Analogy making as amortised model construction

TL;DR

This paper proposes a framework where analogy enables efficient reuse and construction of internal models for decision-making, by formalizing analogies as partial homomorphisms between Markov decision processes.

Contribution

It introduces a formal framework that models analogy as partial homomorphisms, facilitating modular reuse of internal models for flexible adaptation across domains.

Findings

Framework formalizes analogy as partial homomorphisms between MDPs

Modular reuse enables flexible adaptation of policies

Supports resource-efficient model construction and planning

Abstract

Humans flexibly construct internal models to navigate novel situations. To be useful, these internal models must be sufficiently faithful to the environment that resource-limited planning leads to adequate outcomes; equally, they must be tractable to construct in the first place. We argue that analogy plays a central role in these processes, enabling agents to reuse solution-relevant structure from past experiences and amortise the computational costs of both model construction (construal) and planning. Formalising analogies as partial homomorphisms between Markov decision processes, we sketch a framework in which abstract modules, derived from previous construals, serve as composable building blocks for new ones. This modular reuse allows for flexible adaptation of policies and representations across domains with shared structural essence.