Bayesian dynamic programming

1975 ◽  
Vol 7 (2) ◽  
pp. 330-348 ◽  
Author(s):  
Ulrich Rieder
Keyword(s):  
Dynamic Programming ◽  
Weak Convergence ◽  
Decision Model ◽  
Transition Probabilities ◽  
General State ◽  
Parameter Spaces ◽  
State Action ◽  
Total Rewards ◽  
Bayesian Dynamic Programming ◽  
Dynamic Decision Model

We consider a non-stationary Bayesian dynamic decision model with general state, action and parameter spaces. It is shown that this model can be reduced to a non-Markovian (resp. Markovian) decision model with completely known transition probabilities. Under rather weak convergence assumptions on the expected total rewards some general results are presented concerning the restriction on deterministic generalized Markov policies, the criteria of optimality and the existence of Bayes policies. These facts are based on the above transformations and on results of Hindererand Schäl.

Bayesian dynamic programming

1975 ◽  
Vol 7 (02) ◽  
pp. 330-348 ◽  
Author(s):  
Ulrich Rieder
Keyword(s):  
Dynamic Programming ◽  
Weak Convergence ◽  
Decision Model ◽  
Transition Probabilities ◽  
General State ◽  
Parameter Spaces ◽  
State Action ◽  
Total Rewards ◽  
Bayesian Dynamic Programming ◽  
Dynamic Decision Model

We consider a non-stationary Bayesian dynamic decision model with general state, action and parameter spaces. It is shown that this model can be reduced to a non-Markovian (resp. Markovian) decision model with completely known transition probabilities. Under rather weak convergence assumptions on the expected total rewards some general results are presented concerning the restriction on deterministic generalized Markov policies, the criteria of optimality and the existence of Bayes policies. These facts are based on the above transformations and on results of Hindererand Schäl.

scholarly journals Solving Channel Allocation by Reinforcement Learning in Cognitive Enabled Vehicular Ad Hoc Networks

2021 ◽  
Author(s):  
Yunfan Su
Keyword(s):  
Dynamic Programming ◽  
Reinforcement Learning ◽  
Optimal Policy ◽  
Ad Hoc ◽  
Transition Probabilities ◽  
Channel Allocation ◽  
Dynamic Programming Method ◽  
Learning Method ◽  
Time Intervals ◽  
Model Free

Vehicular ad hoc network (VANET) is a promising technique that improves traffic safety and transportation efficiency and provides a comfortable driving experience. However, due to the rapid growth of applications that demand channel resources, efficient channel allocation schemes are required to utilize the performance of the vehicular networks. In this thesis, two Reinforcement learning (RL)-based channel allocation methods are proposed for a cognitive enabled VANET environment to maximize a long-term average system reward. First, we present a model-based dynamic programming method, which requires the calculations of the transition probabilities and time intervals between decision epochs. After obtaining the transition probabilities and time intervals, a relative value iteration (RVI) algorithm is used to find the asymptotically optimal policy. Then, we propose a model-free reinforcement learning method, in which we employ an agent to interact with the environment iteratively and learn from the feedback to approximate the optimal policy. Simulation results show that our reinforcement learning method can acquire a similar performance to that of the dynamic programming while both outperform the greedy method.

scholarly journals Solving Channel Allocation by Reinforcement Learning in Cognitive Enabled Vehicular Ad Hoc Networks

2021 ◽  
Author(s):  
Yunfan Su
Keyword(s):  
Dynamic Programming ◽  
Reinforcement Learning ◽  
Optimal Policy ◽  
Ad Hoc ◽  
Transition Probabilities ◽  
Channel Allocation ◽  
Dynamic Programming Method ◽  
Learning Method ◽  
Time Intervals ◽  
Model Free

Vehicular ad hoc network (VANET) is a promising technique that improves traffic safety and transportation efficiency and provides a comfortable driving experience. However, due to the rapid growth of applications that demand channel resources, efficient channel allocation schemes are required to utilize the performance of the vehicular networks. In this thesis, two Reinforcement learning (RL)-based channel allocation methods are proposed for a cognitive enabled VANET environment to maximize a long-term average system reward. First, we present a model-based dynamic programming method, which requires the calculations of the transition probabilities and time intervals between decision epochs. After obtaining the transition probabilities and time intervals, a relative value iteration (RVI) algorithm is used to find the asymptotically optimal policy. Then, we propose a model-free reinforcement learning method, in which we employ an agent to interact with the environment iteratively and learn from the feedback to approximate the optimal policy. Simulation results show that our reinforcement learning method can acquire a similar performance to that of the dynamic programming while both outperform the greedy method.

Bounds and good policies in stationary finite–stage Markovian decision problems

1980 ◽  
Vol 12 (1) ◽  
pp. 154-173 ◽  
Author(s):  
Gerhard Hübner
Keyword(s):  
Decision Model ◽  
Transition Probabilities ◽  
Planning Horizon ◽  
Decision Problems ◽  
Optimal Decisions ◽  
Optimal Value ◽  
Action Spaces ◽  
Stationary Problems ◽  
Markovian Decision Problems

A stationary Markovian decision model is considered with general state and action spaces where the transition probabilities are weakened to be bounded transition measures (this is useful for many applications). New and improved bounds are given for the optimal value of stationary problems with a large planning horizon if either only a few steps of iteration are carried out or, in addition, a solution of the infinite-stage problem is known. Similar estimates are obtained for the quality of policies which are composed of nearly optimal decisions from the first few steps or from the infinite-stage solution.

The robustness of positive recurrence and recurrence of Markov chains under perturbations of the transition probabilities

1975 ◽  
Vol 12 (04) ◽  
pp. 744-752 ◽  
Author(s):  
Richard L. Tweedie
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Finite Number ◽  
Transition Probabilities ◽  
General State ◽  
Transition Matrices ◽  
Positive Recurrence ◽  
Markov Chain Models ◽  
Countable Space ◽  
General State Space

In many Markov chain models, the immediate characteristic of importance is the positive recurrence of the chain. In this note we investigate whether positivity, and also recurrence, are robust properties of Markov chains when the transition laws are perturbed. The chains we consider are on a fairly general state space : when specialised to a countable space, our results are essentially that, if the transition matrices of two irreducible chains coincide on all but a finite number of columns, then positivity of one implies positivity of both; whilst if they coincide on all but a finite number of rows and columns, recurrence of one implies recurrence of both. Examples are given to show that these results (and their general analogues) cannot in general be strengthened.

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