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

One often encounters the curse of dimensionality in the application ofdynamic programming to determine optimal policies for controlled Markov chains.In this paper, we provide a method to construct sub-optimal policies along witha bound for the deviation of such a policy from the optimum via a linearprogramming approach. The state-space is partitioned and the optimal cost-to-goor value function is approximated by a constant over each partition. Byminimizing a non-negative cost function defined on the partitions, one canconstruct an approximate value function which also happens to be an upper boundfor the optimal value function of the original Markov Decision Process (MDP).As a key result, we show that this approximate value function is {\itindependent} of the non-negative cost function (or state dependent weights asit is referred to in the literature) and moreover, this is the least upperbound that one can obtain once the partitions are specified. Furthermore, weshow that the restricted system of linear inequalities also embeds a family ofMDPs of lower dimension, one of which can be used to construct a lower bound onthe optimal value function. The construction of the lower bound requires thesolution to a combinatorial problem. We apply the linear programming approachto a perimeter surveillance stochastic optimal control problem and obtainnumerical results that corroborate the efficacy of the proposed methodology.

Bounding Procedures for Stochastic Dynamic Programs with Application to the Perimeter Patrol Problem