Related papers: Probabilistic guarantees on the objective value fo…

We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…

Overconservatism has long been recognized as a major issue with robust optimization, despite its key advantages of tractability, performance guarantee, and limited information. To address this issue, a new criterion is proposed that can…

Chance-constrained optimization is a suitable modeling framework for safety-critical applications where violating constraints is nearly unacceptable. The scenario approach is a popular solution method for these problems, due to its…

Variational inequalities are modelling tools used to capture a variety of decision-making problems arising in mathematical optimization, operations research, game theory. The scenario approach is a set of techniques developed to tackle…

Chance constrained program where one seeks to minimize an objective over decisions which satisfy randomly disturbed constraints with a given probability is computationally intractable. This paper proposes an approximate approach to address…

Probabilistic control design is founded on the principle that a rational agent attempts to match modelled with an arbitrary desired closed-loop system trajectory density. The framework was originally proposed as a tractable alternative to…

We study the unconstrained minimization of a smooth and strongly convex population loss function under a stochastic oracle that introduces both additive and multiplicative noise; this is a canonical and widely-studied setting that arises…

Traditional reinforcement learning methods optimize agents without considering safety, potentially resulting in unintended consequences. In this paper, we propose an optimal actor-free policy that optimizes a risk-sensitive criterion based…

We propose a robust regression approach to off-policy evaluation (OPE) for contextual bandits. We frame OPE as a covariate-shift problem and leverage modern robust regression tools. Ours is a general approach that can be used to augment any…

This paper studies distributionally robust optimization for a rich class of risk measures with ambiguity sets defined by $\phi$-divergences. The risk measures are allowed to be non-linear in probabilities, are represented by Choquet…

In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we…

In many real world problems, optimization decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of points…

We present an optimal gradient method for smooth strongly convex optimization. The method is optimal in the sense that its worst-case bound on the distance to an optimal point exactly matches the lower bound on the oracle complexity for the…

Chance constraints provide a principled framework to mitigate the risk of high-impact extreme events by modifying the controllable properties of a system. The low probability and rare occurrence of such events, however, impose severe…

We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…

We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…

Neural networks are becoming increasingly prevalent in software, and it is therefore important to be able to verify their behavior. Because verifying the correctness of neural networks is extremely challenging, it is common to focus on the…

Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…

We consider finite horizon reach-avoid problems for discrete time stochastic systems. Our goal is to construct upper bound functions for the reach-avoid probability by means of tractable convex optimization problems. We achieve this by…

This paper proposes a robust approximation method for solving chance constrained optimization (CCO) of polynomials. Assume the CCO is defined with an individual chance constraint that is affine in the decision variables. We construct a…