An online problem is a problem which grows over time and such that partial solutions are to be generated before the complete problem is known. Moreover, if the problem is an optimization problem, partial solutions must be aimed at optimizing the overall final solution. There may be some uncertain knowledge on how the problems develop. How should we make intermediate decisions? Can we extend exi...

In this paper we consider online learning in finite Markov decision processes (MDPs) with changing cost sequences under full and banditinformation. We propose to view this problem as an instance of online linear optimization. We propose two methods for this problem: MD2 (mirror descent with approximate projections) and the continuous exponential weights algorithm with Dikin walks. We provide a ...

the recent years have witnessed an increasing attention to the methods of multiple attribute decision making in solving the problems of the real world due to their shorter time of calculation and easy application. one of these methods is the ‘permutation method’ which has a strong logic in connection with ranking issues, but when the number of alternatives increases, solving problems through th...

Online computation is a model for formulating decision making under uncertainty. In an online problem, the algorithm does not know the entire input from the beginning; the input is revealed in a sequence of steps. At each step, the algorithm should make its decisions based on the past and without any knowledge about the future. Many important real-life problems such as robot navigation are intr...

Internet facilitates easy access to data, information, and knowledge sources available online. This provides an unprecedented opportunity to empower decision support systems with capabilities of directly accessing problem environment and implementing decisions while effectively combining higher degree of automation with human judgment. The central argument of this work is that in dynamic electr...

We discuss multi-task online learning when a decision maker has to deal simultaneously with M tasks. The tasks are related, which is modeled by imposing that the M–tuple of actions taken by the decision maker needs to satisfy certain constraints. We give natural examples of such restrictions and then discuss a general class of tractable constraints, for which we introduce computationally effici...

This paper considers online stochastic combinatorial optimization problems where uncertainties, i.e., which requests come and when, are characterized by distributions that can be sampled and where time constraints severely limit the number of offline optimizations which can be performed at decision time and/or in between decisions. It proposes online stochastic algorithms that combine the frame...

The Internet is becoming increasingly important as a sales channel. Thus, most large retail firms have adopted a multi-channel strategy that includes both web-based channels and pre-existing off-line channels. Since competition exists between these two channels, for a supply chain with a dual-channel retailer, pricing in one channel will affect the demand in the other channel. This subsequently...

In this report we study a new variant of an online bipartite matching problem, which can be interpreted as a scheduling problem. Then, we have one resource, called server, which is available for one unit in every step of a discrete time model. At most one task with unit demand can occur per time step. It is called request, and speciies a set of time steps when the serving is accepted. These tim...