Optimizing the depth and the direction of prospective planning using information values

Evaluating the future consequences of actions is achievable by simulating a mental search tree into the future. Expanding deep trees, however, is computationally taxing. Therefore, machines and humans use a plan-until-habit scheme that simulates the environment up to a limited depth and then exploits habitual values as proxies for consequences that may arise in the future. Two outstanding questions in this scheme are “in which directions the search tree should be expanded?”, and “when should the expansion stop?”. Here we propose a principled solution to these questions based on a speed/accuracy tradeoff: deeper expansion in the appropriate directions leads to more accurate planning, but at the cost of slower decision-making. Our simulation results show how this algorithm expands the search tree effectively and efficiently in a grid-world environment. We further show that our algorithm can explain several behavioral patterns in animals and humans, namely the effect of time-pressure on the depth of planning, the effect of reward magnitudes on the direction of planning, and the gradual shift from goal-directed to habitual behavior over the course of training. The algorithm also provides several predictions testable in animal/human experiments

Reinforcement Learning: A Survey

This paper surveys the field of reinforcement learning from a computer-science perspective. It is written to be accessible to researchers familiar with machine learning. Both the historical basis of the field and a broad selection of current work are summarized. Reinforcement learning is the problem faced by an agent that learns behavior through trial-and-error interactions with a dynamic environment. The work described here has a resemblance to work in psychology, but differs considerably in the details and in the use of the word ``reinforcement.'' The paper discusses central issues of reinforcement learning, including trading off exploration and exploitation, establishing the foundations of the field via Markov decision theory, learning from delayed reinforcement, constructing empirical models to accelerate learning, making use of generalization and hierarchy, and coping with hidden state. It concludes with a survey of some implemented systems and an assessment of the practical utility of current methods for reinforcement learning.Comment: See http://www.jair.org/ for any accompanying file

A Survey of Monte Carlo Tree Search Methods

Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work

Bootstrapping Monte Carlo Tree Search with an Imperfect Heuristic

We consider the problem of using a heuristic policy to improve the value approximation by the Upper Confidence Bound applied in Trees (UCT) algorithm in non-adversarial settings such as planning with large-state space Markov Decision Processes. Current improvements to UCT focus on either changing the action selection formula at the internal nodes or the rollout policy at the leaf nodes of the search tree. In this work, we propose to add an auxiliary arm to each of the internal nodes, and always use the heuristic policy to roll out simulations at the auxiliary arms. The method aims to get fast convergence to optimal values at states where the heuristic policy is optimal, while retaining similar approximation as the original UCT in other states. We show that bootstrapping with the proposed method in the new algorithm, UCT-Aux, performs better compared to the original UCT algorithm and its variants in two benchmark experiment settings. We also examine conditions under which UCT-Aux works well.Comment: 16 pages, accepted for presentation at ECML'1

Information-rich Task Allocation and Motion Planning for Heterogeneous Sensor Platforms

This paper introduces a novel stratified planning algorithm for teams of heterogeneous mobile sensors that maximizes information collection while minimizing resource costs. The main contribution of this work is the scalable unification of effective algorithms for de- centralized informative motion planning and decentralized high-level task allocation. We present the Information-rich Rapidly-exploring Random Tree (IRRT) algorithm, which is amenable to very general and realistic mobile sensor constraint characterizations, as well as review the Consensus-Based Bundle Algorithm (CBBA), offering several enhancements to the existing algorithms to embed information collection at each phase of the planning process. The proposed framework is validated with simulation results for networks of mobile sensors performing multi-target localization missions.United States. Air Force. Office of Scientific Research (Grant FA9550-08-1-0086)United States. Air Force. Office of Scientific Research. Multidisciplinary University Research Initiative (FA9550-08-1-0356

Influence-Optimistic Local Values for Multiagent Planning --- Extended Version

Recent years have seen the development of methods for multiagent planning under uncertainty that scale to tens or even hundreds of agents. However, most of these methods either make restrictive assumptions on the problem domain, or provide approximate solutions without any guarantees on quality. Methods in the former category typically build on heuristic search using upper bounds on the value function. Unfortunately, no techniques exist to compute such upper bounds for problems with non-factored value functions. To allow for meaningful benchmarking through measurable quality guarantees on a very general class of problems, this paper introduces a family of influence-optimistic upper bounds for factored decentralized partially observable Markov decision processes (Dec-POMDPs) that do not have factored value functions. Intuitively, we derive bounds on very large multiagent planning problems by subdividing them in sub-problems, and at each of these sub-problems making optimistic assumptions with respect to the influence that will be exerted by the rest of the system. We numerically compare the different upper bounds and demonstrate how we can achieve a non-trivial guarantee that a heuristic solution for problems with hundreds of agents is close to optimal. Furthermore, we provide evidence that the upper bounds may improve the effectiveness of heuristic influence search, and discuss further potential applications to multiagent planning.Comment: Long version of IJCAI 2015 paper (and extended abstract at AAMAS 2015