Related papers: Pareto efficiency for the concave order and multiv…
The problem of estimating a normal covariance matrix is considered from a decision-theoretic point of view, where the dimension of the covariance matrix is larger than the sample size. This paper addresses not only the nonsingular case but…
We provide new results for noise-tolerant and sample-efficient learning algorithms under $s$-concave distributions. The new class of $s$-concave distributions is a broad and natural generalization of log-concavity, and includes many…
This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…
This article proposes a new class of risk-sharing rules by exploring the relationship between capital allocation and risk sharing. While the former is concerned with ex-ante allocating capitals to different lines of business within a…
Multi-objective combinatorial optimization seeks Pareto-optimal solutions over exponentially large discrete spaces, yet existing methods sacrifice generality, scalability, or theoretical guarantees. We reformulate it as an online learning…
We systematically study pairwise counter-monotonicity, an extremal notion of negative dependence. A stochastic representation and an invariance property are established for this dependence structure. We show that pairwise…
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We…
In contrast to Part I of this treatise [1] that focuses on the optimization problems associated with single matrix variables, in this paper, we investigate the application of the matrix-monotonic optimization framework in the optimization…
Multi-task learning solves multiple correlated tasks. However, conflicts may exist between them. In such circumstances, a single solution can rarely optimize all the tasks, leading to performance trade-offs. To arrive at a set of optimized…
In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the…
We consider the problem of estimating covariance and precision matrices, and their associated discriminant coefficients, from normal data when the rank of the covariance matrix is strictly smaller than its dimension and the available sample…
This paper is devoted to the search of robust solutions in state space graphs when costs depend on scenarios. We first present axiomatic requirements for preference compatibility with the intuitive idea of robustness.This leads us to…
In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based…
In decision-making, maxitive functions are used for worst-case and best-case evaluations. Maxitivity gives rise to a rich structure that is well-studied in the context of the pointwise order. In this article, we investigate maxitivity with…
Structural results impose sufficient conditions on the model parameters of a Markov decision process (MDP) so that the optimal policy is an increasing function of the underlying state. The classical assumptions for MDP structural results…
This paper studies multiobjective optimal control problems in the continuous-time framework when the space of states and the space of controls are infinite-dimensional and with lighter smoothness assumptions than the usual ones. The paper…
A principal curve serves as a powerful tool for uncovering underlying structures of data through 1-dimensional smooth and continuous representations. On the basis of optimal transport theories, this paper introduces a novel principal curve…
We study the fixed point problem for a system of multivariate operators that are coordinate-wise monotone (i.e., nondecreasing or nonincreasing in each of the variables, independently), in the setting of quasi-ordered sets. We show that…
A multi-condition multi-objective optimization method that can find Pareto front over a defined condition space is developed for the first time using deep reinforcement learning. Unlike the conventional methods which perform optimization at…
In this paper we wish to tackle stochastic programs affected by ambiguity about the probability law that governs their uncertain parameters. Using optimal transport theory, we construct an ambiguity set that exploits the knowledge about the…