# Strongly-Typed Agents are Guaranteed to Interact Safely

## TL;DR

This paper introduces strongly-typed agents, ensuring safe interactions in multi-agent systems, especially under gradient descent, by providing formal guarantees and connecting to concepts like convexity and tensor decomposition.

## Contribution

It formalizes strongly-typed agents and proves they guarantee safe interactions, extending understanding of multi-agent safety in gradient-based learning.

## Key findings

- Strongly-typed agents guarantee safe interactions.
- Gradient descent converges to Nash equilibrium in safe games.
- Connections to convexity, blind source separation, and tensor decomposition.

## Abstract

As artificial agents proliferate, it is becoming increasingly important to ensure that their interactions with one another are well-behaved. In this paper, we formalize a common-sense notion of when algorithms are well-behaved: an algorithm is safe if it does no harm. Motivated by recent progress in deep learning, we focus on the specific case where agents update their actions according to gradient descent. The paper shows that that gradient descent converges to a Nash equilibrium in safe games. The main contribution is to define strongly-typed agents and show they are guaranteed to interact safely, thereby providing sufficient conditions to guarantee safe interactions. A series of examples show that strong-typing generalizes certain key features of convexity, is closely related to blind source separation, and introduces a new perspective on classical multilinear games based on tensor decomposition.