On Learning for Ambiguous Chance Constrained Problems

We study chance constrained optimization problems $\min_x f(x)$ s.t. $P(\left\{ \theta: g(x,\theta)\le 0 \right\})\ge 1-\epsilon$ where $\epsilon\in (0,1)$ is the violation probability, when the distribution $P$ is not known to the decision maker (DM). When the DM has access to a set of distributions $\mathcal{U}$ such that $P$ is contained in $\mathcal{U}$, then the problem is known as the ambiguous chance-constrained problem \cite{erdougan2006ambiguous}. We study ambiguous chance-constrained problem for the case when $\mathcal{U}$ is of the form $\left\{\mu:\frac{\mu (y)}{\nu(y)}\leq C, …

chance cs.lg decision distribution maker math.oc optimization probability set study