Toward an optimized value iteration algorithm for average cost Markov decision processes

2010 ◽  
Author(s):  
Edilson F. Arruda ◽  
Fabricio Ourique ◽  
Anthony Almudevar
Keyword(s):  
Markov Decision Processes ◽  
Average Cost ◽  
Decision Processes ◽  
Iteration Algorithm ◽  
Value Iteration ◽  
Markov Decision ◽  
Value Iteration Algorithm

A Modified Value Iteration Algorithm for Discounted Markov Decision Processes

2015 ◽  
Vol 13 (3) ◽  
pp. 47-57 ◽  
Author(s):  
Sanaa Chafik ◽  
Cherki Daoui
Keyword(s):  
Markov Decision Processes ◽  
Decision Processes ◽  
Iteration Algorithm ◽  
Value Iteration ◽  
Decomposition Technique ◽  
Artificial Data ◽  
Markov Decision ◽  
Speed Up ◽  
Value Iteration Algorithm

As many real applications need a large amount of states, the classical methods are intractable for solving large Markov Decision Processes. The decomposition technique basing on the topology of each state in the associated graph and the parallelization technique are very useful methods to cope with this problem. In this paper, the authors propose a Modified Value Iteration algorithm, adding the parallelism technique. They test their implementation on artificial data using an Open MP that offers a significant speed-up.

Parallel Hierarchical Pre-Gauss-Seidel Value Iteration Algorithm

2018 ◽  
Vol 10 (2) ◽  
pp. 1-22
Author(s):  
Sanaa Chafik ◽  
Abdelhadi Larach ◽  
Cherki Daoui
Keyword(s):  
Markov Decision Processes ◽  
Iteration Scheme ◽  
Decision Processes ◽  
Iteration Algorithm ◽  
Value Iteration ◽  
Markov Decision ◽  
Standard Value ◽  
Number Of Iterations ◽  
Value Iteration Algorithm ◽  
Better Than

The standard Value Iteration (VI) algorithm, referred to as Value Iteration Pre-Jacobi (PJ-VI) algorithm, is the simplest Value Iteration scheme, and the well-known algorithm for solving Markov Decision Processes (MDPs). In the literature, several versions of VI algorithm were developed in order to reduce the number of iterations: the VI Jacobi (VI-J) algorithm, the Value Iteration Pre-Gauss-Seidel (VI-PGS) algorithm and the VI Gauss-Seidel (VI-GS) algorithm. In this article, the authors combine the advantages of VI Pre Gauss-Seidel algorithm, the decomposition technique and the parallelism in order to propose a new Parallel Hierarchical VI Pre-Gauss-Seidel algorithm. Experimental results show that their approach performs better than the traditional VI schemes in the case where the global problem can be decomposed into smaller problems.

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.

BOUNDED-PARAMETER PARTIALLY OBSERVABLE MARKOV DECISION PROCESSES: FRAMEWORK AND ALGORITHM

2013 ◽  
Vol 21 (06) ◽  
pp. 821-863 ◽  
Author(s):  
YAODONG NI ◽  
ZHI-QIANG LIU
Keyword(s):  
Markov Decision Processes ◽  
Real Life ◽  
Decision Processes ◽  
Iteration Algorithm ◽  
Value Iteration ◽  
Planning Under Uncertainty ◽  
Markov Decision ◽  
Real Life Situation ◽  
Partially Observable Markov ◽  
Partially Observable

Partially observable Markov decision processes (POMDPs) are powerful for planning under uncertainty. However, it is usually impractical to employ a POMDP with exact parameters to model the real-life situation precisely, due to various reasons such as limited data for learning the model, inability of exact POMDPs to model dynamic situations, etc. In this paper, assuming that the parameters of POMDPs are imprecise but bounded, we formulate the framework of bounded-parameter partially observable Markov decision processes (BPOMDPs). A modified value iteration is proposed as a basic strategy for tackling parameter imprecision in BPOMDPs. In addition, we design the UL-based value iteration algorithm, in which each value backup is based on two sets of vectors called U-set and L-set. We propose four strategies for computing U-set and L-set. We analyze theoretically the computational complexity and the reward loss of the algorithm. The effectiveness and robustness of the algorithm are shown empirically.

scholarly journals First Order Decision Diagrams for Relational MDPs

2008 ◽  
Vol 31 ◽  
pp. 431-472 ◽  
Author(s):  
C. Wang ◽  
S. Joshi ◽  
R. Khardon
Keyword(s):  
Markov Decision Processes ◽  
Optimal Policy ◽  
Decision Processes ◽  
Compact Representation ◽  
Iteration Algorithm ◽  
Decision Diagrams ◽  
Value Iteration ◽  
First Order ◽  
Relational Structures ◽  
Markov Decision

Markov decision processes capture sequential decision making under uncertainty, where an agent must choose actions so as to optimize long term reward. The paper studies efficient reasoning mechanisms for Relational Markov Decision Processes (RMDP) where world states have an internal relational structure that can be naturally described in terms of objects and relations among them. Two contributions are presented. First, the paper develops First Order Decision Diagrams (FODD), a new compact representation for functions over relational structures, together with a set of operators to combine FODDs, and novel reduction techniques to keep the representation small. Second, the paper shows how FODDs can be used to develop solutions for RMDPs, where reasoning is performed at the abstract level and the resulting optimal policy is independent of domain size (number of objects) or instantiation. In particular, a variant of the value iteration algorithm is developed by using special operations over FODDs, and the algorithm is shown to converge to the optimal policy.

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