Abstract
The aim of this paper is to address optimality of stochastic control strategies via dynamic programming subject to total variational distance uncertainty on the conditional distribution of the controlled process. Utilizing concepts from signed measures, the maximization of a linear functional on the space of probability measures on abstract spaces is investigated, among those probability measures which are within a total variational distance from a nominal probability measure. The maximizing probability measure is found in closed form. These results are then applied to solve minimax stochastic control with deterministic control strategies, under a Markovian assumption on the conditional distributions of the controlled process. The results include: 1) Optimization subject to total variational distance constraints, 2) new dynamic programming recursions, which involve the oscillator seminorm of the value function.
| Original language | English |
|---|---|
| Title of host publication | 2012 IEEE 51st Annual Conference on Decision and Control (CDC) |
| Publisher | IEEE |
| Pages | 1909-1914 |
| Number of pages | 6 |
| ISBN (Electronic) | 978-1-4673-2066-5 |
| ISBN (Print) | 978-1-4673-2065-8 |
| DOIs | |
| Publication status | Published - 2012 |
| MoE publication type | A4 Article in a conference publication |
| Event | IEEE Conference on Decision and Control - , United States Duration: 10 Dec 2012 → 13 Dec 2012 Conference number: 51 |
Conference
| Conference | IEEE Conference on Decision and Control |
|---|---|
| Abbreviated title | CDC |
| Country | United States |
| Period | 10/12/2012 → 13/12/2012 |