Extend transferable belief models with probabilistic priors

In this paper, we extend Smets' transferable belief model (TBM) with probabilistic priors. Our first motivation for the extension is about evidential reasoning when the underlying prior knowledge base is Bayesian. We extend standard Dempster models with prior probabilities to represent beliefs and distinguish between two types of induced mass functions on an extended Dempster model: one for believing and the other essentially for decision-making. There is a natural correspondence between these two mass functions. In the extended model, we propose two conditioning rules for evidential reasoning with probabilistic knowledge base. Our second motivation is about the partial dissociation of betting at the pignistic level from believing at the credal level in TBM. In our extended TBM, we coordinate these two levels by employing the extended Dempster model to represent beliefs at the credal level. Pignistic probabilities are derived not from the induced mass function for believing but from the one for decision-making in the model and hence need not rely on the choice of frame of discernment. Moreover, we show that the above two proposed conditionings and marginalization (or coarsening) are consistent with pignistic transformation in the extended TBM

Deception in Optimal Control

In this paper, we consider an adversarial scenario where one agent seeks to achieve an objective and its adversary seeks to learn the agent's intentions and prevent the agent from achieving its objective. The agent has an incentive to try to deceive the adversary about its intentions, while at the same time working to achieve its objective. The primary contribution of this paper is to introduce a mathematically rigorous framework for the notion of deception within the context of optimal control. The central notion introduced in the paper is that of a belief-induced reward: a reward dependent not only on the agent's state and action, but also adversary's beliefs. Design of an optimal deceptive strategy then becomes a question of optimal control design on the product of the agent's state space and the adversary's belief space. The proposed framework allows for deception to be defined in an arbitrary control system endowed with a reward function, as well as with additional specifications limiting the agent's control policy. In addition to defining deception, we discuss design of optimally deceptive strategies under uncertainties in agent's knowledge about the adversary's learning process. In the latter part of the paper, we focus on a setting where the agent's behavior is governed by a Markov decision process, and show that the design of optimally deceptive strategies under lack of knowledge about the adversary naturally reduces to previously discussed problems in control design on partially observable or uncertain Markov decision processes. Finally, we present two examples of deceptive strategies: a "cops and robbers" scenario and an example where an agent may use camouflage while moving. We show that optimally deceptive strategies in such examples follow the intuitive idea of how to deceive an adversary in the above settings

Decision-Making with Belief Functions: a Review

Approaches to decision-making under uncertainty in the belief function framework are reviewed. Most methods are shown to blend criteria for decision under ignorance with the maximum expected utility principle of Bayesian decision theory. A distinction is made between methods that construct a complete preference relation among acts, and those that allow incomparability of some acts due to lack of information. Methods developed in the imprecise probability framework are applicable in the Dempster-Shafer context and are also reviewed. Shafer's constructive decision theory, which substitutes the notion of goal for that of utility, is described and contrasted with other approaches. The paper ends by pointing out the need to carry out deeper investigation of fundamental issues related to decision-making with belief functions and to assess the descriptive, normative and prescriptive values of the different approaches