Is optimization optimistically biased?

Abstract

Does optimization systematically lead to solutions that appear better than they actually turn out to be when implemented? The answer can be yes if there are errors in estimating objective function coefficients. Even if such errors are unbiased, the calculated value of the objective function for the optimal solution will, in an expected value sense, overstate that solution's true performance. This presupposes that errors in the constraint set are relatively unimportant. The existence of such a bias is shown by proof; Monte Carlo simulations of two realistic water resources optimization problems show its significance for water planners. The most important implication is that the estimated net benefits of model solutions may be exaggerated compared to existing water systems, whose performance is generally known with more accuracy. 221-222]:most would agree that applications of modeling designed to i•l• or aid decision-makers should only rarely, if at all, be designed to provide actual decisions regarding often complex management or policy problems the model output serves only to focus the debate about what to do; it is not itself a substitute for the planning, managing, or policy making process.Model solutions are just one of many inputs to the decision process. Solutions are modified to reflect institutional considerations and are often subjected to extensive simulation. Or optimization may be used just to screen out obviously inferior solutions. Optimization can also yield insights into the workings of the system, the critical issues, and the general form of good solutions.In this paper, we focus on the use of optimization to predict the performance of alternative designs, operating rules, and government policies. We address the following question, Do estimation errors in objective function coefficients cause optimization to have a fundamental bias toward optimism? Specifically, will such errors lead us to expect to gain more than we really will when we implement the optimal solution? Below, we show that under certain circumstances, the answer is yes. 152HOBBS AND HEPENSTAL: IS OPTIMIZATION OPTIMISTICALLY BIASED? 153 HoBBs AND HEPENSTAL: IS OPTIMIZATION OPTIMISTICALLY BIASED. 9 edited by M. A. H. Dempster, pp. 245-262, Academic, San Diego, Calif., 1980.

Assessing Transferability From Simulation to Reality for Reinforcement Learning

“…with mass m, and domain parameters ξ i = {g i , k i , x i } consisting of the gravity acceleration constant, the catapult's spring stiffness, and the catapult's spring pre-extension. 2 This result is consistent with Theorem 2 in [3].…”

“…Furthermore, they demonstrated the "optimistic bias" of a nonlinear program, and mentioned the effect of errors on the parameters of linear constraints. The optimization problem introduced in Section 3 belongs to the class of SPs for which the assumption required in [2] are guaranteed to hold. The most common approaches to solve convex SPs are sample average approximation methods, including: (i) the Multiple Replications Procedure and its derivatives [3,20] which assess a solution's quality by comparing with sampled alternative solutions, and (ii) Retrospective Approximation [24,25] which iteratively improved the solution by lowering the error tolerance.…”

“…This over-fitting can be described by the Simulation Optimization Bias (SOB), which is similar to the bias of an estimator. The SOB is closely related to the Optimality Gap (OG), which has been used by the optimization community since the 1990s [2,3], but has not been transferred to robotics or Reinforcement Learning (RL), yet. Deep RL algorithms recently demonstrated superhuman performance in playing games [5,6] and promising results in (simulated) robotic control tasks [7,8,9].…”

A Regional Approach to Market Monitoring in the West

“…A similar argument appears in Hobbs and Hepenstal, (1989). 59 Examples include the "winner's curse" phenomenon in auctions, where the highest bidder is the most optimistic and therefore sure to be wrong, and the survivorship bias in the estimation of mutual fund or hedge fund returns, where the failed firms are not counted in the averages.…”

Optimization bias in forest management planning solutions due to errors in forest variables

“…It has been noted that uncertainty about the coefficients of the objective function causes optimization to be optimistically biased. This means that the value of the optimal solution will be overestimated if there are random errors in the objective function coefficients (Hobbs and Hepenstal 1989). Errors on the right hand sides of the constraints have the opposite effect (Itami 1974).…”