Robustness to incorrect priors in partially observed stochastic control
نویسندگان
چکیده
We study the continuity properties of optimal solutions to stochastic control problems with respect to initial probability measures and applications of these to the robustness of optimal control policies applied to systems with incomplete or incorrect priors. It is shown that for single and multi-stage optimal cost problems, continuity and robustness cannot be established under weak convergence or Wasserstein convergence in general, but that the optimal cost is continuous in the priors under the convergence in total variation under mild conditions. By imposing further assumptions on the measurement models, robustness and continuity also hold under weak convergence of priors. We thus obtain robustness results and bounds on the mismatch error that occurs due to the application of a control policy which is designed for an incorrectly estimated prior in terms of a distance measure between the true prior and the incorrect one. Positive and negative practical implications of these results in empirical learning for stochastic control will be presented, where almost surely weak convergence of i.i.d. empirical measures occurs but stronger notions of convergence, such as total variation convergence, in general, do not.
منابع مشابه
Robustness and Uncertainty AversionLars
This paper connects robust control theory to the max-min expected utility model of uncertainty aversion. Max-min expected utility theory depicts preferences using multiple prior distributions. Robust control theory regards a unique controlled stochastic process as an approximation by introducing a set of perturbations to it. We link the two approaches by interpreting the perturbations in robust...
متن کاملComparative Analysis of Stochastic Frontier Partially non-parametric and Stochastic Frontier Parametric Methods Case Study: Measuring Cost Efficiency in Wheat Production in Iran
متن کامل
Designinga Neuro-Sliding Mode Controller for Networked Control Systems with Packet Dropout
This paper addresses control design in networked control system by considering stochastic packet dropouts in the forward path of the control loop. The packet dropouts are modelled by mutually independent stochastic variables satisfying Bernoulli binary distribution. A sliding mode controller is utilized to overcome the adverse influences of stochastic packet dropouts in networked control system...
متن کاملMaximum Entropy System Models and Robust Feedback Control
We consider the problem of output feedback control of partially observed automata (finite state machines) when uncertainties in the model or observations are present. The problem is to design a feedback controller that is robust to both structural and parametric uncertainties. We develop a framework that unifies the deterministic and stochastic approaches to this problem. The framework introduc...
متن کاملBayesian Sample size Determination for Longitudinal Studies with Continuous Response using Marginal Models
Introduction Longitudinal study designs are common in a lot of scientific researches, especially in medical, social and economic sciences. The reason is that longitudinal studies allow researchers to measure changes of each individual over time and often have higher statistical power than cross-sectional studies. Choosing an appropriate sample size is a crucial step in a successful study. A st...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2018