Related papers: Pareto efficiency for the concave order and multiv…
Let $P_1,\dots, P_n$ and $Q_1,\dots, Q_n$ be convex polytopes in $\mathbb{R}^n$ such that $P_i\subset Q_i$. It is well-known that the mixed volume has the monotonicity property: $V(P_1,\dots,P_n)\leq V(Q_1,\dots,Q_n)$. We give two criteria…
We introduce a new framework for data denoising, partially inspired by martingale optimal transport. For a given noisy distribution (the data), our approach involves finding the closest distribution to it among all distributions which 1)…
Multi-task learning, which optimizes performance across multiple tasks, is inherently a multi-objective optimization problem. Various algorithms are developed to provide discrete trade-off solutions on the Pareto front. Recently, continuous…
We study efficiency in general collective choice problems where agents have ordinal preferences and randomization is allowed. We explore the structure of preference profiles where ex-ante and ex-post efficiency coincide, offer a unifying…
We adapt the quasi-monotone method from [2] for composite convex minimization in the stochastic setting. For the proposed numerical scheme we derive the optimal convergence rate in terms of the last iterate, rather than on average as it is…
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…
We consider the problem of maximizing an unknown function over a compact and convex set using as few observations as possible. We observe that the optimization of the function essentially relies on learning the induced bipartite ranking…
We study an extremal projection principle for families of operators ordered by domination, induced by fixed bounded linear mappings acting on a source with an additive baseline. Stability is defined through domination of second--order…
Convex combinations of i.i.d. random variables without a finite mean can behave in a strikingly different way from the finite-mean case: as the weight vector becomes more balanced, the resulting combination may become stochastically larger,…
In this note we establish several inequalities and monotonicity properties for the free energy of directed polymers under certain stochastic orders: the usual stochastic order, the Laplace transform order and the convex order. For the…
We study online convex optimization in the random order model, recently proposed by \citet{garber2020online}, where the loss functions may be chosen by an adversary, but are then presented to the online algorithm in a uniformly random…
We present a framework for constructing multivariate risk measures that is inspired from univariate Optimized Certainty Equivalent (OCE) risk measures. We show that this new class of risk measures verifies the desirable properties such as…
Distributed optimization is the standard way of speeding up machine learning training, and most of the research in the area focuses on distributed first-order, gradient-based methods. Yet, there are settings where some…
This paper deals with an implicit Newton-like inertial dynamical system governed by a maximally comonotone inclusion problem in a Hilbert space. Under suitable conditions, we establish not only pointwise estimates and integral estimates for…
In the present paper, several types of efficiency conditions are established for vector optimization problems with cone constraints affected by uncertainty, but with no information of stochastic nature about the uncertain data. Following a…
Optimization problems have been the subject of statistical physics approximations. A specially relevant and general scenario is provided by optimization methods considering tradeoffs between cost and efficiency, where optimal solutions…
We point out the connection of the so-called H\^opital-style rules for monotonicity and oscillation to some well-known properties of concave/convex functions. From this standpoint, we are able to generalize the rules under no…
In multiobjective optimization, most branch and bound algorithms provide the decision maker with the whole Pareto front, and then decision maker could select a single solution finally. However, if the number of objectives is large, the…
Efficiency, the basic concept of multi-objective optimization is investigated for the class of pairwise comparison matrices. A weight vector is called efficient if no alternative weight vector exists such that every pairwise ratio of the…
Optimization problems with stochastic dominance constraints provide a possibility to shape risk by selecting a benchmark random outcome with a desired distribution. The comparison of the relevant random outcomes to the respective benchmarks…