Suboptimality

Suboptimality refers to a state, decision, or outcome that is not the best possible given the available information and constraints. It contrasts with optimality, where no other feasible option yields a higher value of the objective.

In optimization, suboptimality arises when the exact optimum is unattainable due to computational limits, incomplete information, or model misspecification. The suboptimality gap is the difference between the objective value of a chosen solution and the true optimum. Algorithms may provide approximate solutions with provable suboptimality bounds, and relaxations or heuristics are often used to trade solution quality for reduced computational effort.

In decision making and learning, suboptimality manifests as a non-optimal policy or strategy. In reinforcement learning, suboptimality of a policy is the deficit in expected return compared with the optimal policy; cumulative shortfall over time is described by regret. In economics and game theory, bounded rationality and satisficing can lead to suboptimal choices, while market outcomes can be suboptimal due to externalities, information asymmetries, or transaction costs.

Measurement and mitigation of suboptimality involve assessing trade-offs between solution quality and resources such as time and data. Techniques include approximation algorithms with guarantees, heuristic methods, and problem relaxations. Pareto optimality is a related concept that focuses on multiple objectives, where a solution may be suboptimal for one objective but not dominated with respect to others.