We propose distributed online open loop planning (DOOLP), a general framework for online multiagent coordination and decision making under uncertainty. DOOLP is based on online heuristic search in the space defined by a generative model of the domain dynamics, which is exploited by agents to simulate and evaluate the consequences of their potential choices. We also propose distributed online Thompson sampling (DOTS) as an effective instantiation of the DOOLP framework. DOTS models sequences of agent choices by concatenating a number of multiarmed bandits for each agent and uses Thompson sampling for dealing with action value uncertainty. The Bayesian approach underlying Thompson sampling allows to effectively model and estimate uncertainty about (a) own action values and (b) other agents' behavior. This approach yields a principled and statistically sound solution to the exploration-exploitation dilemma when exploring large search spaces with limited resources. We implemented DOTS in a smart factory case study with positive empirical results. We observed effective, robust and scalable planning and coordination capabilities even when only searching a fraction of the potential search space.
Online planning, or local search, repeatedly interleaves a planning loop with an execution loop @cite_1 @cite_8 . An online planning agent requires a probabilistic generative model of its domain dynamics, such as a transition distribution of a DecMDP. Online planning consists of two loops with different frequencies. A high-frequency planning loop samples a plan from a stochastic policy, simulates its consequences w.r.t. some optimization objective (e.g. the expected cumulative reward) and updates the policy in order to increase the probability of generating useful plans w.r.t. the given notion of utility. A low-frequency execution loop consists of sensing the current state of the environment, planning by repeating the inner loop multiple times, and executing the currently most viable action determined by the planning loop. Online planning with its two loops is informally shown in Figure .
@cite_1 @cite_8
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In this paper, we present a method for recognising an agent's behaviour in dynamic, noisy, uncertain domains, and across multiple levels of abstraction. We term this problem on-line plan recognition under uncertainty and view it generally as probabilistic inference on the stochastic process representing the execution of the agent's plan. Our contributions in this paper are twofold. In terms of probabilistic inference, we introduce the Abstract Hidden Markov Model (AHMM), a novel type of stochastic processes, provide its dynamic Bayesian network (DBN) structure and analyse the properties of this network. We then describe an application of the Rao-Blackwellised Particle Filter to the AHMM which allows us to construct an efficient, hybrid inference method for this model. In terms of plan recognition, we propose a novel plan recognition framework based on the AHMM as the plan execution model. The Rao-Blackwellised hybrid inference for AHMM can take advantage of the independence properties inherent in a model of plan execution, leading to an algorithm for online probabilistic plan recognition that scales well with the number of levels in the plan hierarchy. This illustrates that while stochastic models for plan execution can be complex, they exhibit special structures which, if exploited, can lead to efficient plan recognition algorithms. We demonstrate the usefulness of the AHMM framework via a behaviour recognition system in a complex spatial environment using distributed video surveillance data. We focus on effective sample-based planning in the face of underactuation, high-dimensionality, drift, discrete system changes, and stochasticity. These are hallmark challenges for important problems, such as humanoid locomotion. In order to ensure broad applicability, we assume domain expertise is minimal and limited to a generative model. In order to make the method responsive, computational costs that scale linearly with the amount of samples taken from the generative model are required. We bring to bear a concrete method that satisfies all these requirements; it is a receding-horizon open-loop planner that employs cross-entropy optimization for policy construction. In simulation, we empirically demonstrate near-optimal decisions in a small domain and effective locomotion in several challenging humanoid control tasks. We provide a method, based on the theory of Markov decision processes, for efficient planning in stochastic domains. Goals are encoded as reward functions, expressing the desirability of each world state; the planner must find a policy (mapping from states to actions) that maximizes future rewards. Standard goals of achievement, as well as goals of maintenance and prioritized combinations of goals, can be specified in this way. An optimal policy can be found using existing methods, but these methods require time at best polynomial in the number of states in the domain, where the number of states is exponential in the number of propositions (or state variables). By using information about the starting state, the reward function, and the transition probabilities of the domain, we restrict the planner''s attention to a set of world states that are likely to be encountered in satisfying the goal. Using this restricted set of states, the planner can generate more or less complete plans depending on the time it has available. Our approach employs several iterative refinement routines for solving different aspects of the decision making problem. We describe the meta-level control problem of deliberation scheduling , allocating computational resources to these routines. We provide different models corresponding to optimization problems that capture the different circumstances and computational strategies for decision making under time constraints. We consider precursor models in which all decision making is performed prior to execution and recurrent models in which decision making is performed in parallel with execution, accounting for the states observed during execution and anticipating future states. We describe experimental results for both the precursor and recurrent problems that demonstrate planning times that grow slowly as a function of domain size. 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.