Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the finite-state approximation of a discrete-time constrained Markov decision process with compact state space, under the discounted cost criterion. Using the linear programming formulation of the constrained problem,  prove the convergence of the optimal value function of the finite-state model to the optimal value function of the original model. Under further continuity condition on the transition probability of the original model,  also establish a method to compute approximately optimal policies.
['Naci Saldi', 'Serdar Yuksel', 'Tamás Linder']
I am writing a research paper on a idea Finite-state approximations to constrained Markov decision processes with Borel spaces
[{"from": "human", "value": "I am writing a research paper on a idea Finite-state approximations to constrained Markov decision processes with Borel spaces"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the finite-state approximation of a discrete-time constrained Markov decision process with compact state space, under the discounted cost criterion. Using the linear programming formulation of the constrained problem,  prove the convergence of the optimal value function of the finite-state model to the optimal value function of the original model. Under further continuity condition on the transition probability of the original model,  also establish a method to compute approximately optimal policies."}]