TY - GEN
T1 - Risk-averse sequential decision problems with time-consistent stochastic dominance constraints
AU - Dentcheva, Darinka
AU - Ye, Mingsong
AU - Yi, Yunxuan
N1 - Publisher Copyright:
© 2022 IEEE.
PY - 2022
Y1 - 2022
N2 - We discuss ways of comparison of two random sequences and their application in multistage stochastic optimization problems. While various comparisons of stochastic sequences have been proposed in the literature, their integration in a sequential decision problem is non-trivial and usually results in a time-inconsistent evaluations and inconsistent decisions. We propose a framework for constructing stochastic orderings that enable time-consistent comparisons at any stage of the decision process and ensure the dominance property of the optimal policy. We use the comparisons as constraints in multi-stage stochastic problems. Particular attention is paid to constraints based on stochastic dominance of the second-order imposed conditionally; it reflects risk-averse preferences and results in problems amenable to numerical treatment. We derive optimality condition for the new problems in a special case and establish relations to the expected utility theory. Additionally, we propose a numerical method for solving the new problems.
AB - We discuss ways of comparison of two random sequences and their application in multistage stochastic optimization problems. While various comparisons of stochastic sequences have been proposed in the literature, their integration in a sequential decision problem is non-trivial and usually results in a time-inconsistent evaluations and inconsistent decisions. We propose a framework for constructing stochastic orderings that enable time-consistent comparisons at any stage of the decision process and ensure the dominance property of the optimal policy. We use the comparisons as constraints in multi-stage stochastic problems. Particular attention is paid to constraints based on stochastic dominance of the second-order imposed conditionally; it reflects risk-averse preferences and results in problems amenable to numerical treatment. We derive optimality condition for the new problems in a special case and establish relations to the expected utility theory. Additionally, we propose a numerical method for solving the new problems.
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U2 - 10.1109/CDC51059.2022.9993044
DO - 10.1109/CDC51059.2022.9993044
M3 - Conference contribution
AN - SCOPUS:85147014860
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 3605
EP - 3610
BT - 2022 IEEE 61st Conference on Decision and Control, CDC 2022
T2 - 61st IEEE Conference on Decision and Control, CDC 2022
Y2 - 6 December 2022 through 9 December 2022
ER -