## reinforcement learning – Resources on Dynamic Programming with Indefinite Recursion

I am trying to explain the value iteration method that is used in reinforcement learning. The method is used to estimate a solution to a recursive equation like:

$$Return(state_t,action_t) = Reward(state_t,state_{t+1}) + gamma * max begin{bmatrix} Return(state_{t+1}, action_{t+1}==’n’)\ Return(state_{t+1}, action_{t+1}==’e’)\ Return(state_{t+1}, action_{t+1}==’w’)\ Return(state_{t+1}, action_{t+1}==’s’) end{bmatrix}$$

Normally, if the sub-problems(RHS) are overlapping, a problem like this can be solved using recursive or iterative dynamic programming. However, in the case of reinforcement learning the recursion is often mutual, and thus the dynamic programming solution has no natural point of termination.

The value iteration method works by filling up the memorization table with arbitrary values and then repeatedly applying the recursive equation to every cell in the table until the values in the cell converge.

A similar approach is used in the HITS algorithm where the hub and authority values have mutual recursion.

Are there any good resources, preferably online, that deal with the application of dynamic programming to problems with mutual, indefinite recursion?

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### raindog308

I’m Andrew, techno polymath and long-time LowEndTalk community Moderator. My technical interests include all things Unix, perl, python, shell scripting, and relational database systems. I enjoy writing technical articles here on LowEndBox to help people get more out of their VPSes.

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## web development – Solution to notify users Single Page Application (SPA) static resources have updated if users don’t refresh their browsers

Basically you want to trigger an event when the version changes to inform the user that their UI is outdated and they should refresh. If you want to keep it simple this can be done file-based. You basically need these components:

• A JavaScript file (currentversion.js) that dispatches a event about the current version
• Logic in the SPA that periodically reloads currentversion.js file and defines listeners for the “currentversion” event.

The generation of that currentversion.js and `currentVersion` can be automatically generated to contain the correct version on every build.

The idea is to (re)load the currentversion.js as needed to dispatch the current version of the UI. The logic can listen for that event and act when the version has deviated from last known version.

In theory you can have something like:

currentversion.js

`window.dispatchEvent(new CustomEvent('currentversion', { detail: '1.1' }));`

index.html

``````<html>
<body>
<script>
const currentVersion = '1.1';

function startVersionCheck() {
const versionJs = document.getElementById('version-js');
const versionJsUrl = versionJs.src;
const versionCheck = function () {
};
setInterval(versionCheck, 60000);
}

const version = e.detail;
if (currentVersion !== version) {
window.dispatchEvent(new CustomEvent('versionchanged', { detail: version }));
}
});

Both the UI and currentversion.js expose the same version initially. When the value changes in currentversion.js it should eventually trigger the `versionchanged` event on the next reload.