When we talk about recursive self‑improvement (RSI), we often oscillate between treating it as a phenomenon, a mechanism, or a prospect. While many works claim RSI at various scales to achieve autonomous, evolving intelligence, no single formal framework captures these instances. In the classical setting its counterpart is iterative policy improvement, which is covered by the generalized policy iteration (GPI) framework under the assumption that the update rule and evaluation base lie outside the agent. This paper introduces Generalized Agent Iteration (GAI), a formalism that treats iterative policy improvement and RSI as two cases of one learning paradigm. GAI defines an agent as a set of modifiable components within a system and models learning as a cycle of “agent evaluation → agent improvement”. Two pivotal switches distinguish concrete instances: whether the improvement mechanism is part of the agent, and whether the standard against which it is measured originates externally. The first switch separates GPI from RSI, the second determines a system’s polarity—anchored, goal‑drift, or fully self‑referential. By placing existing systems on these two axes we can uniformly locate them and state the defects of RSI one condition at a time. We view this work as a first step toward a formal characterization of RSI grounded in the classical account, enabling comparison of current systems and providing a principled basis for analyzing and designing new ones.
Review: GAI offers a clear taxonomy for RSI, paving the way for systematic theoretical analysis and principled system design.