Tatiana V. Guy

Fully probabilistic control design

Abstract Stochastic control design chooses the controller that makes the closed-loop behavior as close as possible to the desired one. The fully probabilistic design describes both the closed loop and its desired behavior in probabilistic terms and uses Kullback–Leibler divergence as their proximity measure. This approach: (i) unifies stochastic control design methodology; (ii) provides explicit minimizer. The paper completes the previous solutions of various particular cases by formulating and solving the fully probabilistic control design in the general, discrete-time, state-space setting.

Preference elicitation in Fully Probabilistic Design of decision strategies

Any systematic decision-making design selects a decision strategy that makes the resulting closed-loop behaviour close to the desired one. Fully Probabilistic Design (FPD) describes modelled and desired closed-loop behaviours via their distributions. The designed strategy is a minimiser of Kullback-Leibler divergence of these distributions. FPD: i) unifies modelling and aim-expressing languages; ii) directly describes multiple aims and constraints; iii) simplifies an (inevitable) approximate design as it has an explicit minimiser. The paper enriches the theory of FPD, in particular, it: i) improves its axiomatic basis; ii) quantitatively relates FPD to standard Bayesian decision making showing that the set of FPD tasks is a dense extension of Bayesian problem formulations; iii) opens a way to a systematic data-based preference elicitation, i.e., quantitative expression of decision-making aims.

On Support of Imperfect Bayesian Participants

Bayesian decision theory provides a strong theoretical basis for a single-participant decision making under uncertainty, that can be extended to multiple-participant decision making. However, this theory (similarly as others) assumes unlimited abilities of a participant to probabilistically model the participant’s environment and to optimise its decision-making strategy. The proposed methodology solves knowledge and preference elicitation, as well as sharing of individual, possibly fragmental, knowledge and preferences among imperfect participants. The approach helps to overcome the non-realistic assumption on participants’ unlimited abilities.

Cooperative decision making without facilitator

Abstract Estimation, learning, pattern recognition, diagnostics, fault detection and adaptive control are prominent examples of dynamic decision making under uncertainty. Under rather general conditions, they can be cast into a common theoretical framework labelled as Bayesian decision making. Richness of the practically developed variants stems from: (i) domain-specific models used; (ii) adopted approximations fighting with limited perceiving and evaluation abilities of the involved decision-making units, called here participants. While modelling is a well-developed art, the item (ii) still lacks a systematic theoretical framework. This paper provides a promising direction that could become a basis of such framework. It can be characterized as multiple-participant decision making exploiting Bayesian participants equipped with tools for sharing their knowledge and harmonizing their aims and restrictions with their neighbors. Intentional avoiding of the negotiation facilitator makes the solution fully scalable.

Robust estimation of autoregressive processes using a mixture-based filter-bank

Abstract A mixture-based framework for robust estimation of ARX-type processes is presented. The ARX process is presumed to suffer from an unknown noise and/or distortion. The approach taken here is to model the overall degraded process via a mixture. Each component of this mixture uses the same ARX model but explores a different noise/distortion process. Estimation of this mixture unifies the preprocessing and process modelling tasks. The quasi-Bayes (QB) procedure for mixture identification is extended to yield a fast recursive update of the estimator statistics. This allows non-stationary noise/distortion effects to be tracked. An application in on-line outlier-robust estimation of an AR process is given.

MULTIOBJECTIVE PROBABILISTIC MIXTURE CONTROL

Abstract Paper formulates the problem of multiobjective probabilistic mixture control design and proposes its general solution with both system model and target represented by finite probabilistic mixtures. A complete feasible algorithmic solution for mixtures with components formed by normal auto-regression models with external variable is provided.

Fully probabilistic design of hierarchical Bayesian models

The minimum cross-entropy principle is an established technique for design of an unknown distribution, processing linear functional constraints on the distribution. More generally, fully probabilistic design (FPD) chooses the distribution-within the knowledge-constrained set of possible distributions-for which the Kullback-Leibler divergence to the designers ideal distribution is minimized. These principles treat the unknown distribution deterministically. In this paper, fully probabilistic design is applied to hierarchical Bayesian models for the first time, yielding optimal design of a (possibly nonparametric) stochastic model for the unknown distribution. This equips minimum cross-entropy and FPD distributional estimates with measures of uncertainty. It enables robust choice of the optimal model, as well as randomization of this choice. The ability to process non-linear functional constraints in the constructed distribution significantly extends the applicability of these principles. Currently available FPD procedures for (a) merging of external knowledge, (b) approximate learning and stabilized forgetting, (c) decision strategy design, and (d) local adaptive control design, are unified for the first time via the hierarchical FPD framework of this paper.

Theoretical Models of Decision-Making in the Ultimatum Game: Fairness vs. Reason

According to game theory, a human subject playing the ultimatum game should choose more for oneself and offer the least amount possible for co-players (assumption of selfish rationality) (Rubinstein in J Econ Behav Organ 3(4):367–388, [1]). However, economy, sociology and neurology communities repeatedly claim non-rationality of the human behaviour (Werner et al. in Theory of Games and Economic Behavior. Princeton University Press, Princeton, [2]), following the observation that responders reject offers they find too low and proposers often offer more than the smallest amount, thus suggesting that humans’ behaviour is significantly influenced by social norms. We also assume human rationality, but our model describes a human responder via decision process with a reward function respecting fairness as much as the economic profit. This model is positively tested against a set of original experimental data, thus providing an insight into human’s motivation as a social being.

Deliberation-Aware Responder in Multi-proposer Ultimatum Game

The article studies deliberation aspects by modelling a responder in multi-proposers ultimatum game (UG). Compared to the classical UG, deliberative multi-proposers UG suggests that at each round the responder selects the proposer to play with. Any change of the proposer (compared to the previous round) is penalised. The simulation results show that though switching of proposers incurred non-negligible deliberation costs, the economic profit of the deliberation-aware responder was significantly higher in multi-proposer UG compared to the classical UG.

Lazy Fully Probabilistic Design of Decision Strategies

Fully probabilistic design of decision strategies (FPD) extends Bayesian dynamic decision making. The FPD specifies the decision aim via so-called ideal - a probability density, which assigns high probability values to the desirable behaviours and low values to undesirable ones. The optimal decision strategy minimises the Kullback-Leibler divergence of the probability density describing the closed-loop behaviour to this ideal. In spite of the availability of explicit minimisers in the corresponding dynamic programming, it suffers from the curse of dimensionality connected with complexity of the value function. Recently proposed a lazy FPD tailors lazy learning, which builds a local model around the current behaviour, to estimation of the closed-loop model with the optimal strategy. This paper adds a theoretical support to the lazy FPD and outlines its further improvement.