Time to Convergence and Optimality

Time, convergence, and optimality are distinct features of a decision procedure. Compare the feasible solution quality available within the relevant budget and account for delay and verification.

Convergence, solution quality, and elapsed time are separate properties. A procedure can quickly stabilize at a poor solution, slowly improve without reaching its limit, or find an exact answer quickly on a structured problem. A converged numerical procedure also need not have converged to the quantity the decision actually needs.

Compare useful results available within the real budget, including the cost of delay and verification. Anytime methods are designed to return a current solution and potentially improve it with more computation. Human deliberation can borrow the checkpoint idea, but more discussion does not inherit an algorithmic guarantee of improvement.

When to use it

When the tradeoff between decision speed and decision quality needs explicit management; when process design needs to match time constraints to outcome quality; when understanding why fast processes produce suboptimal results and optimal processes take too long; when satisficing would outperform optimizing under time pressure.

How it can help

Define the deadline and quality requirement, evaluate methods at that horizon, retain a usable solution, and examine whether further effort is worth its cost.