Related papers: On Exponential Time Lower Bound of Knapsack under …
In a recent work, Esmer et al. describe a simple method - Approximate Monotone Local Search - to obtain exponential approximation algorithms from existing parameterized exact algorithms, polynomial-time approximation algorithms and, more…
We consider the adversarial multi-armed bandit problem under delayed feedback. We analyze variants of the Exp3 algorithm that tune their step-size using only information (about the losses and delays) available at the time of the decisions,…
We present a non-asymptotic lower bound on the eigenspectrum of the design matrix generated by any linear bandit algorithm with sub-linear regret when the action set has well-behaved curvature. Specifically, we show that the minimum…
In this paper we study the adaptivity of submodular maximization. Adaptivity quantifies the number of sequential rounds that an algorithm makes when function evaluations can be executed in parallel. Adaptivity is a fundamental concept that…
The Knapsack Problem is a classic problem in combinatorial optimisation. Solving these problems may be computationally expensive. Recent years have seen a growing interest in the use of deep learning methods to approximate the solutions to…
The min-knapsack problem with compactness constraints extends the classical knapsack problem, in the case of ordered items, by introducing a restriction ensuring that they cannot be too far apart. This problem has applications in…
We consider the problem of maximizing a monotone submodular function under a knapsack constraint. We show that, for any fixed $\epsilon > 0$, there exists a polynomial-time algorithm with an approximation ratio $1-c/e-\epsilon$, where $c…
We consider the 0-1 Incremental Knapsack Problem (IKP) where the capacity grows over time periods and if an item is placed in the knapsack in a certain period, it cannot be removed afterwards. The contribution of a packed item in each time…
We consider the problem of maximizing a non-negative monotone submodular function subject to a knapsack constraint, which is also known as the Budgeted Submodular Maximization (BSM) problem. Sviridenko (2004) showed that by guessing 3…
One of the central goals of Recurrent Neural Networks (RNNs) is to learn long-term dependencies in sequential data. Nevertheless, the most popular training method, Truncated Backpropagation through Time (TBPTT), categorically forbids…
In stochastic combinatorial optimization, algorithms differ in their adaptivity: whether or not they query realized randomness and adapt to it. Dean et al. (FOCS '04) formalize the adaptivity gap, which compares the performance of fully…
This paper proposes a linear bandit algorithm that is adaptive to environments at two different levels of hierarchy. At the higher level, the proposed algorithm adapts to a variety of types of environments. More precisely, it achieves…
We present an evolutionary algorithm evo-SMC for the problem of Submodular Maximization under Cost constraints (SMC). Our algorithm achieves $1/2$-approximation with a high probability $1-1/n$ within $\mathcal{O}(n^2K_{\beta})$ iterations,…
Submodular maximization has found extensive applications in various domains within the field of artificial intelligence, including but not limited to machine learning, computer vision, and natural language processing. With the increasing…
In order to describe or estimate different quantities related to a specific random variable, it is of prime interest to numerically generate such a variate. In specific situations, the exact generation of random variables might be either…
We study a family of matroid optimization problems with a linear constraint (MOL). In these problems, we seek a subset of elements which optimizes (i.e., maximizes or minimizes) a linear objective function subject to (i) a matroid…
The challenge of identifying the best feasible arm within a fixed budget has attracted considerable interest in recent years. However, a notable gap remains in the literature: the exact exponential rate at which the error probability…
We show, assuming the (randomized) Gap Exponential Time Hypothesis (Gap-ETH), that the following tasks cannot be done in $T(k) \cdot N^{o(k)}$-time for any function $T$ where $N$ denote the input size: - $\left(1 - \frac{1}{e} +…
The subject of this paper is the time complexity of approximating Knapsack, Subset Sum, Partition, and some other related problems. The main result is an $\widetilde{O}(n+1/\varepsilon^{5/3})$ time randomized FPTAS for Partition, which is…
A multiple knapsack constraint over a set of items is defined by a set of bins of arbitrary capacities, and a weight for each of the items. An assignment for the constraint is an allocation of subsets of items to the bins which adheres to…