---
title: "Hansen"
type: concept
related: [Controller, Policy Iteration, Partially Observable Markov Decision Process]
source: https://www.jemoka.com/posts/kbhhansen/
confidence: high
status: active
---

controller POMDP policies with FST. Previous papers had exponential blowups.
Successor function is deterministic.
policy iteration Use FST as policy representation:
deterministic controller POMDP evaluation for all \((a,o,x)\), add a now node x&rsquo; and evaluate them to see if its needed then, we perform pruning everything that&rsquo;s dominated (i.e. \(U(x,s) &lt; U(x&rsquo;, s) \forall s\). i.e. we want to prune everything for which the expected utility of being in node \(x&rsquo;\) dominates the expected utility of \(x\) for all \(x\). prune new nodes that are duplicates in terms of action and transitions When you are done, extract the policy: find the node that maximizes your
heuristic search Optimize value function ran starting at the starting belief state, not for all states. Add nodes only when improvement is seen starting at the beginning.
deterministic controller POMDP evaluation Recall that controllers are defined over belief-states, and, unlike finite state controller evaluation, the transitions are not distributions; so, we have:
\begin{equation} U(x,s) = R(s,a(x)) + \gamma \sum_{s&rsquo;}^{}T(s&rsquo;|s,a(x)) \sum_{o}^{} O(o|s&rsquo;, a(x)) U(x&rsquo;(x,a,o), s&rsquo;) \end{equation}
