On limitations of learning algorithms in competitive environments

TL;DR

This paper explores fundamental limitations of generic learning algorithms in competitive settings, revealing they face constraints similar to G"odel and Turing's theorems, especially due to intransitivity in such environments.

Contribution

It establishes a theoretical connection between limitations of learning algorithms and classical logical and computational constraints, highlighting the role of intransitivity.

Findings

Limitations analogous to G"odel and Turing theorems are inherent in learning algorithms.

Intransitivity in competitive environments contributes to these limitations.

Theoretical insights into the constraints faced by algorithms in adversarial settings.

Abstract

We discuss conceptual limitations of generic learning algorithms pursuing adversarial goals in competitive environments, and prove that they are subject to limitations that are analogous to the constraints on knowledge imposed by the famous theorems of G\"odel and Turing. These limitations are shown to be related to intransitivity, which is commonly present in competitive environments.