Samuel Allen Alexander

Inspired by recent progress in multi-agent Reinforcement Learning (RL), in this work we examine the collective intelligent behaviour of theoretical universal agents by introducing a weighted mixture operation. Given a weighted set of agents, their weighted mixture is a new agent whose expected total reward in any environment is the corresponding weighted average of the original agents' expected total rewards in that environment. Thus, if RL agent intelligence is quantified in terms of performance across environments, the weighted mixture's intelligence is the weighted average of the original agents' intelligences. This operation enables various interesting new theorems that shed light on the geometry of RL agent intelligence, namely: results about symmetries, convex agent-sets, and local extrema. We also show that any RL agent intelligence measure based on average performance across environments, subject to certain weak technical conditions, is identical (up to a constant factor) to performance within a single environment dependent on said intelligence measure.

This is a paper about the general theory of measuring or estimating social intelligence via benchmarks. Hernández-Orallo and Dowe described a problem with certain proposed intelligence measures. The problem suggests that those intelligence measures might not accurately capture social intelligence. We argue that Hernández-Orallo and Dowe's problem is even more general than how they stated it, applying to many subdomains of AGI, not just the one subdomain in which they stated it. We then propose a solution. In our solution, instead of using test-cases within the given AGI subdomain to estimate an AI's intelligence, one would use test-cases in an extended subdomain where test-cases have the ability to simulate the AI being tested. Surprisingly, AIs only designed for the original subdomain can be tested with test-cases in the extended subdomain anyway. By extending the subdomain in this way, we might avoid Hernández-Orallo and Dowe's problem.

Internodons are a formalization of Hennig's concept of species. We present an alternative construction of internodons imposing a tree structure on the genealogical network. We prove that the segments (trivial unary trees) from this tree structure are precisely the internodons. We obtain the following spin-offs. First, the generated tree turns out to be an organismal tree of life. Second, this organismal tree is homeomorphic to the phylogenetic Hennigian species tree of life, implying the discovery of a multi-level tree of life: this phylogenetic tree can be obtained by zooming out from the organismal tree, or conversely, the organismal tree of life can be generated by expanding the phylogenetic nodes into unary trees. Finally, the definition of the organismal tree allows an efficient algorithmic transformation of a given genealogical network into its corresponding phylogenetic species tree of life. The latter will be presented in a separate paper.

Mathematicians and software developers use the word "function" very differently, and yet, sometimes, things that are in practice implemented using the software developer's "function", are mathematically formalized using the mathematician's "function". This mismatch can lead to inaccurate formalisms. We consider a special case of this meta-problem. Various kinds of agents might, in actual practice, make use of private memory, reading and writing to a memory-bank invisible to the ambient environment. In some sense, we humans do this when we silently subvocalize thoughts about the actions we are taking (at least when the environment we're in is too primitive to probe the contents of our brains). Mathematical function formalizations of agents often ignore this ability. We show that in a general agent-environment framework (of which reinforcement learning is a special case), in a technical sense, such private memories do not enable qualitatively different agent behavior.