2021/03/29 by Feiran Zhao, Zhao, Feiran, Keyou You +3 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · #Advanced Bandit Algorithms Research #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2103.15363
openalex publication_date 2021/03/29 · openalex created_date 2021/04/13 · openalex updated_date 2026/07/28
The behaviour of a stochastic dynamical system may be largely influenced by those low-probability, yet extreme events. To address such occurrences, this paper proposes an infinite-horizon risk-constrained Linear Quadratic Regulator (LQR) framework with time-average cost. In addition to the standard LQR objective, the average one-stage predictive variance of the state penalty is constrained to lie within a user-specified level. By leveraging the duality, its optimal solution is first shown to be stationary and affine in the state, i.e., u(x,λ^*) = -K(λ^*)x + l(λ^*), where λ^* is an optimal multiplier, used to address the risk constraint. Then, we establish the stability of the resulting closed-loop system. Furthermore, we propose a primal-dual method with sublinear convergence rate to find an optimal policy u(x,λ^*). Finally, a numerical example is provided to demonstrate the effectiveness of the proposed framework and the primal-dual method.