On the Computability of Solomonoff Induction and Knowledge-Seeking

TL;DR

This paper investigates the limits of Solomonoff induction's computability, classifies its variants within the arithmetical hierarchy, and develops a limit-computable reinforcement learning agent with asymptotic optimality.

Contribution

It quantifies the incomputability of Solomonoff induction, provides computability bounds for knowledge-seeking agents, and introduces a limit-computable asymptotically optimal RL agent.

Findings

Classifies Solomonoff's prior variants within the arithmetical hierarchy.

Derives bounds on the computability of knowledge-seeking agents.

Proposes a limit-computable reinforcement learning agent with asymptotic optimality.

Abstract

Solomonoff induction is held as a gold standard for learning, but it is known to be incomputable. We quantify its incomputability by placing various flavors of Solomonoff's prior M in the arithmetical hierarchy. We also derive computability bounds for knowledge-seeking agents, and give a limit-computable weakly asymptotically optimal reinforcement learning agent.