Related papers: Multistage Knapsack
In a Subgraph Problem we are given some graph and want to find a feasible subgraph that optimizes some measure. We consider Multistage Subgraph Problems (MSPs), where we are given a sequence of graph instances (stages) and are asked to find…
An important goal in algorithm design is determining the best running time for solving a problem (approximately). For some problems, we know the optimal running time, assuming certain conditional lower bounds. In this work, we study the…
In this paper, probabilistic guarantees for constraint sampling of multistage robust convex optimization problems are derived. The dynamic nature of these problems is tackled via the so-called scenario-with-certificates approach. This…
We study the stochastic versions of a broad class of combinatorial problems where the weights of the elements in the input dataset are uncertain. The class of problems that we study includes shortest paths, minimum weight spanning trees,…
In this paper, we consider multi-stage stochastic optimization problems with convex objectives and conic constraints at each stage. We present a new stochastic first-order method, namely the dynamic stochastic approximation (DSA) algorithm,…
We propose a new stochastic gradient method called MOTAPS (Moving Targetted Polyak Stepsize) that uses recorded past loss values to compute adaptive stepsizes. MOTAPS can be seen as a variant of the Stochastic Polyak (SP) which is also a…
We study a dynamic and stochastic knapsack problem in which a decision maker is sequentially presented with items arriving according to a Bernoulli process over $n$ discrete time periods. Items have equal rewards and independent weights…
First-order irreversible phase transitions (IPT's) between an active regime and an absorbing state are studied in two models by means of both simulations and mean-field stability analysis. Hysteresis around coexistence is the result of the…
We study the problem of an online advertising system that wants to optimally spend an advertiser's given budget for a campaign across multiple platforms, without knowing the value for showing an ad to the users on those platforms. We model…
Temporal-Difference (TD) learning with nonlinear smooth function approximation for policy evaluation has achieved great success in modern reinforcement learning. It is shown that such a problem can be reformulated as a stochastic…
The optimal (`equilibrium') macroscopic properties of an economy with $N$ industries endowed with different technologies, $P$ commodities and one consumer are derived in the limit $N\to\infty$ with $n=N/P$ fixed using the replica method.…
Multi-objective optimisation is regarded as one of the most promising ways for dealing with constrained optimisation problems in evolutionary optimisation. This paper presents a theoretical investigation of a multi-objective optimisation…
We study $q$-SAT in the multistage model, focusing on the linear-time solvable 2-SAT. Herein, given a sequence of $q$-CNF fomulas and a non-negative integer $d$, the question is whether there is a sequence of satisfying truth assignments…
In real-world optimisation, it is common to face several sub-problems interacting and forming the main problem. There is an inter-dependency between the sub-problems, making it impossible to solve such a problem by focusing on only one…
In the continuous time mean-variance model, we want to minimize the variance (risk) of the investment portfolio with a given mean at terminal time. However, the investor can stop the investment plan at any time before the terminal time. To…
Temporal point process (TPP) models combined with recurrent neural networks provide a powerful framework for modeling continuous-time event data. While such models are flexible, they are inherently sequential and therefore cannot benefit…
Change point estimation in its offline version is traditionally performed by optimizing over the data set of interest, by considering each data point as the true location parameter and computing a data fit criterion. Subsequently, the data…
Consider the following multi-phase project management problem. Each project is divided into several phases. All projects enter the next phase at the same point chosen by the decision maker based on observations up to that point. Within each…
We study three two-stage optimization problems with a similar structure and different objectives. In the first stage of each problem, the goal is to assign input jobs of positive sizes to unsplittable bags. After this assignment is decided,…
Link state routing protocols such as OSPF or IS-IS currently use only best paths to forward IP packets throughout a domain. The optimality of sub-paths ensures consistency of hop by hop forwarding although paths, calculated using Dijkstra…