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We analyse the conservatism and regret of distributionally robust (DR)stochastic model predictive control (SMPC) when using moment-based ambiguitysets for modeling unknown uncertainties. To quantify the conservatism, wecompare the deterministic constraint tightening while taking a DR approachagainst the optimal tightening when the exact distributions of the stochasticuncertainties are known. Furthermore, we quantify the regret by comparing theperformance when the distributions of the stochastic uncertainties are knownand unknown. Analysing the accumulated sub-optimality of SMPC due to the lackof knowledge about the true distributions of the uncertainties marks the novelcontribution of this work.

Regret and Conservatism of Distributionally Robust Constrained Stochastic Model Predictive Control