This paper addresses the challenge of optimizing under uncertainty when statistical information is insufficient for stochastic programming. It introduces a rigorous algorithmic procedure to determine a robust decision policy based on multiple scenarios. The scenarios are bundled at various levels to reflect the availability of information, and the decision policy is iteratively adjusted to adapt to this structure, removing the dependence on hindsight. The authors propose a method called progressive hedging, which involves solving a sequence of projected problems to generate an improving sequence of policies. The algorithm ensures that the final policy is both admissible and implementable, making it suitable for real-world applications. The paper also discusses the theoretical foundations, including optimality conditions and duality, and provides convergence results for both convex and nonconvex cases.This paper addresses the challenge of optimizing under uncertainty when statistical information is insufficient for stochastic programming. It introduces a rigorous algorithmic procedure to determine a robust decision policy based on multiple scenarios. The scenarios are bundled at various levels to reflect the availability of information, and the decision policy is iteratively adjusted to adapt to this structure, removing the dependence on hindsight. The authors propose a method called progressive hedging, which involves solving a sequence of projected problems to generate an improving sequence of policies. The algorithm ensures that the final policy is both admissible and implementable, making it suitable for real-world applications. The paper also discusses the theoretical foundations, including optimality conditions and duality, and provides convergence results for both convex and nonconvex cases.