Preference Learning in Automated Negotiation Using Gaussian Uncertainty Models

In this paper, we propose a general two-objective Markov Decision Process (MDP) modeling paradigm for automated negotiation with incomplete information, in which preference elicitation alternates with negotiation actions, with the objective to optimize negotiation outcomes. The key ingredient in our MDP framework is a stochastic utility model governed by a Gaussian law, formalizing the agent's belief (uncertainty) over the user's preferences. Our belief model is fairly general and can be updated in real time as new data becomes available, which makes it a fundamental modeling tool

Automated negotiation with Gaussian process-based utility models

Designing agents that can efficiently learn and integrate user's preferences into decision making processes is a key challenge in automated negotiation. While accurate knowledge of user preferences is highly desirable, eliciting the necessary information might be rather costly, since frequent user interactions may cause inconvenience. Therefore, efficient elicitation strategies (minimizing elicitation costs) for inferring relevant information are critical. We introduce a stochastic, inverse-ranking utility model compatible with the Gaussian Process preference learning framework and integrate it into a (belief) Markov Decision Process paradigm which formalizes automated negotiation processes with incomplete information. Our utility model, which naturally maps ordinal preferences (inferred from the user) into (random) utility values (with the randomness reflecting the underlying uncertainty), provides the basic quantitative modeling ingredient for automated (agent-based) negotiation

Stochastic monotonicity of Markovian Multiclass Queueing Networks

Multiclass queueing networks (McQNs) extend the classical concept of the Jackson network by allowing jobs of different classes to visit the same server. Although such a generalization seems rather natural, from a structural perspective, there is a sig-nificant gap between the two concepts. Nice analytical features of Jackson networks, such as stability conditions, product–form equilibrium distributions, and stochastic mono-tonicity, do not immediately carry over to the multiclass framework. The aim of this paper is to shed some light on this structural gap, focusing on monotonicity properties. To this end, we introduce and study a class of Markov processes, which we call Q-processes, modeling the time evolution of the network configuration of any open, work-conservative McQN having exponential service times and Poisson input. We define a new monotonicity notion tailored for this class of processes. Our main result is that we show monotonicity for a large class of McQN models, covering virtually all instances of practical interest. This leads to interesting properties that are commonly encountered for “traditional” queueing processes, such as (i) monotonicity with respect to external arrival rates and (ii) star-convexity of the stability region (with respect to the external arrival rates); such properties are well known for Jackson networks but had not been established at this level of gen-erality. This research was partly motivated by the recent development of a simulation-based method that allows one to numerically determine the stability region of a McQN parameterized in terms of the arrival-rates vector

Strong bounds on perturbations

This paper provides strong bounds on perturbations over a collection of independent random variables, where 'strong' has to be understood as uniform w.r.t. some functional norm. Our analysis is based on studying the concept of weak differentiability. By applying a fundamental result from the theory of Banach spaces, we show that weak differentiability implies norm Lipschitz continuity. This result leads to bounds on the sensitivity of finite products of probability measures, in norm sense. We apply our results to derive bounds on perturbations for the transient waiting times in a G/G/1 queue