Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach
This work addresses risk and uncertainty in decision-making for applications like finance or robotics, though it is incremental as it builds on existing CVaR and MDP frameworks.
The paper tackles decision-making in Markov decision processes by minimizing a conditional-value-at-risk objective to account for risk and modeling errors, showing that this approach unifies risk-sensitive and robust decision-making and presenting an approximate value-iteration algorithm with error guarantees.
In this paper we address the problem of decision making within a Markov decision process (MDP) framework where risk and modeling errors are taken into account. Our approach is to minimize a risk-sensitive conditional-value-at-risk (CVaR) objective, as opposed to a standard risk-neutral expectation. We refer to such problem as CVaR MDP. Our first contribution is to show that a CVaR objective, besides capturing risk sensitivity, has an alternative interpretation as expected cost under worst-case modeling errors, for a given error budget. This result, which is of independent interest, motivates CVaR MDPs as a unifying framework for risk-sensitive and robust decision making. Our second contribution is to present an approximate value-iteration algorithm for CVaR MDPs and analyze its convergence rate. To our knowledge, this is the first solution algorithm for CVaR MDPs that enjoys error guarantees. Finally, we present results from numerical experiments that corroborate our theoretical findings and show the practicality of our approach.