A Better Fit Need Not Be a Better Policy: Retraining in Persistent Graph Environments

Graph-based predictions can alter the features and outcomes used for later training. We formulate this interaction as a stateful graph-feedback process and compare repeated refitting with continued deployment of the initial classifier. A common-state comparison isolates the contribution of refitting, while a policy comparison also captures the contribution of the graph states generated by deployment. We instantiate the framework in two settings. (i) For synthetic node classification, we establish well-posedness and existence of an invariant distribution, and derive a finite-horizon condition under which lower loss on common states transfers to lower policy loss. Experiments across independently generated synthetic datasets show that fitting and induced-state contributions can reinforce or offset one another. An end-to-end study further shows that the update policy can reverse the performance ordering of GNN architectures. (ii) In a user–product graph simulation, explanation recourse changes product descriptions while historical rating labels remain fixed. Most implemented description edits continue to place the corresponding products above the eligibility threshold after refitting, while aggregate loss changes remain small. These results show that a better fit on an updated graph state may yield a worse deployment policy.