Horizon-Scaled Net Computational Value:A Potential-Based Heuristic for Computational Metareasoning

This paper asks a simple question: can a computation that looks too expensive when judged only by its immediate benefit still be worth doing if its value is spread across several future decisions? To study this, I built a heuristic called Net Computational Value (NCV), which scales the estimated benefit of a computation (like probing for more information) by the number of remaining decision steps, H. What we get: In a synthetic decision-tree search environment, scaling probe decisions by H changes how aggressively the agent gathers information before acting. Tested across depth, branching factor, and observation noise, this helped in harder settings — deep trees, many branches, high noise — with gains of roughly 5-15%. What fails: Two important limitations. First, the environment resets information at every decision step, so the results don't actually demonstrate the "value of information persisting across future decisions" that motivated the idea — they show a narrower effect of tuning probing aggressiveness. Second, the statistical comparison between policies shares random number streams that diverge once the two policies take different actions, so the reported significance numbers should be read cautiously, not taken as strict paired evidence. Both issues are documented in detail, along with about seven earlier broken prototype attempts and exactly what was wrong in each, in a full appendix. Conclusion: The results are a mixed, regime-dependent finding about when a simple probing-aggressiveness heuristic helps versus hurts — not confirmed evidence that horizon-scaling captures genuine delayed value of computation, as originally hoped. Application: The main practical value here is the documented process — the appendix works as a case study in how metareasoning/value-of-information simulations can silently break (mismatched potentials, shared random streams, reset environments), useful for anyone building similar computational-metareasoning experiments and wanting to avoid the same pitfalls.