Finite state dynamic programming with the total reward criterion

1986 ◽  
Vol 30 (1) ◽  
pp. A1-A14 ◽  
Author(s):  
R. Dawen
Keyword(s):  
Dynamic Programming ◽  
State Dynamic ◽  
Total Reward ◽  
Finite State ◽  
Reward Criterion

MARKOV MATHEMATICAL MODEL OF DYNAMIC ADAPTIVE TESTING OF AN ACTIVE AGENT

2018 ◽  
pp. 29-35
Author(s):  
N. V. Brovka ◽  
P. P. Dyachuk ◽  
M. V. Noskov ◽  
I. P. Peregudova
Keyword(s):  
Mathematical Model ◽  
Finite State Machine ◽  
Active Agent ◽  
Adaptive Testing ◽  
State Machine ◽  
Learning Activities ◽  
Independent Learning ◽  
Complex Object ◽  
Total Reward ◽  
Finite State

The problem and the goal.The urgency of the problem of mathematical description of dynamic adaptive testing is due to the need to diagnose the cognitive abilities of students for independent learning activities. The goal of the article is to develop a Markov mathematical model of the interaction of an active agent (AA) with the Liquidator state machine, canceling incorrect actions, which will allow mathematically describe dynamic adaptive testing with an estimated feedback.The research methodologyconsists of an analysis of the results of research by domestic and foreign scientists on dynamic adaptive testing in education, namely: an activity approach that implements AA developmental problem-solving training; organizational and technological approach to managing the actions of AA in terms of evaluative feedback; Markow’s theory of cement and reinforcement learning.Results.On the basis of the theory of Markov processes, a Markov mathematical model of the interaction of an active agent with a finite state machine, canceling incorrect actions, was developed. This allows you to develop a model for diagnosing the procedural characteristics of students ‘learning activities, including: building axiograms of total reward for students’ actions; probability distribution of states of the solution of the problem of identifying elements of the structure of a complex object calculate the number of AA actions required to achieve the target state depending on the number of elements that need to be identified; construct a scatter plot of active agents by target states in space (R, k), where R is the total reward AA, k is the number of actions performed.Conclusion.Markov’s mathematical model of the interaction of an active agent with a finite state machine, canceling wrong actions allows you to design dynamic adaptive tests and diagnostics of changes in the procedural characteristics of educational activities. The results and conclusions allow to formulate the principles of dynamic adaptive testing based on the estimated feedback.

Nash equilibria in a class of Markov stopping games with total reward criterion

2021 ◽  
Author(s):  
Rolando Cavazos-Cadena ◽  
Mario Cantú-Sifuentes ◽  
Imelda Cerda-Delgado
Keyword(s):  
Nash Equilibria ◽  
Total Reward ◽  
Stopping Games ◽  
Reward Criterion

EXISTENCE OF OPTIMAL STATIONARY POLICIES IN FINITE DYNAMIC PROGRAMS WITH NONNEGATIVE REWARDS

2001 ◽  
Vol 15 (4) ◽  
pp. 557-564 ◽  
Author(s):  
Rolando Cavazos-Cadena ◽  
Raúl Montes-de-Oca
Keyword(s):  
Control Policy ◽  
Stationary Policy ◽  
Reward Function ◽  
Total Reward ◽  
Dynamic Programs ◽  
Finite State ◽  
Markov Decision ◽  
Optimal Stationary Policy ◽  
Action Spaces ◽  
Discounted Criterion

This article concerns Markov decision chains with finite state and action spaces, and a control policy is graded via the expected total-reward criterion associated to a nonnegative reward function. Within this framework, a classical theorem guarantees the existence of an optimal stationary policy whenever the optimal value function is finite, a result that is obtained via a limit process using the discounted criterion. The objective of this article is to present an alternative approach, based entirely on the properties of the expected total-reward index, to establish such an existence result.

scholarly journals On the total reward variance for continuous-time Markov reward chains

2006 ◽  
Vol 43 (04) ◽  
pp. 1044-1052 ◽  
Author(s):  
Nico M. Van Dijk ◽  
Karel Sladký
Keyword(s):  
Growth Rate ◽  
Discrete Time ◽  
Continuous Time ◽  
Asymptotically Linear ◽  
State Spaces ◽  
Total Reward ◽  
Finite State ◽  
Markov Reward ◽  
Discrete Time Case

As an extension of the discrete-time case, this note investigates the variance of the total cumulative reward for continuous-time Markov reward chains with finite state spaces. The results correspond to discrete-time results. In particular, the variance growth rate is shown to be asymptotically linear in time. Expressions are provided to compute this growth rate.

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