Addressing climate change requires coordinated policy efforts of nations worldwide. These efforts are informed by scientific reports, which rely in part on Integrated Assessment Models (IAMs), prominent tools used to assess the economic impacts of climate policies. However, traditional IAMs optimize policies based on a single objective, limiting their ability to capture the trade-offs among economic growth, temperature goals, and climate justice. As a result, policy recommendations have been criticized for perpetuating inequalities, fueling disagreements during policy negotiations. We introduce JUSTICE, the first framework integrating IAM with Multi-Objective Multi-Agent Reinforcement Learning (MOMARL). By incorporating multiple objectives, JUSTICE generates policy recommendations that shed light on equity while balancing climate and economic goals. Further, using multiple agents can provide a realistic representation of the interactions among the diverse policy actors. We identify equitable Pareto-optimal policies using our framework, which facilitates deliberative decision-making by presenting policymakers with the inherent trade-offs in climate and economic policy.

Abstract Policy gradient methods have become one of the most popular classes of algorithms for multi-agent reinforcement learning. A key challenge, however, that is not addressed by many of these methods is multi-agent credit assignment: assessing an agent’s contribution to the overall performance, which is crucial for learning good policies. We propose a novel algorithm called Dr.Reinforce that explicitly tackles this by combining difference rewards with policy gradients to allow for learning decentralized policies when the reward function is known. By differencing the reward function directly, Dr.Reinforce avoids difficulties associated with learning the Q-function as done by counterfactual multi-agent policy gradients (COMA), a state-of-the-art difference rewards method. For applications where the reward function is unknown, we show the effectiveness of a version of Dr.Reinforce that learns an additional reward network that is used to estimate the difference rewards.

Abstract Due to its perceptual limitations, an agent may have too little information about the environment to act optimally. In such cases, it is important to keep track of the action-observation history to uncover hidden state information. Recent deep reinforcement learning methods use recurrent neural networks (RNN) to memorize past observations. However, these models are expensive to train and have convergence difficulties, especially when dealing with high dimensional data. In this paper, we propose influence-aware memory, a theoretically inspired memory architecture that alleviates the training difficulties by restricting the input of the recurrent layers to those variables that influence the hidden state information. Moreover, as opposed to standard RNNs, in which every piece of information used for estimating Q values is inevitably fed back into the network for the next prediction, our model allows information to flow without being necessarily stored in the RNN’s internal memory. Results indicate that, by letting the recurrent layers focus on a small fraction of the observation variables while processing the rest of the information with a feedforward neural network, we can outperform standard recurrent architectures both in training speed and policy performance. This approach also reduces runtime and obtains better scores than methods that stack multiple observations to remove partial observability.

Model-based reinforcement learning (MBRL) has drawn considerable interest in recent years, given its promise to improve sample efficiency. Moreover, when using deep-learned models, it is possible to learn compact and generalizable models from data. In this work, we study MuZero, a state-of-the-art deep model-based reinforcement learning algorithm that distinguishes itself from existing algorithms by learning a value-equivalent model. Despite MuZero’s success and impact in the field of MBRL, existing literature has not thoroughly addressed why MuZero performs so well in practice. Specifically, there is a lack of in-depth investigation into the value-equivalent model learned by MuZero and its effectiveness in model-based credit assignment and policy improvement, which is vital for achieving sample efficiency in MBRL. To fill this gap, we explore two fundamental questions through our empirical analysis: 1) to what extent does MuZero achieve its learning objective of a value-equivalent model, and 2) how useful are these models for policy improvement? Among various other insights, we conclude that MuZero’s learned model cannot effectively generalize to evaluate unseen policies. This limitation constrains the extent to which we can additionally improve the current policy by planning with the model.

Multi-objective reinforcement learning (MORL) is used to solve problems involving multiple objectives. An MORL agent must make decisions based on the diverse signals provided by distinct reward functions. Training an MORL agent yields a set of solutions (policies), each presenting distinct trade-offs among the objectives (expected returns). MORL enhances explainability by enabling fine-grained comparisons of policies in the solution set based on their trade-offs as opposed to having a single policy. However, the solution set is typically large and multi-dimensional, where each policy (e.g., a neural network) is represented by its objective values. We propose an approach for clustering the solution set generated by MORL. By considering both policy behavior and objective values, our clustering method can reveal the relationship between policy behaviors and regions in the objective space. This approach can enable decision makers (DMs) to identify overarching trends and insights in the solution set rather than examining each policy individually. We tested our method in four multi-objective environments and found it outperformed traditional k-medoids clustering. Additionally, we include a case study that demonstrates its real-world application.

This paper explores the impact of variable pragmatic competence on communicative success through simulating language learning and conversing between speakers and listeners with different levels of reasoning abilities.Through studying this interaction, we hypothesize that matching levels of reasoning between communication partners would create a more beneficial environment for communicative success and language learning.Our research findings indicate that learning from more explicit, literal language is advantageous, irrespective of the learner's level of pragmatic competence.Furthermore, we find that integrating pragmatic reasoning during language learning, not just during evaluation, significantly enhances overall communication performance.This paper provides key insights into the importance of aligning reasoning levels and incorporating pragmatic reasoning in optimizing communicative interactions.

This work investigates formal generalization error bounds that apply to support vector machines (SVMs) in realizable and agnostic learning problems. We focus on recently observed parallels between probably approximately correct (PAC)-learning bounds, such as compression and complexity-based bounds, and novel error guarantees derived within scenario theory. Scenario theory provides nonasymptotic and distributional-free error bounds for models trained by solving data-driven decision-making problems. Relevant theorems and assumptions are reviewed and discussed. We propose a numerical comparison of the tightness and effectiveness of theoretical error bounds for support vector classifiers trained on several randomized experiments from 13 real-life problems. This analysis allows for a fair comparison of different approaches from both conceptual and experimental standpoints. Based on the numerical results, we argue that the error guarantees derived from scenario theory are often tighter for realizable problems and always yield informative results, i.e., probability bounds tighter than a vacuous [0, 1] interval. This work promotes scenario theory as an alternative tool for model selection, structural-risk minimization, and generalization error analysis of SVMs. In this way, we hope to bring the communities of scenario and statistical learning theory closer, so that they can benefit from each other's insights.

One of the main challenges of multi-agent learning lies in establishing convergence of the algorithms, as, in general, a collection of individual, self-serving agents is not guaranteed to converge with their joint policy, when learning concurrently. This is in stark contrast to most single-agent environments, and sets a prohibitive barrier for deployment in practical applications, as it induces uncertainty in long term behavior of the system. In this work, we apply the concept of trapping regions, known from qualitative theory of dynamical systems, to create safety sets in the joint strategy space for decentralized learning. We propose a binary partitioning algorithm for verification that candidate sets form trapping regions in systems with known learning dynamics, and a heuristic sampling algorithm for scenarios where learning dynamics are not known. We demonstrate the applications to a regularized version of Dirac Generative Adversarial Network, a four-intersection traffic control scenario run in a state of the art open-source microscopic traffic simulator SUMO, and a mathematical model of economic competition.

We present a review that unifies decision-support methods for exploring the solutions produced by multi-objective optimization (MOO) algorithms. As MOO is applied to solve diverse problems, approaches for analyzing the trade-offs offered by these algorithms are scattered across fields. We provide an overview of the current advances on this topic, including methods for visualization, mining the solution set, and uncertainty exploration as well as emerging research directions, including interactivity, explainability, and support on ethical aspects. We synthesize these methods drawing from different fields of research to enable building a unified approach, independent of the application. Our goals are to reduce the entry barrier for researchers and practitioners on using MOO algorithms and to provide novel research directions.

Distributed robots that survey and assist with search & rescue operations usually deal with unknown environments with limited communication. This paper focuses on distributed & cooperative multi-robot area coverage strategies of unknown environments, having constrained communication. Due to restricted communication there is performance loss for the multi-robot team, in terms of increased number of steps to cover an area. From simulation results, it is shown that enabling partial communication amongst robots can recover a significant amount of performance by decreasing the number of steps required for area coverage. Additionally it is found that partially communicating robots that predict the paths of peers do not perform significantly different from robots that are only partially communicating. This is found due to predictions spreading the robots away from one another, which reduces meeting times and instances of inter-robot data sharing.

Learning to cooperate with other agents is challenging when those agents also possess the ability to adapt to our own behavior. Practical and theoretical approaches to learning in cooperative settings typically assume that other agents’ behaviors are stationary, or else make very specific assumptions about other agents’ learning processes. The goal of this work is to understand whether we can reliably learn to cooperate with other agents without such restrictive assumptions, which are unlikely to hold in real-world applications. Our main contribution is a set of impossibility results, which show that no learning algorithm can reliably learn to cooperate with all possible adaptive partners in a repeated matrix game, even if that partner is guaranteed to cooperate with some stationary strategy. Motivated by these results, we then discuss potential alternative assumptions which capture the idea that an adaptive partner will only adapt rationally to our behavior.

Learning effective policies for real-world problems is still an open challenge for the field of reinforcement learning (RL). The main limitation being the amount of data needed and the pace at which that data can be obtained. In this paper, we study how to build lightweight simulators of complicated systems that can run sufficiently fast for deep RL to be applicable. We focus on domains where agents interact with a reduced portion of a larger environment while still being affected by the global dynamics. Our method combines the use of local simulators with learned models that mimic the influence of the global system. The experiments reveal that incorporating this idea into the deep RL workflow can considerably accelerate the training process and presents several opportunities for the future.

How can we plan efficiently in a large and complex environment when the time budget is limited? Given the original simulator of the environment, which may be computationally very demanding, we propose to learn online an approximate but much faster simulator that improves over time. To plan reliably and efficiently while the approximate simulator is learning, we develop a method that adaptively decides which simulator to use for every simulation, based on a statistic that measures the accuracy of the approximate simulator. This allows us to use the approximate simulator to replace the original simulator for faster simulations when it is accurate enough under the current context, thus trading off simulation speed and accuracy. Experimental results in two large domains show that when integrated with POMCP, our approach allows to plan with improving efficiency over time.

Due to its high sample complexity, simulation is, as of today, critical for the successful application of reinforcement learning. Many real-world problems, however, exhibit overly complex dynamics, making their full-scale simulation computationally slow. In this paper, we show how to factorize large networked systems of many agents into multiple local regions such that we can build separate simulators that run independently and in parallel. To monitor the influence that the different local regions exert on one another, each of these simulators is equipped with a learned model that is periodically trained on real trajectories. Our empirical results reveal that distributing the simulation among different processes not only makes it possible to train large multi-agent systems in just a few hours but also helps mitigate the negative effects of simultaneous learning.

Recent years have seen the application of deep reinforcement learning techniques to cooperative multi-agent systems, with great empirical success. However, given the lack of theoretical insight, it remains unclear what the employed neural networks are learning, or how we should enhance their learning power to address the problems on which they fail. In this work, we empirically investigate the learning power of various network architectures on a series of one-shot games. Despite their simplicity, these games capture many of the crucial problems that arise in the multi-agent setting, such as an exponential number of joint actions or the lack of an explicit coordination mechanism. Our results extend those in Castellini et al. (Proceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems, AAMAS'19.International Foundation for Autonomous Agents and Multiagent Systems, pp 1862-1864, 2019) and quantify how well various approaches can represent the requisite value functions, and help us identify the reasons that can impede good performance, like sparsity of the values or too tight coordination requirements.

Making decisions in complex environments is a key challenge in artificial intelligence (AI). Situations involving multiple decision makers are particularly complex, leading to computational intractability of principled solution methods. A body of work in AI has tried to mitigate this problem by trying to distill interaction to its essence: how does the policy of one agent influence another agent? If we can find more compact representations of such influence, this can help us deal with the complexity, for instance by searching the space of influences rather than the space of policies. However, so far these notions of influence have been restricted in their applicability to special cases of interaction. In this paper we formalize influence-based abstraction (IBA), which facilitates the elimination of latent state factors without any loss in value, for a very general class of problems described as factored partially observable stochastic games (fPOSGs). On the one hand, this generalizes existing descriptions of influence, and thus can serve as the foundation for improvements in scalability and other insights in decision making in complex multiagent settings. On the other hand, since the presence of other agents can be seen as a generalization of single agent settings, our formulation of IBA also provides a sufficient statistic for decision making under abstraction for a single agent. We also give a detailed discussion of the relations to such previous works, identifying new insights and interpretations of these approaches. In these ways, this paper deepens our understanding of abstraction in a wide range of sequential decision making settings, providing the basis for new approaches and algorithms for a large class of problems.

Decentralized online planning can be an attractive paradigm for cooperative multi-agent systems, due to improved scalability and robustness. A key difficulty of such approach lies in making accurate predictions about the decisions of other agents. In this paper, we present a trainable online decentralized planning algorithm based on decentralized Monte Carlo Tree Search, combined with models of teammates learned from previous episodic runs. By only allowing one agent to adapt its models at a time, under the assumption of ideal policy approximation, successive iterations of our method are guaranteed to improve joint policies, and eventually lead to convergence to a Nash equilibrium. We test the efficiency of the algorithm by performing experiments in several scenarios of the spatial task allocation environment introduced in [Claes et al., 2015]. We show that deep learning and convolutional neural networks can be employed to produce accurate policy approximators which exploit the spatial features of the problem, and that the proposed algorithm improves over the baseline planning performance for particularly challenging domain configurations.

The field of Human Activity Recognition (HAR) focuses on obtaining and analysing data captured from monitoring devices (e.g. sensors). There is a wide range of applications within the field; for instance, assisted living, security surveillance, and intelligent transportation. In HAR, the development of Activity Recognition models is dependent upon the data captured by these devices and the methods used to analyse them, which directly affect performance metrics. In this work, we address the issue of accurately recognising human activities using different Machine Learning (ML) techniques. We propose a new feature representation based on consecutive occurring observations and compare it against previously used feature representations using a wide range of classification methods. Experimental results demonstrate that techniques based on the proposed representation outperform the baselines and a better accuracy was achieved for both highly and less frequent actions. We also investigate how the addition of further features and their pre-processing techniques affect performance results leading to state-of-the-art accuracy on a Human Activity Recognition dataset.

How can we plan efficiently in real time to control an agent in a complex environment that may involve many other agents? While existing sample-based planners have enjoyed empirical success in large POMDPs, their performance heavily relies on a fast simulator. However, real-world scenarios are complex in nature and their simulators are often computationally demanding, which severely limits the performance of online planners. In this work, we propose influence-augmented online planning, a principled method to transform a factored simulator of the entire environment into a local simulator that samples only the state variables that are most relevant to the observation and reward of the planning agent and captures the incoming influence from the rest of the environment using machine learning methods. Our main experimental results show that planning on this less accurate but much faster local simulator with POMCP leads to higher real-time planning performance than planning on the simulator that models the entire environment.

Multi-agent active perception is a task where a team of agents cooperatively gathers observations to compute a joint estimate of a hidden variable. The task is decentralized and the joint estimate can only be computed after the task ends by fusing observations of all agents. The objective is to maximize the accuracy of the estimate. The accuracy is quantified by a centralized prediction reward determined by a centralized decision-maker who perceives the observations gathered by all agents after the task ends. In this paper, we model multi-agent active perception as a decentralized partially observable Markov decision process (Dec-POMDP) with a convex centralized prediction reward. We prove that by introducing individual prediction actions for each agent, the problem is converted into a standard Dec-POMDP with a decentralized prediction reward. The loss due to decentralization is bounded, and we give a sufficient condition for when it is zero. Our results allow application of any Dec-POMDP solution algorithm to multi-agent active perception problems, and enable planning to reduce uncertainty without explicit computation of joint estimates. We demonstrate the empirical usefulness of our results by applying a standard Dec-POMDP algorithm to multi-agent active perception problems, showing increased scalability in the planning horizon.

This paper introduces MDP homomorphic networks for deep reinforcement learning. MDP homomorphic networks are neural networks that are equivariant under symmetries in the joint state-action space of an MDP. Current approaches to deep reinforcement learning do not usually exploit knowledge about such structure. By building this prior knowledge into policy and value networks using an equivariance constraint, we can reduce the size of the solution space. We specifically focus on group-structured symmetries (invertible transformations). Additionally, we introduce an easy method for constructing equivariant network layers numerically, so the system designer need not solve the constraints by hand, as is typically done. We construct MDP homomorphic MLPs and CNNs that are equivariant under either a group of reflections or rotations. We show that such networks converge faster than unstructured baselines on CartPole, a grid world and Pong.

Learning from demonstration (LfD) is useful in settings where hand-coding behaviour or a reward function is impractical. It has succeeded in a wide range of problems but typically relies on manually generated demonstrations or specially deployed sensors and has not generally been able to leverage the copious demonstrations available in the wild: those that capture behaviours that were occurring anyway using sensors that were already deployed for another purpose, e.g., traffic camera footage capturing demonstrations of natural behaviour of vehicles, cyclists, and pedestrians. We propose video to behaviour (ViBe), a new approach to learn models of behaviour from unlabelled raw video data of a traffic scene collected from a single, monocular, initially uncalibrated camera with ordinary resolution. Our approach calibrates the camera, detects relevant objects, tracks them through time, and uses the resulting trajectories to perform LfD, yielding models of naturalistic behaviour. We apply ViBe to raw videos of a traffic intersection and show that it can learn purely from videos, without additional expert knowledge.

Designing "teams of intelligent agents that successfully coordinate and learn about their complex environments inhabited by other agents (such as humans)" is one of the major goals of AI, and it is the challenge that I aim to address in my research. In this paper I give an overview of some of the foundations, insights and challenges in this field of Interactive Learning and Decision Making.

The stochastic shortest path problem is of crucial importance for the development of sustainable transportation systems. Existing methods based on the probability tail model seek for the path that maximizes the probability of arriving at the destination before a deadline. However, they suffer from low accuracy and/or high computational cost. We design a novel Q-learning method where the converged Q-values have the practical meaning as the actual probabilities of arriving on time so as to improve accuracy. By further adopting dynamic neural networks to learn the value function, our method can scale well to large road networks with arbitrary deadlines. Experimental results on real road networks demonstrate the significant advantages of our method over other counterparts.

The POMDP is a powerful framework for reasoning under outcome and information uncertainty, but constructing an accurate POMDP model is difficult. Bayes-Adaptive Partially Observable Markov Decision Processes (BA-POMDPs) extend POMDPs to allow the model to be learned during execution. BA-POMDPs are a Bayesian RL approach that, in principle, allows for an optimal trade-off between exploitation and exploration. Unfortunately, BA-POMDPs are currently impractical to solve for any non-trivial domain. In this paper, we extend the Monte-Carlo Tree Search method POMCP to BA-POMDPs and show that the resulting method, which we call BA-POMCP, is able to tackle problems that previous solution methods have been unable to solve. Additionally, we introduce several techniques that exploit the BA-POMDP structure to improve the efficiency of BA-POMCP along with proof of their convergence.

This article describes the Multiagent Decision Process (MADP) Toolbox, a software library to support planning and learning for intelligent agents and multiagent systems in uncertain environments. Key features are that it supports partially observable environments and stochastic transition models; has unified support for single- and multiagent systems; provides a large number of models for decision-theoretic decision making, including one-shot and sequential decision making under various assumptions of observability and cooperation, such as Dec-POMDPs and POSGs; provides tools and parsers to quickly prototype new problems; provides an extensive range of planning and learning algorithms for single- and multiagent systems; is released under the GNU GPL v3 license; and is written in C++ and designed to be extensible via the object-oriented paradigm.

In multiagent e-marketplaces, buying agents need to select good sellers by querying other buyers (called advisors). Partially Observable Markov Decision Processes (POMDPs) have shown to be an effective framework for optimally selecting sellers by selectively querying advisors. However, current solution methods do not scale to hundreds or even tens of agents operating in the e-market. In this paper, we propose the Mixture of POMDP Experts (MOPE) technique, which exploits the inherent structure of trust-based domains, such as the seller selection problem in e-markets, by aggregating the solutions of smaller sub-POMDPs. We propose a number of variants of the MOPE approach that we analyze theoretically and empirically. Experiments show that MOPE can scale up to a hundred agents thereby leveraging the presence of more advisors to significantly improve buyer satisfaction.

With renewable energy becoming more common, energy prices fluctuate more depending on environmental factors such as the weather. Consuming energy without taking volatile prices into consideration can not only become expensive, but may also increase the peak load, which requires energy providers to generate additional energy using less environment-friendly methods. In the Netherlands, pumping stations that maintain the water levels of polder canals are large energy consumers, but the controller software currently used in the industry does not take real-time energy availability into account. We investigate if existing AI planning techniques have the potential to improve upon the current solutions. In particular, we propose a light weight but realistic simulator and investigate if an online planning method (UCT) can utilise this simulator to improve the cost-efficiency of pumping station control policies. An empirical comparison with the current control algorithms indicates that substantial cost, and thus peak load, reduction can be attained.

Many solution methods for Markov Decision Processes (MDPs) exploit structure in the problem and are based on value function factorization. Especially multiagent settings, however, are known to suffer from an exponential increase in value component sizes as interactions become denser, restricting problem sizes and types that can be handled. We present an approach to mitigate this limitation for certain types of multiagent systems, exploiting a property that can be thought of as "anonymous influence" in the factored MDP. We show how representational benefits from anonymity translate into computational efficiencies, both for variable elimination in a factor graph and for the approximate linear programming solution to factored MDPs. Our methods scale to factored MDPs that were previously unsolvable, such as the control of a stochastic disease process over densely connected graphs with 50 nodes and 25 agents.

In cooperative multi-agent sequential decision making under uncertainty, agents must coordinate to find an optimal joint policy that maximises joint value. Typical algorithms exploit additive structure in the value function, but in the fully-observable multi-agent MDP (MMDP) setting such structure is not present. We propose a new optimal solver for transition-independent MMDPs, in which agents can only affect their own state but their reward depends on joint transitions. We represent these dependencies compactly in conditional return graphs (CRGs). Using CRGs the value of a joint policy and the bounds on partially specified joint policies can be efficiently computed. We propose CoRe, a novel branch-and-bound policy search algorithm building on CRGs. CoRe typically requires less runtime than available alternatives and finds solutions to previously unsolvable problems.

In this paper, we introduce a new formulation for the value function of a zero-sum Partially Observable Stochastic Game (zs-POSG) in terms of a ‘plan-time sufficient statistic’, a distribution over joint sets of information. We prove that this value function exhibits concavity and convexity with respect to appropriately chosen subspaces of the statistic space. We anticipate that this result is a key pre-cursor for developing solution methods that exploit such structure. Finally, we show that the formulation allow us to reduce a finite zs-POSG to a ‘centralized’ model with shared observations, thereby transferring results for the latter (narrower) class of games to games with individual observations.

Online, sample-based planning algorithms for POMDPs have shown great promise in scaling to problems with large state spaces, but they become intractable for large action and observation spaces. This is particularly problematic in multiagent POMDPs where the action and observation space grows exponentially with the number of agents. To combat this intractability, we propose a novel scalable approach based on sample-based planning and factored value functions that exploits structure present in many multiagent settings. This approach applies not only in the planning case, but also in the Bayesian reinforcement learning setting. Experimental results show that we are able to provide high quality solutions to large multiagent planning and learning problems.

A key challenge in the design of multi-sensor systems is the efficient allocation of scarce resources such as bandwidth, CPU cycles, and energy, leading to the dynamic sensor selection problem in which a subset of the available sensors must be selected at each timestep. While partially observable Markov decision processes (POMDPs) provide a natural decision-theoretic model for this problem, the computational cost of POMDP planning grows exponentially in the number of sensors, making it feasible only for small problems. We propose a new POMDP planning method that uses greedy maximization to greatly improve scalability in the number of sensors. We show that, under certain conditions, the value function of a dynamic sensor selection POMDP is submodular and use this result to bound the error introduced by performing greedy maximization. Experimental results on a real-world dataset from a multi-camera tracking system in a shopping mall show it achieves similar performance to existing methods but incurs only a fraction of the computational cost, leading to much better scalability in the number of cameras.

In this article, we propose new algorithms for multi-objective coordination graphs (MO-CoGs). Key to the efficiency of these algorithms is that they compute a convex coverage set (CCS) instead of a Pareto coverage set (PCS). Not only is a CCS a sufficient solution set for a large class of problems, it also has important characteristics that facilitate more efficient solutions. We propose two main algorithms for computing a CCS in MO-CoGs. Convex multi-objective variable elimination (CMOVE) computes a CCS by performing a series of agent eliminations, which can be seen as solving a series of local multi-objective subproblems. Variable elimination linear support (VELS) iteratively identifies the single weight vector, w, that can lead to the maximal possible improvement on a partial CCS and calls variable elimination to solve a scalarized instance of the problem for w. VELS is faster than CMOVE for small and medium numbers of objectives and can compute an ε-approximate CCS in a fraction of the runtime. In addition, we propose variants of these methods that employ AND/OR tree search instead of variable elimination to achieve memory efficiency. We analyze the runtime and space complexities of these methods, prove their correctness, and compare them empirically against a naive baseline and an existing PCS method, both in terms of memory-usage and runtime. Our results show that, by focusing on the CCS, these methods achieve much better scalability in the number of agents than the current state of the art.

This article presents the state-of-the-art in optimal solution methods for decentralized partially observable Markov decision processes (Dec-POMDPs), which are general models for collaborative multiagent planning under uncertainty. Building off the generalized multiagent A* (GMAA*) algorithm, which reduces the problem to a tree of one-shot collaborative Bayesian games (CBGs), we describe several advances that greatly expand the range of Dec-POMDPs that can be solved optimally. First, we introduce lossless incremental clustering of the CBGs solved by GMAA*, which achieves exponential speedups without sacrificing optimality. Second, we introduce incremental expansion of nodes in the GMAA* search tree, which avoids the need to expand all children, the number of which is in the worst case doubly exponential in the node's depth. This is particularly beneficial when little clustering is possible. In addition, we introduce new hybrid heuristic representations that are more compact and thereby enable the solution of larger Dec-POMDPs. We provide theoretical guarantees that, when a suitable heuristic is used, both incremental clustering and incremental expansion yield algorithms that are both complete and search equivalent. Finally, we present extensive empirical results demonstrating that GMAA*-ICE, an algorithm that synthesizes these advances, can optimally solve Dec-POMDPs of unprecedented size.

Multiagent Partially Observable Markov Decision Processes (MPOMDPs) provide a powerful framework for optimal decision making under the assumption of instantaneous communication. We focus on a delayed communication setting (MPOMDP-DC), in which broadcasted information is delayed by at most one time step. This model allows agents to act on their most recent (private) observation. Such an assumption is a strict generalization over having agents wait until the global information is available and is more appropriate for applications in which response time is critical. In this setting, however, value function backups are significantly more costly, and naive application of incremental pruning, the core of many state-of-the-art optimal POMDP techniques, is intractable. In this paper, we overcome this problem by demonstrating that computation of the MPOMDP-DC backup can be structured as a tree and introducing two novel tree-based pruning techniques that exploit this structure in an effective way. We experimentally show that these methods have the potential to outperform naive incremental pruning by orders of magnitude, allowing for the solution of larger problems.

This paper presents a theoretical advance by which factored POSGs can be decomposed into local models. We formalize the interface between such local models as the influence agents can exert on one another; and we prove that this interface is sufficient for decoupling them. The resulting influence-based abstraction substantially generalizes previous work on exploiting weakly-coupled agent interaction structures. Therein lie several important contributions. First, our general formulation sheds new light on the theoretical relationships among previous approaches, and promotes future empirical comparisons that could come by extending them beyond the more specific problem contexts for which they were developed. More importantly, the influence-based approaches that we generalize have shown promising improvements in the scalability of planning for more restrictive models. Thus, our theoretical result here serves as the foundation for practical algorithms that we anticipate will bring similar improvements to more general planning contexts, and also into other domains such as approximate planning, decision-making in adversarial domains, and online learning.

Planning under uncertainty for multiagent systems can be formalized as a decentralized partially observable Markov decision process. We advance the state of the art for opti-mal solution of this model, building on the Multiagent A* heuristic search method. A key insight is that we can avoid the full expansion of a search node that generates a number of children doubly exponential in the node’s depth. Instead we incrementally expand the children of a node only when a next child might have the highest heuristic value. We tar-get a subsequent bottleneck by introducing a more memory-efficient representation for our heuristic functions. Proof is given that the resulting algorithm is correct and experiments demonstrate a significant speedup over the state of the art, allowing for optimal solutions over longer horizons for many benchmark problems.

Decision-theoretic planning is a popular approach to sequential decision making problems, because it treats uncertainty in sensing and acting in a principled way. In single-agent frameworks like MDPs and POMDPs, planning can be carried out by resorting to Q-value functions: an optimal Q-value function Q* is computed in a recursive manner by dynamic programming, and then an optimal policy is extracted from Q*. In this paper we study whether similar Q-value functions can be defined for decentralized POMDP models (Dec-POMDPs), and how policies can be extracted from such value functions. We define two forms of the optimal Q-value function for Dec-POMDPs: one that gives a normative description as the Q-value function of an optimal pure joint policy and another one that is sequentially rational and thus gives a recipe for computation. This computation, however, is infeasible for all but the smallest problems. Therefore, we analyze various approximate Q-value functions that allow for efficient computation. We describe how they relate, and we prove that they all provide an upper bound to the optimal Q-value function Q*. Finally, unifying some previous approaches for solving Dec-POMDPs, we describe a family of algorithms for extracting policies from such Q-value functions, and perform an experimental evaluation on existing test problems, including a new firefighting benchmark problem.

Coevolutionary algorithms search for test cases as part of the search process. The resulting adaptive evaluation function takes away the need to define a fixed evaluation function, but may also be unstable and thereby prevent reliable progress. Recent work in coevolution has therefore focused on algorithms that guarantee progress with respect to a given solution concept. The Nash Memory archive guarantees monotonicity with respect to the game-theoretic solution concept of the Nash equilibrium, but is limited to symmetric games. We present an extension of the Nash Memory that guarantees monotonicity for asymmetric games. The Parallel Nash Memory is demonstrated in experiments, and its performance on general sum games is discussed.