School of Mathematical Sciences

Distributionally Robust Optimisation with Bayesian Ambiguity Sets

Date(s)
Thursday 12th December 2024 (14:00-15:00)
Contact
Event Convenor Contact: William.Salkeld@nottingham.ac.uk
Description
Speaker's Name: Theo Damoulas
Speaker's Affiliation: University of Warwick
Speaker's Research Theme(s): Statistics and Probability,
Abstract:
Decision making under uncertainty is challenging as the data-generating process (DGP) is often unknown. Bayesian inference proceeds by estimating the DGP through posterior beliefs on the model's parameters. However, minimising the expected risk under these beliefs can lead to suboptimal decisions due to model uncertainty or limited, noisy observations. To address this, we introduce (https://arxiv.org/abs/2411.16829) Distributionally Robust Optimisation with Bayesian Ambiguity Sets (DRO-BAS) which hedges against model uncertainty by optimising the worst-case risk over a posterior-informed ambiguity set. We provide two such sets, based on posterior expectations (DRO-BAS(PE)) or posterior predictives (DRO-BAS(PP)) and prove that both admit, under conditions, strong dual formulations leading to efficient single-stage stochastic programs which are solved with a sample average approximation. For DRO-BAS(PE) this covers all conjugate exponential family members while for DRO-BAS(PP) this is shown under conditions on the predictive's moment generating function. Our DRO-BAS formulations Pareto dominate existing Bayesian DRO on the Newsvendor problem and achieve faster solve times with comparable robustness on the Portfolio problem.

Venue: Chemistry X 2

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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