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Many real-world multi-objective optimisation problems rely on computationally expensive function evaluations. Multi-objective Bayesian optimisation (BO) can be used to alleviate the computation time to find an approximated set of Pareto…

We present a method to include robustness into a multi-criteria optimization (MCO) framework for intensity-modulated proton therapy (IMPT). The approach allows one to simultaneously explore the trade-off between different objectives as well…

Submodularity is an important property of set functions and has been extensively studied in the literature. It models set functions that exhibit a diminishing returns property, where the marginal value of adding an element to a set…

Robust Markov Decision Processes (MDPs) are a powerful framework for modeling sequential decision-making problems with model uncertainty. This paper proposes the first first-order framework for solving robust MDPs. Our algorithm interleaves…

Our goal is to compute a policy that guarantees improved return over a baseline policy even when the available MDP model is inaccurate. The inaccurate model may be constructed, for example, by system identification techniques when the true…

It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…

Many sequential decision-making problems that are currently automated, such as those in manufacturing or recommender systems, operate in an environment where there is either little uncertainty, or zero risk of catastrophe. As companies and…

This work studies equilibrium problems under uncertainty where firms maximize their profits in a robust way when selling their output. Robust optimization plays an increasingly important role when best guaranteed objective values are to be…

Robust optimization (RO) has emerged as one of the leading paradigms to efficiently model parameter uncertainty. The recent connections between RO and problems in statistics and machine learning domains demand for solving RO problems in…

Multi-objective reinforcement learning (MORL) is the generalization of standard reinforcement learning (RL) approaches to solve sequential decision making problems that consist of several, possibly conflicting, objectives. Generally, in…

A variety of approaches has been developed to deal with uncertain optimization problems. Often, they start with a given set of uncertainties and then try to minimize the influence of these uncertainties. Depending on the approach used, the…

The decomposition-based method has been recognized as a major approach for multi-objective optimization. It decomposes a multi-objective optimization problem into several single-objective optimization subproblems, each of which is usually…

Optimization of conflicting functions is of paramount importance in decision making, and real world applications frequently involve data that is uncertain or unknown, resulting in multi-objective optimization (MOO) problems of stochastic…

Executing multiple tasks concurrently is important in many robotic applications. Moreover, the prioritization of tasks is essential in applications where safety-critical tasks need to precede application-related objectives, in order to…

Recently, there has been a renewed interest in decomposition-based approaches for evolutionary multiobjective optimization. However, the impact of the choice of the underlying scalarizing function(s) is still far from being well understood.…

Motion planning is a fundamental problem and focuses on finding control inputs that enable a robot to reach a goal region while safely avoiding obstacles. However, in many situations, the state of the system may not be known but only…

The objective-based forecasting considers the asymmetric and non-linear impacts of forecasting errors on decision objectives, thus improving the effectiveness of its downstream decision-making process. However, existing objective-based…

Multi-objective Bayesian optimization aims to find the Pareto front of trade-offs between a set of expensive objectives while collecting as few samples as possible. In some cases, it is possible to evaluate the objectives separately, and a…

In this paper, we develop a stochastic set-valued optimization (SVO) framework tailored for robust machine learning. In the SVO setting, each decision variable is mapped to a set of objective values, and optimality is defined via set…

The pooling problem has applications, e.g., in petrochemical refining, water networks, and supply chains and is widely studied in global optimization. To date, it has largely been treated deterministically, neglecting the influence of…