Related papers: Dueling Convex Optimization with General Preferenc…
This paper investigates general and generalized differentiation properties of the optimal value function associated with perturbed optimization problems. Fundamental results on nearly convex sets and functions in infinite-dimensional spaces…
We consider the closely related problems of bandit convex optimization with two-point feedback, and zero-order stochastic convex optimization with two function evaluations per round. We provide a simple algorithm and analysis which is…
We present a general technique for the analysis of first-order methods. The technique relies on the construction of a duality gap for an appropriate approximation of the objective function, where the function approximation improves as the…
We consider the well-studied dueling bandit problem, where a learner aims to identify near-optimal actions using pairwise comparisons, under the constraint of differential privacy. We consider a general class of utility-based preference…
We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…
This paper investigates the fusion of absolute (reward) and relative (dueling) feedback in stochastic bandits, where both feedback types are gathered in each decision round. We derive a regret lower bound, demonstrating that an efficient…
This article explores distributed convex optimization with globally-coupled constraints, where the objective function is a general nonsmooth convex function, the constraints include nonlinear inequalities and affine equalities, and the…
The problem of minimizing the difference of two lower semicontinuous, proper, convex functions (a DC function) on a nonempty closed convex set in a locally convex Hausdorff topological vector space is studied in this paper. The focus is…
In this work, we consider a distributed online convex optimization problem, with time-varying (potentially adversarial) constraints. A set of nodes, jointly aim to minimize a global objective function, which is the sum of local convex…
Distributed demand response is a typical distributed optimization problem that requires coordination among multiple agents to satisfy demand response requirements. However, existing distributed algorithms for this problem still face…
We provide new insight into a {\em generalized conditional subgradient} algorithm and a {\em generalized mirror descent} algorithm for the convex minimization problem \[ \min_x \; \{f(Ax) + h(x)\}.\] As Bach showed in [{\em SIAM J. Optim.},…
This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
The paper deals with the optimal control problem described by second order evolution differential inclusions; to this end first we use an auxiliary problem with second order discrete and discrete-approximate inclusions. Then applying…
We revisit the classical dual ascent algorithm for minimization of convex functionals in the presence of linear constraints, and give convergence results which apply even for non-convex functionals. We describe limit points in terms of the…
Approximating a convex function by a polyhedral function that has a limited number of facets is a fundamental problem with applications in various fields, from mitigating the curse of dimensionality in optimal control to bi-level…
This paper develops a continuous-time primal-dual accelerated method with an increasing damping coefficient for a class of convex optimization problems with affine equality constraints. This paper analyzes critical values for parameters in…
This paper derives a discrete dual problem for a prototypical hybrid high-order method for convex minimization problems. The discrete primal and dual problem satisfy a weak convex duality that leads to a priori error estimates with…
In this paper, we focus on the decentralized composite optimization for convex functions. Because of advantages such as robust to the network and no communication bottle-neck in the central server, the decentralized optimization has…
This paper studies the application of the blended dynamics approach towards distributed optimization problem where the global cost function is given by a sum of local cost functions. The benefits include (i) individual cost function need…