English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In the theory of Partially Observed Markov Decision Processes (POMDPs),existence of optimal policies have in general been established via convertingthe original partially observed stochastic control problem to a fully observedone on the belief space, leading to a belief-MDP. However, computing an optimalpolicy for this fully observed model, and so for the original POMDP, usingclassical dynamic or linear programming methods is challenging even if theoriginal system has finite state and action spaces, since the state space ofthe fully observed belief-MDP model is always uncountable. Furthermore, thereexist very few rigorous value function approximation and optimal policyapproximation results, as regularity conditions needed often require a tediousstudy involving the spaces of probability measures leading to properties suchas Feller continuity. In this paper, we study a planning problem for POMDPswhere the system dynamics and measurement channel model are assumed to beknown. We construct an approximate belief model by discretizing the beliefspace using only finite window information variables. We then find optimalpolicies for the approximate model and we rigorously establish near optimalityof the constructed finite window control policies in POMDPs under mildnon-linear filter stability conditions and the assumption that the measurementand action sets are finite (and the state space is real vector valued). We alsoestablish a rate of convergence result which relates the finite window memorysize and the approximation error bound, where the rate of convergence isexponential under explicit and testable exponential filter stabilityconditions. While there exist many experimental results and few rigorousasymptotic convergence results, an explicit rate of convergence result is newin the literature, to our knowledge.

Near Optimality of Finite Memory Feedback Policies in Partially Observed Markov Decision Processes