Related papers: Intractability of approximate multi-dimensional no…
We study multi-objective reinforcement learning with nonlinear preferences over trajectories. That is, we maximize the expected value of a nonlinear function over accumulated rewards (expected scalarized return or ESR) in a multi-objective…
Integer Linear Programming with $n$ binary variables and $m$ many $0/1$-constraints can be solved in time $2^{\tilde O(m^2)} \text{poly}(n)$ and it is open whether the dependence on $m$ is optimal. Several seemingly unrelated problems,…
We consider the problem of maximizing a monotone submodular function subject to a knapsack constraint. Our main contribution is an algorithm that achieves a nearly-optimal, $1 - 1/e - \epsilon$ approximation, using…
This paper studies approximate solutions of a linear fractional vector optimization problem without requiring boundedness of the constraint set. We establish necessary and sufficient conditions for approximating weakly efficient points of…
In this paper, we study the distributed optimization problem using approximate first-order information. We suppose the agent can repeatedly call an inexact first-order oracle of each individual objective function and exchange information…
We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector-valued function, defined as solution of a non-homogeneous version of the eigenproblem. This approximation step is…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
Given a set of $m$ agents and a set of $n$ items, where agent $A$ has utility $u_{A,i}$ for item $i$, our goal is to allocate items to agents to maximize fairness. Specifically, the utility of an agent is the sum of its utilities for items…
We study the problem of optimizing nonlinear objective functions over bipartite matchings. While the problem is generally intractable, we provide several efficient algorithms for it, including a deterministic algorithm for maximizing convex…
We use the optimized trigonometric finite basis method to find energy eigenvalues and eigenfunctions of the time-independent Schrodinger equation with high accuracy. We apply this method to the quartic anharmonic oscillator and the harmonic…
We present several new results about smoothed analysis of multiobjective optimization problems. Motivated by the discrepancy between worst-case analysis and practical experience, this line of research has gained a lot of attention in the…
The paper focuses on unconditionally optimal error analysis of the fully discrete Galerkin finite element methods for a general nonlinear parabolic system in $\R^d$ with $d=2,3$. In terms of a corresponding time-discrete system of PDEs as…
In the $d$-Scattered Set problem we are asked to select at least $k$ vertices of a given graph, so that the distance between any pair is at least $d$. We study the problem's (in-)approximability and offer improvements and extensions of…
In this paper we present a new algorithm for solving linear programs that requires only $\tilde{O}(\sqrt{rank(A)}L)$ iterations to solve a linear program with $m$ constraints, $n$ variables, and constraint matrix $A$, and bit complexity…
Submodular maximization is a general optimization problem with a wide range of applications in machine learning (e.g., active learning, clustering, and feature selection). In large-scale optimization, the parallel running time of an…
It is known that greedy methods perform well for maximizing monotone submodular functions. At the same time, such methods perform poorly in the face of non-monotonicity. In this paper, we show - arguably, surprisingly - that invoking the…
We present an algorithm that given a linear program with $n$ variables, $m$ constraints, and constraint matrix $A$, computes an $\epsilon$-approximate solution in $\tilde{O}(\sqrt{rank(A)}\log(1/\epsilon))$ iterations with high probability.…
We consider the maximization problem in the value oracle model of functions defined on $k$-tuples of sets that are submodular in every orthant and $r$-wise monotone, where $k\geq 2$ and $1\leq r\leq k$. We give an analysis of a…
A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…