In this seminar, Fra ncesco Giliberto will give a talk about Optimal Information Relaxatio n Bounds for Multi-Stage Stochastic Optimization.
Th is paper addresses the computation of tight optimistic bounds for mul ti-stage stochastic optimization problems using information relaxatio n duality. We introduce a specific class of penalty functions, bi-lin ear in decisions and the innovations of the underlying stochastic pro cess, to penalize anticipative policies. Our approach provides a gene ric framework for deriving such bounds, notably without requiring exp licit knowledge or approximation of the problem’s value functions. We formulate a minimax problem to find the optimal penalty parameters within this specific class, yielding the tightest bound achievable w ith these penalties. We show that for convex problems, this minimax p roblem can be equivalently reformulated as a standard stochastic prog ram with expectation constraints. Furthermore, we propose an iterativ e algorithm to solve the minimax problem directly. The methodology of fers a computationally tractable approach to generate bounds that are stronger than simple perfect information relaxations, thereby improv ing the evaluation of heuristic policies.
DESCRIPTION: In this seminar, Francesco Giliberto will give a talk abo ut Optimal Information Relaxation Bounds for Multi-Stage Stochastic O ptimization. This paper addresses the computation of tight opti mistic bounds for multi-stage stochastic optimization problems using information relaxation duality. We introduce a specific class of pena lty functions, bi-linear in decisions and the innovations of the unde rlying stochastic process, to penalize anticipative policies. Our app roach provides a generic framework for deriving such bounds, notably without requiring explicit knowledge or approximation of the problem� ��s value functions. We formulate a minimax problem to find the optim al penalty parameters within this specific class, yielding the tighte st bound achievable with these penalties. We show that for convex pro blems, this minimax problem can be equivalently reformulated as a sta ndard stochastic program with expectation constraints. Furthermore, w e propose an iterative algorithm to solve the minimax problem directl y. The methodology offers a computationally tractable approach to gen erate bounds that are stronger than simple perfect information relaxa tions, thereby improving the evaluation of heuristic policies. END:VEVENT END:VCALENDAR