we propose a method to construct the initial rule-base for each agent using the solution of the underlying MDP. This drastically improves the performance of the algorithm in comparison with random initialization of the rule-base. We assess the performance of our proposed method using several benchmark problems in comparison with some state-of-the-art methods. Experimental results show that our algorithm achieves better or similar reward when compared with other methods. However, from the runtime point of view, our method is superior to all previous methods. Using a compact fuzzy rule-base not only decreases the amount of memory used but also significantly speeds up the learning phase.

Fast Q-Learning for Improved Finite Length Performance of Irregular Repetition Slotted ALOHA

In this paper, we study the problem of designing adaptive Medium Access Control (MAC) solutions for wireless sensor networks (WSNs) under the Irregular Repetition Slotted ALOHA (IRSA) protocol. In particular, we optimize the degree distribution employed by IRSA for finite frame sizes. Motivated by characteristics of WSNs, such as the restricted computational resources and partial observability, we model the design of IRSA as a Decentralized Partially Observable Markov Decision Process (Dec-POMDP). We have theoretically analyzed our solution in terms of optimality of the learned IRSA design and derived guarantees for finding near-optimal policies. These guarantees are generic and can be applied in resource allocation problems that exhibit the waterfall effect , which in our setting manifests itself as a severe degradation in the overall throughput of the network above a particular channel load. Furthermore, we combat the inherent non-stationarity of the learning environment in WSNs by advancing classical Q-learning through the use of virtual experience (VE), a technique that enables the update of multiple state-action pairs per learning iteration and, thus, accelerates convergence. Our simulations confirm the superiority of our learning-based MAC solution compared to traditional IRSA and provide insights into the effect of WSN characteristics on the quality of learned policies.

Multi-Agent Planning under Uncertainty with Monte Carlo Q-Value Function

Decentralized partially observable Markov decision processes (Dec-POMDPs) are general multi-agent models for planning under uncertainty, but are intractable to solve. Doubly exponential growth of the search space as the horizon increases makes a brute-force search impossible. Heuristic methods can guide the search towards the right direction quickly and have been successful in different domains. In this paper, we propose a new Q-value function representation—Monte Carlo Q-value function Q MC , which is proved to be an upper bound of the optimal Q-value function Q * . We introduce two Monte Carlo tree search enhancements—heavy playout for a simulation policy and adaptive samples—to speed up computation of Q MC . Then, we present a clustering and expansion with Monte-Carlo algorithm (CEMC)—an offline planning algorithm using Q MC as Q-value function, which is based on the generalized multi-agent A* with incremental clustering and expansion (GMAA*-ICE or ICE). CEMC calculates Q-value functions as required, without computing and storing all Q-value functions. An extended policy pruning strategy is used in CEMC. Finally, we present empirical results demonstrating that CEMC outperforms the best heuristic algorithm with a compact Q-value presentation in term of runtime for the same horizon, and has less memory usage for larger problems.

Modeling and Planning with Macro-Actions in Decentralized POMDPs.

Decentralized partially observable Markov decision processes (Dec-POMDPs) are general models for decentralized multi-agent decision making under uncertainty. However, they typically model a problem at a low level of granularity, where each agent's actions are primitive operations lasting exactly one time step. We address the case where each agent has macro-actions: temporally extended actions that may require different amounts of time to execute. We model macro-actions as options in a Dec-POMDP, focusing on actions that depend only on information directly available to the agent during execution. Therefore, we model systems where coordination decisions only occur at the level of deciding which macro-actions to execute. The core technical difficulty in this setting is that the options chosen by each agent no longer terminate at the same time. We extend three leading Dec-POMDP algorithms for policy generation to the macro-action case, and demonstrate their effectiveness in both standard benchmarks and a multi-robot coordination problem. The results show that our new algorithms retain agent coordination while allowing high-quality solutions to be generated for significantly longer horizons and larger state-spaces than previous Dec-POMDP methods. Furthermore, in the multi-robot domain, we show that, in contrast to most existing methods that are specialized to a particular problem class, our approach can synthesize control policies that exploit opportunities for coordination while balancing uncertainty, sensor information, and information about other agents.

Multi-agent reinforcement learning based on local communication

Aiming at the locality and uncertainty of observations in large-scale multi-agent application scenarios, the model of Decentralized Partially Observable Markov Decision Processes (DEC-POMDP) is considered, and a novel multi-agent reinforcement learning algorithm based on local communication is proposed. For a distributed learning environment, the elements of reinforcement learning are difficult to describe effectively in local observation situation, and the learning behaviour of each individual agent is influenced by its teammates. The local communication with consensus protocol is utilized to agree on the global observing environment, and thus that a part of strategies generated by repeating observations are eliminated, and the agent team gradually reach uniform opinion on the state of the event or object to be observed, they can thus approach a unique belief space regardless of whether each individual agent can perform a complete or partial observation. The simulation results show that the learning strategy space is reduced, and the learning speed is improved.

Centralized Optimization for Dec-POMDPs Under the Expected Average Reward Criterion

In this paper, the decentralized partially observable Markov decision process (Dec-POMDP) systems with discrete state and action spaces are studied from a gradient point of view. Dec-POMDPs have recently emerged as a promising approach to optimizing multiagent decision making in the partially observable stochastic environment. However, the decentralized nature of the Dec-POMDP framework results in a lack of shared belief state, which makes the decision maker impossible to estimate the system state based on local information. In contrast to the belief-based policy, this paper focuses on optimizing the decentralized observation-based policy, which is easily to be applied and does not have the sharing problem. By analyzing the gradient of the objective function, we have developed a centralized stochastic gradient policy iteration algorithm to find the optimal policy on the basis of gradient estimates from a single sample path. This algorithm does not need any specific assumption and can be applied to most practical Dec-POMDP problems. One numerical example is provided to demonstrate the effectiveness of the algorithm.

Multi-agent learning based routing for delay minimization in Cognitive Radio Networks

To overcome the problem of underutilizing licensed spectrum, Cognitive Radio Networks (CRNs) have emerged in which Secondary Users (SUs) are allowed to access opportunistically the licensed spectrum allocated exclusively to Primary Users (PUs). In the CRNs, routing process is essential to send data from source SUs to destination SUs. In the CRNs, a distributed routing solution should be considered for the CRNs, since the SUs use only local information to perform routing. Also, when there are multiple data flows generated by SUs, a multi-agent routing solution should be considered, since the routing performance of each SU is affected by routing decisions of other SUs. Recent real samples analysis has shown that the PUs spectrum usage pattern at the time domain exhibits the data traffic properties. So, we consider the data traffic for the PUs and the SUs, that have obtained incomplete information on PUs traffic through sensing, decide to exploit short lived spectrum holes between the PUs data packets for routing. In this paper, we introduce a distributed cooperative multi-agent routing problem in multi-hop CRNs, modeled using Decentralized Partially Observable Markov Decision Process (DEC-POMDP), in which the SUs want to minimize the end-to-end delay while keeping their interference to the PUs below a certain threshold. Then, a learning based scheme is developed for solving the problem. Simulation results demonstrate the convergence of the proposed learning based scheme and show that the performance of the proposed method is close to optimal method (that unlike the proposed method, assumes the SUs have complete information on PUs traffic and uses Q-learning for routing of SUs flows). Also, simulation results show that the proposed scheme maintains the end-to-end delay experienced by the packets in a low level and greatly outperforms related work at interference control.

Decentralized control of multi-robot partially observable Markov decision processes using belief space macro-actions

This work focuses on solving general multi-robot planning problems in continuous spaces with partial observability given a high-level domain description. Decentralized Partially Observable Markov Decision Processes (Dec-POMDPs) are general models for multi-robot coordination problems. However, representing and solving Dec-POMDPs is often intractable for large problems. This work extends the Dec-POMDP model to the Decentralized Partially Observable Semi-Markov Decision Process (Dec-POSMDP) to take advantage of the high-level representations that are natural for multi-robot problems and to facilitate scalable solutions to large discrete and continuous problems. The Dec-POSMDP formulation uses task macro-actions created from lower-level local actions that allow for asynchronous decision-making by the robots, which is crucial in multi-robot domains. This transformation from Dec-POMDPs to Dec-POSMDPs with a finite set of automatically-generated macro-actions allows use of efficient discrete-space search algorithms to solve them. The paper presents algorithms for solving Dec-POSMDPs, which are more scalable than previous methods since they can incorporate closed-loop belief space macro-actions in planning. These macro-actions are automatically constructed to produce robust solutions. The proposed algorithms are then evaluated on a complex multi-robot package delivery problem under uncertainty, showing that our approach can naturally represent realistic problems and provide high-quality solutions for large-scale problems.

Learning for Decentralized Control of Multiagent Systems in Large, Partially-Observable Stochastic Environments

Decentralized partially observable Markov decision processes (Dec-POMDPs) provide a general framework for multiagent sequential decision-making under uncertainty. Although Dec-POMDPs are typically intractable to solve for real-world problems, recent research on macro-actions (i.e., temporally-extended actions) has significantly increased the size of problems that can be solved. However, current methods assume the underlying Dec-POMDP model is known a priori or a full simulator is available during planning time. To accommodate more realistic scenarios, when such information is not available, this paper presents a policy-based reinforcement learning approach, which learns the agent policies based solely on trajectories generated by previous interaction with the environment (e.g., demonstrations). We show that our approach is able to generate valid macro-action controllers and develop an expectationmaximization (EM) algorithm (called Policy-based EM or PoEM), which has convergence guarantees for batch learning. Our experiments show PoEM is a scalable learning method that can learn optimal policies and improve upon hand-coded “expert” solutions.

Optimally Solving Dec-POMDPs as Continuous-State MDPs

Decentralized partially observable Markov decision processes (Dec-POMDPs) provide a general model for decision-making under uncertainty in 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 decentralized. 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. To provide scalability, we refine this approach by combining heuristic search and compact representations that exploit the structure present in multi-agent domains, without losing the ability to converge to an optimal solution. In particular, we introduce a feature-based heuristic search value iteration (FB-HSVI) algorithm that relies on feature-based compact representations, point-based updates and efficient action selection. A theoretical analysis demonstrates that FB-HSVI terminates in finite time with an optimal solution. We include an extensive empirical analysis using well-known benchmarks, thereby demonstrating that our approach provides significant scalability improvements compared to the state of the art.

Multi-agent reinforcement learning as a rehearsal for decentralized planning

Decentralized partially observable Markov decision processes (Dec-POMDPs) are a powerful tool for modeling multi-agent planning and decision-making under uncertainty. Prevalent Dec-POMDP solution techniques require centralized computation given full knowledge of the underlying model. Multi-agent reinforcement learning (MARL) based approaches have been recently proposed for distributed solution of Dec-POMDPs without full prior knowledge of the model, but these methods assume that conditions during learning and policy execution are identical. In some practical scenarios this may not be the case. We propose a novel MARL approach in which agents are allowed to rehearse with information that will not be available during policy execution. The key is for the agents to learn policies that do not explicitly rely on these rehearsal features. We also establish a weak convergence result for our algorithm, RLaR, demonstrating that RLaR converges in probability when certain conditions are met. We show experimentally that incorporating rehearsal features can enhance the learning rate compared to non-rehearsal-based learners, and demonstrate fast, (near) optimal performance on many existing benchmark Dec-POMDP problems. We also compare RLaR against an existing approximate Dec-POMDP solver which, like RLaR, does not assume a priori knowledge of the model. While RLaR׳s policy representation is not as scalable, we show that RLaR produces higher quality policies for most problems and horizons studied.

UAV Using Dec-POMDP Model for Increasing the Level of Security in the Company

One of the most important jobs for every company has always been keeping a high level of security. Various methods of information systems are being applied to ensure and increase the level of security. Unmanned aerial vehicles (UAV) that spread very rapidly in recent years are being applied in various fields. Autonomously controlled UAVs can fulfill almost any job. Markov decision processes on the other hand, play significant role among algorithms that deal with decision-making problems.This article proposes model that uses UAVs and can be used to support and improve information systems security level of a company. The most significant property of drones used in proposed model is that they do their job by directly connecting and sending information to each other. To get the best result decentralized partially observable Markov decision process (Dec-POMDP) was used. To gauge the level of security, calculations of the data were shown with fuzzy data set. In the end, details of the model and proposals are given.