The paper asks whether recursive self-improvement (RSI) should be understood as a phenomenon, a mechanism, or a future possibility, and argues that existing examples lack a common formal description. It proposes Generalized Agent Iteration (GAI), a framework that treats both classical iterative policy improvement and RSI as one learning paradigm. In GAI, an agent is a configuration of modifiable components, and learning proceeds through repeated cycles of evaluating and improving that configuration. Two dimensions distinguish different cases: whether the improvement mechanism belongs to the agent, and whether the standard used for evaluation comes from outside the agent. The first dimension separates generalized policy iteration from RSI, while the second classifies systems as anchored, subject to goal drift, or fully self-referential. The authors use these coordinates to place existing systems on a shared map and to state potential defects of RSI as individual conditions rather than as a single undefined problem. They present GAI as an initial formal basis for comparing existing systems and analyzing or designing future self-improving agents.
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