Related papers: The duration problem with multiple exchanges
In this paper, we consider the parameterized complexity of the following scheduling problem. We must schedule a number of jobs on $m$ machines, where each job has unit length, and the graph of precedence constraints consists of a set of…
This paper considers the portfolio management problem of optimal investment, consumption and life insurance. We are concerned with time inconsistency of optimal strategies. Natural assumptions, like different discount rates for consumption…
In classical secretary problems, a sequence of $n$ elements arrive in a uniformly random order, and we want to choose a single item, or a set of size $K$. The random order model allows us to escape from the strong lower bounds for the…
We consider infinite horizon dynamic programming problems, where the control at each stage consists of several distinct decisions, each one made by one of several agents. In an earlier work we introduced a policy iteration algorithm, where…
Reinforcement learning can greatly benefit from the use of options as a way of encoding recurring behaviours and to foster exploration. An important open problem is how can an agent autonomously learn useful options when solving particular…
We study the problem of cutting a length-$n$ string of positive real numbers into $k$ pieces so that every piece has sum at least $b$. The problem can also be phrased as transforming such a string into a new one by merging adjacent numbers.…
We consider a repeated auction where the buyer's utility for an item depends on the time that elapsed since his last purchase. We present an algorithm to build the optimal bidding policy, and then, because optimal might be impractical, we…
Duplicate detection is the problem of identifying whether a given item has previously appeared in a (possibly infinite) stream of data, when only a limited amount of memory is available. Unfortunately the infinite stream setting is…
This paper introduces a novel scheduling problem, where jobs occupy a triangular shape on the time line. This problem is motivated by scheduling jobs with different criticality levels. A measure is introduced, namely the binary tree ratio.…
This paper introduces a heuristic framework for the Best Secretary Problem, where one item must be selected using rank information only. We develop five data-responsive rules extending classical fixed-cutoff methods: an expected-record…
We propose a method for finding approximate solutions to multiple-choice knapsack problems. To this aim we transform the multiple-choice knapsack problem into a bi-objective optimization problem whose solution set contains solutions of the…
When facing many options, we narrow down our focus to very few of them. Although behaviors like this can be a sign of heuristics, they can actually be optimal under limited cognitive resources. Here we study the problem of how to optimally…
Sequential decision-making problems with multiple objectives arise naturally in practice and pose unique challenges for research in decision-theoretic planning and learning, which has largely focused on single-objective settings. This…
We study variants of the secretary problem, where $N$, the number of candidates, is a random variable, and the decision maker wants to maximize the probability of success -- picking the largest number among the $N$ candidates -- using only…
This paper considers a problem where multiple users make repeated decisions based on their own observed events. The events and decisions at each time step determine the values of a utility function and a collection of penalty functions. The…
The paper deals with finite-state Markov decision processes (MDPs) with integer weights assigned to each state-action pair. New algorithms are presented to classify end components according to their limiting behavior with respect to the…
This paper studies questionnaire design as a formal decision problem, focusing on one element of the design process: skip sequencing. We propose that a survey planner use an explicit loss function to quantify the trade-off between cost and…
The main objective of this paper is to develop a martingale-type solution to optimal consumption--investment choice problems ([Merton, 1969] and [Merton, 1971]) under time-varying incomplete preferences driven by externalities such as…
We consider the dynamic inventory problem with non-stationary demands. It has long been known that non-stationary (s, S) policies are optimal for this problem. However, finding optimal policy parameters remains a computational challenge as…
The interval scheduling problem is one variant of the scheduling problem. In this paper, we propose a novel variant of the interval scheduling problem, whose definition is as follows: given jobs are specified by their {\em release times},…