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 setting (MMDP) 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 the available alternatives and finds solutions to problems previously unsolvable.
Scalability is a major issue in multi-agent planning under uncertainty. In response to this challenge, two important lines of work have been developed. One line of work proposed approximate solutions by imposing and exploiting an additive structure in the value function @cite_20 . This approach has been applied in a range of stochastic planning settings, fully and partially observable alike, both from a single-agent perspective @cite_13 @cite_6 and multi-agent @cite_16 @cite_4 @cite_9 @cite_21 . The drawback of such methods is that typically no bounds on the efficiency loss can be given. We focus on optimal solutions, required to deal with strategic behaviour in a mechanism @cite_2 @cite_19 .
@cite_4 @cite_9 @cite_21 @cite_6 @cite_19 @cite_2 @cite_16 @cite_13 @cite_20
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We present a technique for computing approximately optimal solutions to stochastic resource allocation problems modeled as Markov decision processes (MDPS). We exploit two key properties to avoid explicitly enumerating the very large state and action spaces associated with these problems. Fist, the problems are composed of multiple tasks whose utilities are independent. Second, the actions taken with respect to (or resources allocated to) a task do not influence the status of any other task. We can therefore view each task as an MDP. However these MDPS are weakly coupled by resource constraints: actions selected for one MDP restrict the actions available to others. We describe heuristic techniques for dealing with several classes of constraints that use the solutions for individual MDPS to construct an approximate global solution. We demonstrate this technique on problems involving thousands of tasks, approximating the solution to problems that are far beyond the reach of standard methods. Learning in multiagent systems suffers from the fact that both the state and the action space scale exponentially with the number of agents. In this paper we are interested in using Q-learning to learn the coordinated actions of a group of cooperative agents, using a sparse representation of the joint state-action space of the agents. We first examine a compact representation in which the agents need to explicitly coordinate their actions only in a predefined set of states. Next, we use a coordination-graph approach in which we represent the Q-values by value rules that specify the coordination dependencies of the agents at particular states. We show how Q-learning can be efficiently applied to learn a coordinated policy for the agents in the above framework. We demonstrate the proposed method on the predator-prey domain, and we compare it with other related multiagent Q-learning 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. This paper presents two new approaches to decomposing and solving large Markov decision problems (MDPs), a partial decoupling method and a complete decoupling method. In these approaches, a large, stochastic decision problem is divided into smaller pieces. The first approach builds a cache of policies for each part of the problem independently, and then combines the pieces in a separate, light-weight step. A second approach also divides the problem into smaller pieces, but information is communicated between the different problem pieces, allowing intelligent decisions to be made about which piece requires the most attention. Both approaches can be used to find optimal policies or approximately optimal policies with provable bounds. These algorithms also provide a framework for the efficient transfer of knowledge across problems that share similar structure. We address efficient planning of maintenance activities in infrastructural networks, inspired by the real-world problem of servicing a highway network. A road authority is responsible for the quality, throughput and maintenance costs of the network, while the actual maintenance is performed by autonomous, third-party contractors. From a (multi-agent) planning and scheduling perspective, many interesting challenges can be identified. First, planned maintenance activities might have an uncertain duration due to unexpected delays. Second, since maintenance activities influence the traffic flow in the network, careful coordination of the planned activities is required in order to minimise their impact on the network throughput. Third, as we are dealing with selfish agents in a private-values setting, the road authority faces an incentive-design problem to truthfully elicit agent costs, complicated by the fact that it needs to balance multiple objectives. The main contributions of this work are: 1) multi-agent coordination on a network level through a novel combination of planning under uncertainty and dynamic mechanism design, applied to real-world problems, 2) accurate modelling and solving of maintenance-planning problems and 3) empirical exploration of the complexities that arise in these problems. We introduce a formal model of the problem domain, present experimental insights and identify open challenges for both the planning and scheduling as well as the mechanism design communities. Consider a multi-agent system in a dynamic and uncertain environment. Each agent's local decision problem is modeled as a Markov decision process (MDP) and agents must coordinate on a joint action in each period, which provides a reward to each agent and causes local state transitions. A social planner knows the model of every agent's MDP and wants to implement the optimal joint policy, but agents are self-interested and have private local state. We provide an incentive-compatible mechanism for eliciting state information that achieves the optimal joint plan in a Markov perfect equilibrium of the induced stochastic game. In the special case in which local problems are Markov chains and agents compete to take a single action in each period, we leverage Gittins allocation indices to provide an efficient factored algorithm and distribute computation of the optimal policy among the agents. Distributed, optimal coordinated learning in a multi-agent variant of the multi-armed bandit problem is obtained as a special case. We present an algorithm for coordinated decision making in cooperative multiagent settings, where the agents' value function canbe represented as a sum of context-specific value rules. The task of finding an optimal joint action in this setting leads to an algorithm where the coordination structure between agents depends on the current state of the system and even on the actual mmaerical values assigned to the value rules. We apply this framework to the task of multiagent planning in dynamic systems, showing how a joint value function of the associated Markov Decision Process can be approximated as a set of value rules using an efficient linear programming algorithm. The agents then apply the coordination graph algorithm at each iteration of the process to decide on the highest-value joint action, potentially leading to a different coordination pattern at each step of the plan. Many large Markov decision processes (MDPs) can be represented compactly using a structured representation such as a dynamic Bayesian network. Unfortunately, the compact representation does not help standard MDP algorithms, because the value function for the MDP does not retain the structure of the process description. We argue that in many such MDPs, structure is approximately retained. That is, the value functions are nearly additive: closely approximated by a linear function over factors associated with small subsets of problem features. Based on this idea, we present a convergent, approximate value determination algorithm for structured MDPs. The algorithm maintains an additive value function, alternating dynamic programming steps with steps that project the result back into the restricted space of additive functions. We show that both the dynamic programming and the projection steps can be computed efficiently, despite the fact that the number of states is exponential in the number of state variables.