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We introduce PRAXIS, a co-evolutionary framework modeling generators, learners, and symbolic archives as interacting dynamical processes to analyze self-improving systems with nonstationary objectives. Theoretical analysis proves that KL-constrained generator updates and controlled archive-weight movement bound objective drift, while archive updates confer a persistent utility advantage. Experimental results across diverse tasks demonstrate generator stabilization, learner loss reduction, and archive concentration, aligning with the theoretical predictions.
Self-improving AI systems can achieve stable learning dynamics and persistent utility advantages by strategically managing objective drift through co-evolutionary symbolic archives.
Self-improving learning systems adapt data selection, optimization, and auxiliary symbolic components, inducing nonstationary objectives outside standard learning assumptions. We introduce \textsc{PRAXIS}, a co-evolutionary framework that models generators, learners, and symbolic archives as interacting dynamical processes. We prove that KL-constrained generator updates and controlled archive-weight movement bound one-step objective drift, that archive updates suppress a program relative to any fixed comparator with a persistent cumulative utility advantage under sub-Gaussian noise, and that stochastic gradient descent achieves an average-stationarity guarantee whose degradation is governed by cumulative objective drift. Experiments across visual robustness, relational graph reasoning, and algorithmic graph reasoning exhibit generator stabilization, decreasing learner loss, and archive concentration consistent with these theoretical mechanisms.
