Mathematical Framing for Different Agent Strategies

TL;DR

This paper presents a unified mathematical framework for analyzing and comparing diverse AI agent strategies, facilitating better understanding and design of complex agent systems.

Contribution

It introduces a probabilistic formulation of agent strategies and the novel 'Degrees of Freedom' concept to guide strategy selection.

Findings

Provides a common language for agent strategy analysis

Introduces the 'Degrees of Freedom' concept for strategy differentiation

Enhances clarity in agent design and evaluation

Abstract

We introduce a unified mathematical and probabilistic framework for understanding and comparing diverse AI agent strategies. We bridge the gap between high-level agent design concepts, such as ReAct, multi-agent systems, and control flows, and a rigorous mathematical formulation. Our approach frames agentic processes as a chain of probabilities, enabling a detailed analysis of how different strategies manipulate these probabilities to achieve desired outcomes. Our framework provides a common language for discussing the trade-offs inherent in various agent architectures. One of our many key contributions is the introduction of the "Degrees of Freedom" concept, which intuitively differentiates the optimizable levers available for each approach, thereby guiding the selection of appropriate strategies for specific tasks. This work aims to enhance the clarity and precision in designing and evaluating AI agents, offering insights into maximizing the probability of successful actions within complex agentic systems.