From 905e8c340af27971b0b82e330d6db244360b28ca Mon Sep 17 00:00:00 2001 From: Gilles Louppe Date: Tue, 19 Dec 2017 10:56:17 +0100 Subject: [PATCH] aixi --- figures/lec10/aixi-action.png | Bin 0 -> 100455 bytes figures/lec10/brain.jpg | Bin 0 -> 757325 bytes figures/lec10/mc-aixi.png | Bin 0 -> 108424 bytes figures/lec10/optimal-action.png | Bin 0 -> 207916 bytes figures/lec10/simulation.png | Bin 0 -> 94634 bytes figures/lec10/tm.png | Bin 0 -> 58524 bytes lecture10.md | 106 ++++++++++++++++++++++++++++++- 7 files changed, 104 insertions(+), 2 deletions(-) create mode 100644 figures/lec10/aixi-action.png create mode 100644 figures/lec10/brain.jpg create mode 100644 figures/lec10/mc-aixi.png create mode 100644 figures/lec10/optimal-action.png create mode 100644 figures/lec10/simulation.png create mode 100644 figures/lec10/tm.png diff --git a/figures/lec10/aixi-action.png b/figures/lec10/aixi-action.png new file mode 100644 index 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https://futureoflife.org/wp-content/uploads/2017/01/Jurgen-Schmidhuber.pdf?x56934 +http://machineintelligence.org/universal-ai.pdf --- @@ -61,6 +62,8 @@ https://futureoflife.org/wp-content/uploads/2017/01/Jurgen-Schmidhuber.pdf?x5693 .center.width-40[![](figures/lec10/go.png)] +.footnote[Credits: [Andrej Karpathy, Where will AGI come from?](https://docs.google.com/presentation/d/119VW6ueBGLQXsw-jGMboGP2-WuOnyMAOYLgd44SL6xM)] + --- class: smaller @@ -71,6 +74,8 @@ class: smaller .center[Can we run AlphaGo on a robot for the Amazon Picking Challenge?] +.footnote[Credits: [Andrej Karpathy, Where will AGI come from?](https://docs.google.com/presentation/d/119VW6ueBGLQXsw-jGMboGP2-WuOnyMAOYLgd44SL6xM)] + --- class: smaller @@ -88,6 +93,8 @@ class: smaller - *Clear and fast evaluation*: not good - *Huge dataset available*: **challenge** +.footnote[Credits: [Andrej Karpathy, Where will AGI come from?](https://docs.google.com/presentation/d/119VW6ueBGLQXsw-jGMboGP2-WuOnyMAOYLgd44SL6xM)] + --- # Artificial general intelligence @@ -99,7 +106,7 @@ class: smaller - *plan*; - *learn*; - *communicate* in natural language; - - integrate all these skills towards *common goals*. + - integrate all these skills towards *common goals*. --- @@ -129,12 +136,14 @@ What happens when our computers get smarter than we are? Nick Bostrom Several working **hypothesis**: - *Supervised learning*: "It works, just scale up!" - *Unsupervised learning*: "It will work, if we only scale up!" -- *AIXI*: "Guys, I can write down optimal AI." +- *AIXI*: "Guys, I can write down an equation for optimal AI." - *Brain simulation*: "This will work one day, right?" - *Artificial life*: "Let just do what Nature did." Or maybe something else? +.footnote[Credits: [Andrej Karpathy, Where will AGI come from?](https://docs.google.com/presentation/d/119VW6ueBGLQXsw-jGMboGP2-WuOnyMAOYLgd44SL6xM)] + --- class: middle, center @@ -143,6 +152,69 @@ class: middle, center --- +# Start with an equation + +$$\Upsilon(\pi) := \sum\_{\mu \in E} 2^{-K(\mu)} V^{\pi}\_\mu$$ + +- $\Upsilon(\pi)$ *formally* defines the **universal intelligence** of an agent $\pi$. +- $\mu$ is the environment of the agent and $E$ is the set of all computable reward bounded environments. +- $V^{\pi}\_\mu = \mathbb{E}\[ \sum\_{i=1}^\infty R\_i \]$ is the expected sum of future rewards when the agent $\pi$ interacts with environment $\mu$. +- $K(.)$ is the Kolmogorov complexity, such that $2^{-K(\mu)}$ weights the agent's performance in each environment, inversely proportional to its complexity. + - Intuitively, $K(\mu)$ measures the complexity of the shortest Universal Turing Machine program that describes the environment $\mu$. + +--- + +# AIXI + +$$\bar{\Upsilon} = \max\_\pi \Upsilon(\pi) = \Upsilon(\pi^{AIXI})$$ + +- $\pi^{AIXI}$ is a **perfect** theoretical agent. +- It always picks the action which has the greatest expected reward. +- For every environment $\mu \in E$, the agent must: + - Take into account how likely it is that it is facing $\mu$ given the interaction history so far, and the prior probability of $\mu$. + - Consider all possible future interactions that might occur. + - Evaluate how likely they are. + - Then select the action that maximizes the expected future reward. + +--- + +# System identification + +- Which Turing machine is the agent in? If it knew, it could plan perfectly. +- Let's use the *Bayes rule* to update the agent beliefs given its experience so far. + +.center.width-100[![](figures/lec10/tm.png)] + +.footnote[Credits: [Andrej Karpathy, Where will AGI come from?](https://docs.google.com/presentation/d/119VW6ueBGLQXsw-jGMboGP2-WuOnyMAOYLgd44SL6xM)] + +--- + +# Optimal action + +.center.width-100[![](figures/lec10/optimal-action.png)] + +.footnote[Credits: [Andrej Karpathy, Where will AGI come from?](https://docs.google.com/presentation/d/119VW6ueBGLQXsw-jGMboGP2-WuOnyMAOYLgd44SL6xM)] + +??? + +The equation embodies in one line the major ideas of Bayes, Ockham, Epicurus, +Turing, von Neumann, Bellman, Kolmogorov, and Solomonoff. The AIXI agent is +rigorously shown by [Hut05] to be optimal in many different senses of the word. + +--- + +# Intractability + +.center.width-100[![](figures/lec10/aixi-action.png)] + +.footnote[Credits: [Andrej Karpathy, Where will AGI come from?](https://docs.google.com/presentation/d/119VW6ueBGLQXsw-jGMboGP2-WuOnyMAOYLgd44SL6xM)] + +--- + +# Monte Carlo approximation + +.center.width-100[![](figures/lec10/mc-aixi.png)] + --- @@ -152,6 +224,36 @@ class: middle, center --- +# Whole brain emulation + +.center.width-50[![](figures/lec10/brain.jpg)] + +- A hypothesis for AGI is **whole brain simulation**. + - A low-level brain model is built by scanning and mapping a biological brain in detail and copying its state into a computer system. + - The simulation is *so faithful* that it will behave in essentially the same way as the original. +- Ongoing initiatives: BRAIN, Blue Brain Project, Human Brain Project, NeuraLink, etc. + +--- + +# Obstacles + +- How to *measure* a complete brain state? +- At what level of abstraction? +- How to model the dynamics? +- How do you simulate the environment to feed into senses? +- Various **ethical dilemmas**. + +--- + +# Mind upload + +- **Hypothetically**, whole brain emulation would enable *mind upload*. + - The mental state of a particular brain substrate could be scanned and copied into a computer. + - The computer could then run a simulation of the brain's information processing, such that it responds in the same way as the original brain. +- That is, simulation would be indistinguishable from reality. + +.center.width-70[![](figures/lec10/simulation.png)] + --- class: middle, center

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