On Tractability, Complexity, and Mixed-Integer Convex Programming Representability of Distributionally Favorable Optimization
arxiv(2024)
摘要
Distributionally Favorable Optimization (DFO) is an important framework for
decision-making under uncertainty, with applications across fields such as
reinforcement learning, online learning, robust statistics, chance-constrained
programming, and two-stage stochastic optimization without relatively complete
recourse. In contrast to the traditional Distributionally Robust Optimization
(DRO) paradigm, DFO presents a unique challenge – the application of the inner
infimum operator often fails to retain the convexity. In light of this
challenge, we study the tractability and complexity of DFO. We establish
sufficient and necessary conditions for determining when DFO problems are
tractable or intractable. Despite the typical nonconvex nature of DFO problems,
our findings show that they are mixed-integer convex programming representable
(MICP-R), thereby enabling solutions via standard optimization solvers.
Finally, we numerically validate the efficacy of our MICP-R formulations.
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