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Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor…
The soft capacitated facility location problem (SCFLP) is a classic combinatorial optimization problem, with its variants widely applied in the fields of operations research and computer science. In the SCFLP, given a set $\mathcal{F}$ of…
In this paper, we consider the multiple probabilistic covering location problem (MPCLP), which attempts to open a fixed number of facilities to maximize the total covered customer demand under a joint probabilistic coverage setting. We…
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…
Packing problems constitute an important class of optimization problems, both because of their high practical relevance and theoretical appeal. However, despite the large number of variants that have been studied in the literature, most…
A standard type of uncertainty set in robust optimization is budgeted uncertainty, where an interval of possible values for each parameter is given and the total deviation from their lower bounds is bounded. In the two-stage setting,…
We consider the problem of decentralized power allocation for competitive rate-maximization in a frequency-selective Gaussian interference channel under bounded channel uncertainty. We formulate a distribution-free robust framework for the…
We investigate {\em multidimensional covering mechanism-design} problems, wherein there are $m$ items that need to be covered and $n$ agents who provide covering objects, with each agent $i$ having a private cost for the covering objects he…
Robust design of autonomous systems under uncertainty is an important yet challenging problem. This work proposes a robust controller that consists of a state estimator and a tube based predictive control law. The class of linear systems…
In this paper, we introduce a mixed integer quadratic formulation for the congested variant of the partial set covering location problem, which involves determining a subset of facility locations to open and efficiently allocating customers…
Soft robots were introduced in large part to enable safe, adaptive interaction with the environment, and this interaction relies fundamentally on contact. However, modeling and planning contact-rich interactions for soft robots remain…
Robust classification becomes challenging when each class consists of multiple subclasses. Examples include multi-font optical character recognition and automated protein function prediction. In correlation-based nearest-neighbor…
We study optimal policy learning under combined budget and minimum coverage constraints. We show that the problem admits a knapsack-type structure and that the optimal policy can be characterized by an affine threshold rule involving both…
Routing and scheduling problems are fundamental problems in combinatorial optimization, and also have many applications. Most variations of these problems are NP-Hard, so we need to use heuristics to solve these problems on large instances,…
Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by…
We explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this…
In this paper, we consider approximability issues of the following four problems: triangle packing, full sibling reconstruction, maximum profit coverage and 2-coverage. All of them are generalized or specialized versions of set-cover and…
Robust Optimization is becoming increasingly important in machine learning applications. This paper studies the problem of robust submodular minimization subject to combinatorial constraints. Constrained Submodular Minimization arises in…
Bilevel optimization problems embed the optimality of a subproblem as a constraint of another optimization problem. We introduce the concept of near-optimality robustness for bilevel optimization, protecting the upper-level solution…
The pursuit of robustness has recently been a popular topic in reinforcement learning (RL) research, yet the existing methods generally suffer from efficiency issues that obstruct their real-world implementation. In this paper, we introduce…