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In Interval Bound Propagation 101 I derived the general IBP machinery: interval arithmetic over matrices via Rump’s algorithm, and how to propagate those bounds through a feed-forward network layer by layer. This post grounds that theory in a small worked example: a concrete network, a from-scratch numpy implementation of IBP, and the visualizations that fall out of it.
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The purpose of this post is to explain the basics of the Interval Bound Propagation (IBP) method. It is powerful tool which allows to provide guarantees about output ranges of a neural network. I mostly follow the notation from deep reinforcement learning (RL), therefore the typical neural network for which I want to compute bounds is a neural policy.
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From https://www.nature.com/articles/s42256-022-00568-3 (which is for supervised learning)
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Say you want to estimate a distribution of a latent vector $Z$ based on observations $X$. You can do that with variational inference!
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Conspectus of Sutton & Barto “Reinforcement Learning: An Introduction”
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Conspectus of Sutton & Barto “Reinforcement Learning: An Introduction”
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One of the core concepts of basic reinforcement learning are a Markov Process and a Markov Reward Process.