scholarly journals Optimally Solving Dec-POMDPs as Continuous-State MDPs

2016 ◽  
Vol 55 ◽  
pp. 443-497 ◽  
Author(s):  
Jilles Steeve Dibangoye ◽  
Christopher Amato ◽  
Olivier Buffet ◽  
François Charpillet
Keyword(s):  
Heuristic Search ◽  
Piecewise Linear ◽  
Optimal Solution ◽  
Value Iteration ◽  
Compact Representations ◽  
Continuous State ◽  
Markov Decision ◽  
Feature Based ◽  
Multi Agent ◽  
Partially Observable

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.

scholarly journals Goal-HSVI: Heuristic Search Value Iteration for Goal POMDPs

2018 ◽  
Author(s):  
Karel Horák ◽  
Branislav Bošanský ◽  
Krishnendu Chatterjee
Keyword(s):  
Heuristic Search ◽  
Infinite Horizon ◽  
Decision Processes ◽  
Value Iteration ◽  
Planning Under Uncertainty ◽  
Total Cost ◽  
Markov Decision ◽  
Standard Models ◽  
Target States ◽  
Partially Observable

Partially observable Markov decision processes (POMDPs) are the standard models for planning under uncertainty with both finite and infinite horizon. Besides the well-known discounted-sum objective, indefinite-horizon objective (aka Goal-POMDPs) is another classical objective for POMDPs. In this case, given a set of target states and a positive cost for each transition, the optimization objective is to minimize the expected total cost until a target state is reached. In the literature, RTDP-Bel or heuristic search value iteration (HSVI) have been used for solving Goal-POMDPs. Neither of these algorithms has theoretical convergence guarantees, and HSVI may even fail to terminate its trials. We give the following contributions: (1) We discuss the challenges introduced in Goal-POMDPs and illustrate how they prevent the original HSVI from converging. (2) We present a novel algorithm inspired by HSVI, termed Goal-HSVI, and show that our algorithm has convergence guarantees. (3) We show that Goal-HSVI outperforms RTDP-Bel on a set of well-known examples.

scholarly journals A Framework for Sequential Planning in Multi-Agent Settings

2005 ◽  
Vol 24 ◽  
pp. 49-79 ◽  
Author(s):  
P. J. Gmytrasiewicz ◽  
P. Doshi
Keyword(s):  
Traditional Approach ◽  
Value Functions ◽  
Value Iteration ◽  
Markov Decision ◽  
Multi Agent ◽  
Carry Over ◽  
The Cost ◽  
Partially Observable ◽  
Belief States ◽  
Do So

This paper extends the framework of partially observable Markov decision processes (POMDPs) to multi-agent settings by incorporating the notion of agent models into the state space. Agents maintain beliefs over physical states of the environment and over models of other agents, and they use Bayesian updates to maintain their beliefs over time. The solutions map belief states to actions. Models of other agents may include their belief states and are related to agent types considered in games of incomplete information. We express the agents' autonomy by postulating that their models are not directly manipulable or observable by other agents. We show that important properties of POMDPs, such as convergence of value iteration, the rate of convergence, and piece-wise linearity and convexity of the value functions carry over to our framework. Our approach complements a more traditional approach to interactive settings which uses Nash equilibria as a solution paradigm. We seek to avoid some of the drawbacks of equilibria which may be non-unique and do not capture off-equilibrium behaviors. We do so at the cost of having to represent, process and continuously revise models of other agents. Since the agent's beliefs may be arbitrarily nested, the optimal solutions to decision making problems are only asymptotically computable. However, approximate belief updates and approximately optimal plans are computable. We illustrate our framework using a simple application domain, and we show examples of belief updates and value functions.

scholarly journals Sparse Tree Search Optimality Guarantees in POMDPs with Continuous Observation Spaces

2020 ◽  
Author(s):  
Michael H. Lim ◽  
Claire Tomlin ◽  
Zachary N. Sunberg
Keyword(s):  
Optimal Solution ◽  
Tree Search ◽  
Continuous Observation ◽  
Theoretical Justification ◽  
Continuous State ◽  
Markov Decision ◽  
Simplified Algorithm ◽  
Partially Observable ◽  
Online Sampling ◽  
And Control

Partially observable Markov decision processes (POMDPs) with continuous state and observation spaces have powerful flexibility for representing real-world decision and control problems but are notoriously difficult to solve. Recent online sampling-based algorithms that use observation likelihood weighting have shown unprecedented effectiveness in domains with continuous observation spaces. However there has been no formal theoretical justification for this technique. This work offers such a justification, proving that a simplified algorithm, partially observable weighted sparse sampling (POWSS), will estimate Q-values accurately with high probability and can be made to perform arbitrarily near the optimal solution by increasing computational power.

Massively parallel motion planning algorithms under uncertainty using POMDP

2015 ◽  
Vol 35 (8) ◽  
pp. 928-942 ◽  
Author(s):  
Taekhee Lee ◽  
Young J. Kim
Keyword(s):  
Parallel Algorithms ◽  
Massively Parallel ◽  
Value Iteration ◽  
Parallel Motion ◽  
Continuous State ◽  
Markov Decision ◽  
Compute Data ◽  
Data Interleaving ◽  
Parallel Formulation ◽  
Partially Observable

We present new parallel algorithms that solve continuous-state partially observable Markov decision process (POMDP) problems using the GPU (gPOMDP) and a hybrid of the GPU and CPU (hPOMDP). We choose the Monte Carlo value iteration (MCVI) method as our base algorithm and parallelize this algorithm using the multi-level parallel formulation of MCVI. For each parallel level, we propose efficient algorithms to utilize the massive data parallelism available on modern GPUs. Our GPU-based method uses the two workload distribution techniques, compute/data interleaving and workload balancing, in order to obtain the maximum parallel performance at the highest level. Here we also present a CPU–GPU hybrid method that takes advantage of both CPU and GPU parallelism in order to solve highly complex POMDP planning problems. The CPU is responsible for data preparation, while the GPU performs Monte Cacrlo simulations; these operations are performed concurrently using the compute/data overlap technique between the CPU and GPU. To the best of the authors’ knowledge, our algorithms are the first parallel algorithms that efficiently execute POMDP in a massively parallel fashion utilizing the GPU or a hybrid of the GPU and CPU. Our algorithms outperform the existing CPU-based algorithm by a factor of 75–99 based on the chosen benchmark.

scholarly journals IPOMDP-Net: A Deep Neural Network for Partially Observable Multi-Agent Planning Using Interactive POMDPs

2019 ◽  
Vol 33 ◽  
pp. 6062-6069 ◽  
Author(s):  
Yanlin Han ◽  
Piotr Gmytrasiewicz
Keyword(s):  
Neural Network ◽  
Network Architecture ◽  
State Of The Art ◽  
Neural Computing ◽  
Neural Network Architecture ◽  
Markov Decision ◽  
Planning Algorithm ◽  
Multi Agent ◽  
Partially Observable ◽  
Multi Agent Planning

This paper introduces the IPOMDP-net, a neural network architecture for multi-agent planning under partial observability. It embeds an interactive partially observable Markov decision process (I-POMDP) model and a QMDP planning algorithm that solves the model in a neural network architecture. The IPOMDP-net is fully differentiable and allows for end-to-end training. In the learning phase, we train an IPOMDP-net on various fixed and randomly generated environments in a reinforcement learning setting, assuming observable reinforcements and unknown (randomly initialized) model functions. In the planning phase, we test the trained network on new, unseen variants of the environments under the planning setting, using the trained model to plan without reinforcements. Empirical results show that our model-based IPOMDP-net outperforms the other state-of-the-art modelfree network and generalizes better to larger, unseen environments. Our approach provides a general neural computing architecture for multi-agent planning using I-POMDPs. It suggests that, in a multi-agent setting, having a model of other agents benefits our decision-making, resulting in a policy of higher quality and better generalizability.

scholarly journals COG-DICE: An Algorithm for Solving Continuous-Observation Dec-POMDPs

2017 ◽  
Author(s):  
Madison Clark-Turner ◽  
Christopher Amato
Keyword(s):  
Markov Decision Process ◽  
Real World ◽  
Decision Process ◽  
Extended Version ◽  
Continuous Observation ◽  
Solution Methods ◽  
Markov Decision ◽  
Multi Agent ◽  
Partially Observable Markov ◽  
Partially Observable

The decentralized partially observable Markov decision process (Dec-POMDP) is a powerful model for representing multi-agent problems with decentralized behavior. Unfortunately, current Dec-POMDP solution methods cannot solve problems with continuous observations, which are common in many real-world domains. To that end, we present a framework for representing and generating Dec-POMDP policies that explicitly include continuous observations. We apply our algorithm to a novel tagging problem and an extended version of a common benchmark, where it generates policies that meet or exceed the values of equivalent discretized domains without the need for finding an adequate discretization.

scholarly journals Perception-Aware Point-Based Value Iteration for Partially Observable Markov Decision Processes

2019 ◽  
Author(s):  
Mahsa Ghasemi ◽  
Ufuk Topcu
Keyword(s):  
Markov Decision Processes ◽  
Active Role ◽  
Decision Processes ◽  
Iteration Algorithm ◽  
Value Iteration ◽  
Greedy Strategy ◽  
Markov Decision ◽  
Partially Observable Markov ◽  
Observation Selection ◽  
Partially Observable

In conventional partially observable Markov decision processes, the observations that the agent receives originate from fixed known distributions. However, in a variety of real-world scenarios, the agent has an active role in its perception by selecting which observations to receive. We avoid combinatorial expansion of the action space from integration of planning and perception decisions, through a greedy strategy for observation selection that minimizes an information-theoretic measure of the state uncertainty. We develop a novel point-based value iteration algorithm that incorporates this greedy strategy to pick perception actions for each sampled belief point in each iteration. As a result, not only the solver requires less belief points to approximate the reachable subspace of the belief simplex, but it also requires less computation per iteration. Further, we prove that the proposed algorithm achieves a near-optimal guarantee on value function with respect to an optimal perception strategy, and demonstrate its performance empirically.

scholarly journals Online Planning Algorithms for POMDPs

2008 ◽  
Vol 32 ◽  
pp. 663-704 ◽  
Author(s):  
S. Ross ◽  
J. Pineau ◽  
S. Paquet ◽  
B. Chaib-draa
Keyword(s):  
Heuristic Search ◽  
State Of The Art ◽  
Sequential Decision Making ◽  
Sequential Decision ◽  
Time Step ◽  
Advantages And Disadvantages ◽  
Online Planning ◽  
Markov Decision ◽  
Heuristic Search Methods ◽  
Partially Observable

Partially Observable Markov Decision Processes (POMDPs) provide a rich framework for sequential decision-making under uncertainty in stochastic domains. However, solving a POMDP is often intractable except for small problems due to their complexity. Here, we focus on online approaches that alleviate the computational complexity by computing good local policies at each decision step during the execution. Online algorithms generally consist of a lookahead search to find the best action to execute at each time step in an environment. Our objectives here are to survey the various existing online POMDP methods, analyze their properties and discuss their advantages and disadvantages; and to thoroughly evaluate these online approaches in different environments under various metrics (return, error bound reduction, lower bound improvement). Our experimental results indicate that state-of-the-art online heuristic search methods can handle large POMDP domains efficiently.

Partially Observable Markov Decision Processes and Robotics

2022 ◽  
Vol 5 (1) ◽  
Author(s):  
Hanna Kurniawati
Keyword(s):  
Autonomous Systems ◽  
Optimal Solution ◽  
Lessons Learned ◽  
Annual Review ◽  
Publication Date ◽  
Mathematical Framework ◽  
Planning Under Uncertainty ◽  
Markov Decision ◽  
Partially Observable Markov ◽  
Partially Observable

Planning under uncertainty is critical to robotics. The partially observable Markov decision process (POMDP) is a mathematical framework for such planning problems. POMDPs are powerful because of their careful quantification of the nondeterministic effects of actions and the partial observability of the states. But for the same reason, they are notorious for their high computational complexity and have been deemed impractical for robotics. However, over the past two decades, the development of sampling-based approximate solvers has led to tremendous advances in POMDP-solving capabilities. Although these solvers do not generate the optimal solution, they can compute good POMDP solutions that significantly improve the robustness of robotics systems within reasonable computational resources, thereby making POMDPs practical for many realistic robotics problems. This article presents a review of POMDPs, emphasizing computational issues that have hindered their practicality in robotics and ideas in sampling-based solvers that have alleviated such difficulties, together with lessons learned from applying POMDPs to physical robots. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 5 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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