Name
Abstract | ||
|---|---|---|
In stochastic control applications, typically only an ideal model (controlled transition kernel) is assumed and the control design is based on the given model, raising the problem of performance loss due to the mismatch between the assumed model and the actual model. Toward this end, we study continuity properties of discrete-time stochastic control problems with respect to system models (i.e., controlled transition kernels) and robustness of optimal control policies designed for incorrect models applied to the true system. We study both fully observed and partially observed setups under an infinite horizon discounted expected cost criterion. We show that continuity can be established under total variation convergence of the transition kernels under mild assumptions and with further restrictions on the dynamics and observation model under weak and setwise convergence of the transition kernels. Using these continuity properties, we establish convergence results and error bounds due to mismatch that occurs by the application of a control policy which is designed for an incorrectly estimated system model to a true model, thus establishing positive and negative results on robustness. Compared to the existing literature, we obtain strictly refined robustness results that are applicable even when the incorrect models can be investigated under weak convergence and setwise convergence criteria (with respect to a true model), in addition to the total variation criteria. These entail positive implications on empirical learning in (data-driven) stochastic control since often system models are learned through empirical training data where typically a weak convergence criterion applies but stronger convergence criteria do not. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1137/18M1208058 | SIAM JOURNAL ON CONTROL AND OPTIMIZATION |
Keywords | DocType | Volume |
stochastic control,robustness,incorrect models,partially observed models,learning | Journal | 58 |
Issue | ISSN | Citations |
2 | 0363-0129 | 1 |
PageRank | References | Authors |
0.41 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ali Devran Kara | 1 | 1 | 1.09 |
| Serdar Yüksel | 2 | 457 | 53.31 |