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Value iteration algorithm for mean-field games
(Elsevier, 2020-09)
In the literature, existence of mean-field equilibria has been established for discrete-time mean field games under both the discounted cost and the average cost optimality criteria. In this paper, we provide a value ...
Weak Feller property of non-linear filters
(Elsevier, 2019-12)
Weak Feller property of controlled and control-free Markov chains leads to many desirable properties. In control-free setups this leads to the existence of invariant probability measures for compact spaces and applicability ...
Approximations for constrained Markov decision problems
(Springer, 2018)
This chapter studies the finite-state approximation of a discrete-time constrained Markov decision process with compact state space, under the discounted and average cost criteria. Using the linear programming formulation ...
Finite-action approximation of Markov decision processes
(Birkhäuser Basel, 2018)
In this chapter, we study the finite-action approximation of optimal control policies for discrete-time Markov decision processes (MDPs) with Borel state and action spaces, under discounted and average cost criteria. One ...
Finite model approximations in decentralized stochastic control
(Birkhäuser Basel, 2018)
In this chapter, we study the approximation of static and dynamic team problems using finite models which are obtained through the uniform discretization, on a finite grid, of the observation and action spaces of agents. ...
Finite-state approximation of Markov decision processes
(Springer, 2018)
In this chapter we study the finite-state approximation problem for computing near optimal policies for discrete-time MDPs with Borel state and action spaces, under discounted and average costs criteria. Even though existence ...
Finite approximations in discrete-time stochastic control : quantized models and asymptotic optimality
(Birkhäuser Basel, 2018)
In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how ...
Approximations for partially observed Markov decision processes
(Birkhäuser Basel, 2018)
This chapter studies the finite-model approximation of discrete-time partially observed Markov decision process. We will find that by performing the standard reduction method, where one transforms a partially observed model ...
Markov-Nash equilibria in mean-field games with discounted cost
(Society for Industrial and Applied Mathematics Publications, 2018)
In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number $N$ of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space of each agent is a Polish ...
Finite approximations in discrete-time stochastic control quantized models and asymptotic optimality introduction and summary
(Birkhäuser Basel, 2018)
Control and optimization of dynamical systems in the presence of stochastic uncertainty is a mature field with a large range of applications. A comprehensive treatment of such problems can be found in excellent books and ...
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