Definition. Path-emulation regret [ftip-0089]
Definition. Path-emulation regret [ftip-0089]
Fix the evaluation interface of Convention [ftip-005D]. Let \(P_{t+s}^{\rm act}\) be the protocol that returns the artifact reached after \(s\geq 1\) additional realized training steps from checkpoint \(t\). Let \(\mathcal K_{\leq t}\) be the saved checkpoint history available through \(t\), and let \(\widehat P_{t+s}(\mathcal K_{\leq t})\) instead return the artifact forecast from that history. Their signed path-emulation regret and absolute path-emulation regret are \[ \begin {aligned} \operatorname {Reg}^{\rm path}_{\rm ev}(t,s) &=J_{\rm ev}(P_{t+s}^{\rm act}) -J_{\rm ev}(\widehat P_{t+s}(\mathcal K_{\leq t})),\\ \operatorname {AReg}^{\rm path}_{\rm ev}(t,s) &=\left |\operatorname {Reg}^{\rm path}_{\rm ev}(t,s)\right |. \end {aligned} \]
The sign distinguishes an optimistic forecast from a pessimistic one; the absolute value measures discrepancy without cancellation across checkpoints. Both use the same task law, inference budget, and evaluator. Parameter error alone is not substituted for evaluation error. The NExt extrapolation and recovery schedule described in Sections 4.1--4.3 and 5.1 motivates this comparison Low-rank optimization trajectories modeling for LLM RLVR acceleration[chen2026lowrank], but the paper does not state this regret definition.