Risk-averse risk-constrained optimal control

Abstract: Multistage risk-averse optimal control problems with nested conditional risk mappings are gaining popularity in various application domains. Risk-averse formulations interpolate between the classical expectation-based stochastic and minimax optimal control. This way, risk-averse problems aim at hedging against extreme low-probability events without being overly conservative. At the same time, risk-based constraints may be employed either as surrogates for chance (probabilistic) constraints or as a robustification of expectation-based constraints. Such multistage problems, however, have been identified as particularly hard to solve. We propose a decomposition method for such nested problems that allows us to solve them via efficient numerical optimization methods. Alongside, we propose a new form of risk constraints which accounts for the propagation of uncertainty in time.