SCENARIOS AND POLICY AGGREGATION IN OPTIMIZATION UNDER UNCERTAINTY

SCENARIOS AND POLICY AGGREGATION IN OPTIMIZATION UNDER UNCERTAINTY

December 1987 | R.T. Rockafellar, R. J-B Wets
This paper presents a rigorous algorithmic procedure for determining a robust decision policy in optimization under uncertainty, where scenarios are used to model uncertain elements. The key idea is to aggregate scenarios at various levels to reflect the availability of information and iteratively adjust the decision policy to adapt to this structure. The paper introduces the concept of "implementable policies," which do not rely on hindsight, and develops a method to generate such policies by aggregating the optimal solutions of individual scenario subproblems. The aggregation is done using a projection operator that depends on scenario weights, leading to a "contingent policy" that is then refined to an implementable policy. The paper also discusses the use of Lagrangian and augmented Lagrangian methods to solve the optimization problem, and presents convergence results for both convex and nonconvex cases. The algorithm is shown to be effective in generating policies that are robust to uncertainty and can be implemented in practice. The paper concludes with a discussion of the computational aspects of the algorithm, including the use of parallel processing and the potential for further improvements in efficiency.This paper presents a rigorous algorithmic procedure for determining a robust decision policy in optimization under uncertainty, where scenarios are used to model uncertain elements. The key idea is to aggregate scenarios at various levels to reflect the availability of information and iteratively adjust the decision policy to adapt to this structure. The paper introduces the concept of "implementable policies," which do not rely on hindsight, and develops a method to generate such policies by aggregating the optimal solutions of individual scenario subproblems. The aggregation is done using a projection operator that depends on scenario weights, leading to a "contingent policy" that is then refined to an implementable policy. The paper also discusses the use of Lagrangian and augmented Lagrangian methods to solve the optimization problem, and presents convergence results for both convex and nonconvex cases. The algorithm is shown to be effective in generating policies that are robust to uncertainty and can be implemented in practice. The paper concludes with a discussion of the computational aspects of the algorithm, including the use of parallel processing and the potential for further improvements in efficiency.
Reach us at info@futurestudyspace.com