Preface

I wrote this post during my scholarship at MATS. My goal is to describe a research direction of the learning theoretic agenda (LTA). Namely, a natural infra-Bayesian learning algorithm proposal that arguably leads to Pareto-optimal solutions in repeated games. The idea originates from Vanessa, I'm expanding a draft of her into a more accessible description.

The expected audience are people who are interested in ongoing work on LTA. It is especially suitable for people who are looking for a research direction to pursue in this area.

Introduction

There has been much work on the theory of agents who cooperate in the Prisoner's dilemma and other situations. Some call this behavior superrationality. For example, functional decision theory (FDT) is a decision theory that prescribes such behavior. The strongest results so far are those coming from "modal combat", e.g. Critch. However, these results are of very limited scope: among other issues, they describe agents crafted for specific games, rather than general reasoners that produce superrational behavior in a "naturalized" manner (i.e. as a special case of the general rules of reasoning.)

At the same time, understanding multi-agent learning theory is another major open problem. Attempts to prove convergence to game-theoretic solution concepts (a much weaker goal than superrationality) in a learning-theoretic setting are impeded by the so-called grain-of-truth problem (originally observed by Kalai and Lehrer, its importance was emphasized by Hutter). An agent can learn to predict the environment via Bayesian learning only if it assigns non-zero prior probability to that environment, i.e. its prior contains a grain of truth. What's the grain-of-truth problem? Suppose Alice's environment contains another agent, Bob. If Alice is a Bayesian agent, she can learn to predict Bob's behavior only if her prior assigns a positive probability to Bob's behavior. (That is, Alice's prior contains a grain of truth.) If Bob has the same complexity level as Alice, then Alice is not able to represent all possible environments. Thus, in general, Alice's prior doesn't contain a grain of truth. A potential solution based on "reflective oracles" was proposed by Leike, Taylor and Fallenstein. However it involves arbitrarily choosing a fixed point out of an enormous space of possibilities, and requires that all agents involved choose ...

Posts

Wikitag Contributions

Comments