open-ended

Open-ended systems endlessly produce interesting things.

Open-endedness is inherently observer-dependent—interestingness/novelty/compression.

Trying to define it objectively—that it is a property of the system, measurable from the outside without reference to any observer—, like unbounded novelty, ever-increasing complexity, ongoing adaptive activity, … is silly.
There’s no pre-specified objective that can capture it (see Why Greatness Cannot Be Planned).
But then what is it that drives our sense for interestingness / sense for open-ended systems?
Engineering shortcut: Train on the entire internet, use it as a model of human interestingness, i.e. automated PicBreeder.
How far can this shortcut take us? What are the actual principles behind human interestingness?
See also: https://www.crosslabs.org/blog/subjective-open-endedness, https://www.oreilly.com/radar/open-endedness-the-last-grand-challenge-youve-never-heard-of/

From the perspective of an observer, a system is open-ended if and only if the sequence of artifacts it produces is both novel and learnable.

I.e. you have a system $S$ producing artefacts $X_{1\dots t\dots T}\in \mathcal{X}$ and an observer $O$ making statistical models $Y_t$ which based on $X$ up to $X_t$, which have a prediction error $l$ for arttifacts until $X_T$.

A system displays novelty if if artifacts become increasingly unpredictable with respect to the observersmodel at any fixed time $t$:

$$\forall t,\forall T>t,\exists T^{\prime }>T:\mathbb{E}[l(t,T^{\prime })]>\mathbb{E}[l(t,T)]$$

… there is always something more surprising coming in the future.

A system is learnable whenever conditioning on a longer history makes artifacts more predictable:

$$\forall T,\forall t<T,\forall T>t^{\prime }>t:\mathbb{E}[l(t^{\prime },T)]<\mathbb{E}[l,(,T)]$$

This can also be defined in terms of compression:

The observer $O$ processes an artifact $X_T$ to determine its information content given a history $h_t=X_{1:t}$ of past ones. $O$ posses a history-dependent compression map $C_{h_t}:\mathcal{X}\to \{0,1{\}}^{\ast }$ - the map encodes $X_T$ into a binary string of length $|C_{h_t}(X_T)$.

A system displays novelty if the information content increases, i.e. complexity increrases according to the observer:

$$\forall t,\forall T>t,\exists T^{\prime }>T:|C_{h_t}(X_{T^{\prime }})>|C_{h_t}(X_T)|$$

A system is learnable if conditioning on a longer history increaes compressibility:

$$\forall T,\forall t<T,\forall T>t^{\prime }>t:|C_{h_{t^{\prime }}}(X_T)|<|C_{h_t}(X_T)|$$

In other words, with a longer history (more data), the observer musst be able to keep extracting additional patterns that help it compress future artifacts.

Lossy compression is also allowed loss(decompress(compress(X)), X) < epsilon, can also get rid of explicit epsilon and analyse properties of the “rate-distortion” curves.

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Circular transclusion detected: general/Open-Endedness-is-Essential-for-Artificial-Superhuman-Intelligence

Circular transclusion detected: general/Open-Endedness-is-Essential-for-Artificial-Superhuman-Intelligence

Circular transclusion detected: general/Open-Endedness-is-Essential-for-Artificial-Superhuman-Intelligence

Circular transclusion detected: general/Open-Endedness-is-Essential-for-Artificial-Superhuman-Intelligence

Open-ended exploration

The problem afflicting both classes of learning algorithms reduces to one of insufficient exploration: SL, largely trapped in the offline regime, fails to perform any exploration, while RL, limited to exploring the interior of a static simulation, largely ignores the greater expanse of possibilities that the simulation cannot express.
We require a more general kind of exploration, which searches beyond the confines of a static data generator, such as a finite dataset or static simulator. This generalized form of exploration must deliberately and continually seek out promising data to expand the learning agent’s repertoire of capabilities. Such expansion necessarily entails searching outside of what can be sampled from a static data generator.
This open-ended exploration process, summarized in figure 1, defines a new data-seeking outer-loop that continually expands the data generator used by the inner loop learning process, which itself may use more limited forms of exploration to optimally sample from this data generator. Within each inner loop, the data generator is static, but as a whole, this open-ended exploration process defines a dynamic, adaptive search process that generates the data necessary for training a likewise open-ended learner that, over time, may attain increasingly general capabilities.

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unboundedness of the universe

A place where anything can be expressed (universal computation) is a place where anything can happen
Computation is a metaphor for expression, but expression happens through a medium. In our universe the medium is physical reality.
Invention: When anything is possible, every end is a beginning.
The easiest way here again is code, inventing tools.
Current RL: immutable environments. Actions are about attached conditional things (mario jumps), but invention changes the outer environment and leaves behind a detached artifact (mario crafts a sword).
→ Endless possibility of detached conditional things (language is one of them).
The API of earth (particles in the ground) sucks.
→ Koding koding koding?

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