This paper studies the problem of constructing robust classifiers when the training is plagued with uncertainty. The problem is posed as a Chance-Constrained Program (CCP) which ensures that the uncertain datapoints are classified correctly with high probability. Unfortunately such a CCP turns out to be intractable. The key novelty is in employing Bernstein bounding schemes to relax the CCP as ...

We consider fuzzy stochastic programming problems with a crisp objective function and linear constraints whose coefficients are fuzzy random variables, in particular of type L-R. To solve this type of problems, we formulate deterministic counterparts of chance-constrained programming with fuzzy stochastic coefficients, by combining constraints on probability of satisfying constraints, as well a...

Autonomous agents operating in partially observable stochastic environments often face the problem of optimizing expected performance while bounding the risk of violating safety constraints. Such problems can be modeled as chance-constrained POMDP’s (CCPOMDP’s). Our first contribution is a systematic derivation of execution risk in POMDP domains, which improves upon how chance constraints are h...

This paper discusses joint rectangular geometric chance constrained programs. When the stochastic parameters are elliptically distributed and pairwise independent, we present a reformulation of the joint rectangular geometric chance constrained programs. As the reformulation is not convex, we propose new convex approximations based on variable transformation together with piecewise linear appro...

We propose a stochastic algorithm for the global optimization of chance constrained problems. We assume that the probability measure with which the constraints are evaluated is known only through its moments. The algorithm proceeds in two phases. In the first phase the probability distribution is (coarsely) discretized and solved to global optimality using a stochastic algorithm. We only assume...

Chance constrained programming is an effective and convenient approach to control riskin decision making under uncertainty. However, due to unknown probability distributions ofrandom parameters, the solution obtained from a chance constrained optimization problem canbe biased. In addition, instead of knowing the true distributions of random parameters, inpractice, only a series ...

We consider chance-constrained programs in which the probability distribution of the random parameters is deterministic and known. Two prominent approaches to deal with these programs are sampling approximations and robust approximations. In the last decade, there has been enormous interest in both these areas of research. This article aims to provide a brief summary of a select number of publi...

In this paper we study ambiguous chance constrained problems where the distributions of the random parameters in the problem are themselves uncertain. We focus primarily on the special case where the uncertainty set Q of the distributions is of the form Q = {Q : ρp(Q, Q0) ≤ β}, where ρp denotes the Prohorov metric. The ambiguous chance constrained problem is approximated by a robust sampled pro...