scholarly journals The Convergence of a Cooperation Markov Decision Process System

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 955
Author(s):  
Xiaoling Mo ◽  
Daoyun Xu ◽  
Zufeng Fu
Keyword(s):  
Markov Decision Process ◽  
Decision Process ◽  
Optimal Strategy ◽  
Value Function ◽  
Single Agent ◽  
Two Agents ◽  
Markov Decision ◽  
Process System ◽  
Multi Agent ◽  
Game Environment

In a general Markov decision progress system, only one agent’s learning evolution is considered. However, considering the learning evolution of a single agent in many problems has some limitations, more and more applications involve multi-agent. There are two types of cooperation, game environment among multi-agent. Therefore, this paper introduces a Cooperation Markov Decision Process (CMDP) system with two agents, which is suitable for the learning evolution of cooperative decision between two agents. It is further found that the value function in the CMDP system also converges in the end, and the convergence value is independent of the choice of the value of the initial value function. This paper presents an algorithm for finding the optimal strategy pair (πk0,πk1) in the CMDP system, whose fundamental task is to find an optimal strategy pair and form an evolutionary system CMDP(πk0,πk1). Finally, an example is given to support the theoretical results.

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 Value Function Transfer for Deep Multi-Agent Reinforcement Learning Based on N-Step Returns

2019 ◽  
Author(s):  
Yong Liu ◽  
Yujing Hu ◽  
Yang Gao ◽  
Yingfeng Chen ◽  
Changjie Fan
Keyword(s):  
Reinforcement Learning ◽  
Knowledge Transfer ◽  
Value Function ◽  
Single Agent ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Markov Decision ◽  
Dimensional State Space ◽  
Multi Agent ◽  
Function Transfer

Many real-world problems, such as robot control and soccer game, are naturally modeled as sparse-interaction multi-agent systems. Reutilizing single-agent knowledge in multi-agent systems with sparse interactions can greatly accelerate the multi-agent learning process. Previous works rely on bisimulation metric to define Markov decision process (MDP) similarity for controlling knowledge transfer. However, bisimulation metric is costly to compute and is not suitable for high-dimensional state space problems. In this work, we propose more scalable transfer learning methods based on a novel MDP similarity concept. We start by defining the MDP similarity based on the N-step return (NSR) values of an MDP. Then, we propose two knowledge transfer methods based on deep neural networks called direct value function transfer and NSR-based value function transfer. We conduct experiments in image-based grid world, multi-agent particle environment (MPE) and Ms. Pac-Man game. The results indicate that the proposed methods can significantly accelerate multi-agent reinforcement learning and meanwhile get better asymptotic performance.

On Optimal Terminal Wealth Problems with Random Trading Times and Drawdown Constraints

2014 ◽  
Vol 46 (01) ◽  
pp. 121-138 ◽  
Author(s):  
Ulrich Rieder ◽  
Marc Wittlinger
Keyword(s):  
Markov Decision Process ◽  
Decision Process ◽  
Value Function ◽  
Stationary Policy ◽  
General Utility ◽  
Investment Problem ◽  
Markov Decision ◽  
Optimal Stationary Policy ◽  
Running Maximum ◽  
The Value Function

We consider an investment problem where observing and trading are only possible at random times. In addition, we introduce drawdown constraints which require that the investor's wealth does not fall under a prior fixed percentage of its running maximum. The financial market consists of a riskless bond and a stock which is driven by a Lévy process. Moreover, a general utility function is assumed. In this setting we solve the investment problem using a related limsup Markov decision process. We show that the value function can be characterized as the unique fixed point of the Bellman equation and verify the existence of an optimal stationary policy. Under some mild assumptions the value function can be approximated by the value function of a contracting Markov decision process. We are able to use Howard's policy improvement algorithm for computing the value function as well as an optimal policy. These results are illustrated in a numerical example.

On Optimal Terminal Wealth Problems with Random Trading Times and Drawdown Constraints

2014 ◽  
Vol 46 (1) ◽  
pp. 121-138 ◽  
Author(s):  
Ulrich Rieder ◽  
Marc Wittlinger
Keyword(s):  
Markov Decision Process ◽  
Decision Process ◽  
Value Function ◽  
Stationary Policy ◽  
General Utility ◽  
Investment Problem ◽  
Markov Decision ◽  
Optimal Stationary Policy ◽  
Running Maximum ◽  
The Value Function

We consider an investment problem where observing and trading are only possible at random times. In addition, we introduce drawdown constraints which require that the investor's wealth does not fall under a prior fixed percentage of its running maximum. The financial market consists of a riskless bond and a stock which is driven by a Lévy process. Moreover, a general utility function is assumed. In this setting we solve the investment problem using a related limsup Markov decision process. We show that the value function can be characterized as the unique fixed point of the Bellman equation and verify the existence of an optimal stationary policy. Under some mild assumptions the value function can be approximated by the value function of a contracting Markov decision process. We are able to use Howard's policy improvement algorithm for computing the value function as well as an optimal policy. These results are illustrated in a numerical example.

Optimal Occupation in the Complete Graph

1993 ◽  
Vol 7 (3) ◽  
pp. 369-385 ◽  
Author(s):  
Kyle Siegrist
Keyword(s):  
Markov Decision Process ◽  
Complete Graph ◽  
Decision Process ◽  
Value Function ◽  
Comparison Result ◽  
State Action ◽  
Optimal Policies ◽  
Markov Decision ◽  
The Cost ◽  
The Value Function

We consider N sites (N ≤ ∞), each of which may be either occupied or unoccupied. Time is discrete, and at each time unit a set of occupied sites may attempt to capture a previously unoccupied site. The attempt will be successful with a probability that depends on the number of sites making the attempt, in which case the new site will also be occupied. A benefit is gained when new sites are occupied, but capture attempts are costly. The problem of optimal occupation is formulated as a Markov decision process in which the admissible actions are occupation strategies and the cost is a function of the strategy and the number of occupied sites. A partial order on the state-action pairs is used to obtain a comparison result for stationary policies and qualitative results concerning monotonicity of the value function for the n-stage problem (n ≤ ∞). The optimal policies are partially characterized when the cost depends on the action only through the total number of occupation attempts made.

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