We consider a continuous-time linear-quadratic Gaussian control problem with partial observations and costly information acquisition. More precisely, we assume the drift of the state process to be governed by an unobservable Ornstein--Uhlenbeck process. The decision maker can additionally acquire information on the hidden state by conducting costly tests, thereby augmenting the available information.
Combining the Kalman--Bucy filter with a dynamic programming approach, we show that the problem can be reduced to a deterministic control problem for the conditional variance of the unobservable state. Optimal controls and value functions are derived in a semi-explicit form, and we present an extensive study of the qualitative properties of the model.
We demonstrate that both the optimal cost and the marginal cost increase with model uncertainty. We identify a critical threshold: below this level, it is optimal not to acquire additional information, whereas above this threshold, continuous information acquisition is optimal, with the rate increasing as uncertainty grows. For quadratic information costs, we derive the precise asymptotic behavior of the acquisition rate as uncertainty approaches zero and infinity.
In the design of closed-loop networked control systems (NCSs), induced transmission delay between sensors and the control station is an often-present issue which compromises control performance and may even cause instability. A very relevant scenario in which network-induced delay needs to be investigated is costly usage of communication resources. More precisely, advanced communication technologies, e.g. 5G, are capable of offering latency-varying information exchange for different prices. Therefore, induced delay becomes a decision variable. It is then the matter of decision maker's willingn…
In the item there are presented Interval Structure allow to extend the class of multicriteria decision making problems including incomplete Initial Information. this step will facilitate dada gathering in pairs matching for decision making.
We define decision-making functions which arise from studying the multidimensional generalization of the weighted Bajraktarević means. It allows a nonlinear approach to optimization problems. These functions admit several interesting (from the point of view of decision-making) properties, for example, delegativity (which states that each subgroup of decision-makers can aggregate their decisions and efforts), casuativity (each decision affects the final outcome except two trivial cases) and convexity-type properties. Beyond establishing the most important properties of such means, we solve thei…
Dynamic Cloud Service-Capacity Deployment with Costly Response Readiness
Guanghua School of Management, Peking University（北京大学光华管理学院）；Department of Industrial Engineering and Decision Analytics, The Hong Kong University of Science and Technology（香港科技大学工业工程与决策分析系）；Department of AI for Management, School of Management and Engineering, School of Computer Science, Nanjing University（南京大学计算机科学与技术学院、工程管理学院的AI管理系）
From this set of procedures for given clause we shall choose only interrogation of experts on pairs decisions. It is widely widespread method. It makes the whole chapter in the theory of the decision-making, well investigated with the formal point of view. In the modern theory of decision-making at gathering the initial information for mathematical model it practically does not have alternative.
It is introduced the concept of Superiority Degree one competitive decision over another. On the basis of this concept the mathematics theoretic structure is developed, which is part of pairs comparisons branch in modern decision making theory. It will be useful for practice and interesting for scientific research.
When choosing between candidate nest sites, a honeybee swarm reliably chooses the most valuable site and even when faced with the choice between near-equal value sites, it makes highly efficient decisions. Value-sensitive decision-making is enabled by a distributed social effort among the honeybees, and it leads to decision-making dynamics of the swarm that are remarkably robust to perturbation and adaptive to change. To explore and generalize these features to other networks, we design distributed multi-agent network dynamics that exhibit a pitchfork bifurcation, ubiquitous in biological mode…
The collective decision-making exhibited by animal groups provides enormous inspiration for multi-agent control system design as it embodies several features that are desirable in engineered networks, including robustness and adaptability, low computational effort, and an intrinsically decentralized architecture. However, many of the mechanistic models for collective decision-making are described at the population-level abstraction and are challenging to implement in an engineered system. We develop simple and easy-to-implement models of opinion dynamics that realize the empirically observed c…
A decision maker records measurements of a finite-state Markov chain corrupted by noise. The goal is to decide when the Markov chain hits a specific target state. The decision maker can choose from a finite set of sampling intervals to pick the next time to look at the Markov chain. The aim is to optimize an objective comprising of false alarm, delay cost and cumulative measurement sampling cost. Taking more frequent measurements yields accurate estimates but incurs a higher measurement cost. Making an erroneous decision too soon incurs a false alarm penalty. Waiting too long to declare the ta…
The weighted OWA (WOWA) is a function that aggregates a set of values with weights assigned based on the rank and relative importance of each value. The weighted OWA of uncertain objective functions can generalize many of the criteria that is used in decision making under uncertainty. In this paper, we apply the WOWA criterion to two-stage decision making problems, and present decomposition algorithms to solve them. The algorithms are applied to location-transportation problem with uncertain demands and computational results are presented.
We consider the optimal duration allocation in a decision making queue. Decision making tasks arrive at a given rate to a human operator. The correctness of the decision made by human evolves as a sigmoidal function of the duration allocated to the task. Each task in the queue loses its value continuously. We elucidate on this trade-off and determine optimal policies for the human operator. We show the optimal policy requires the human to drop some tasks. We present a receding horizon optimization strategy, and compare it with the greedy policy.
Fairness is a major concern in contemporary decision problems. In these situations, the objective is to maximize fairness while preserving the efficacy of the underlying decision-making problem. This paper examines repeated decisions on problems involving multiple stakeholders and a central decision maker. Repetition of the decision-making provides additional opportunities to promote fairness while increasing the complexity from symmetry to finding solutions. This paper presents a general mathematical programming framework for the proposed fairness-over-time (FOT) decision-making problem. The …
According to Blackwell's Theorem it is equivalent to compare channels by either a garbling order or optimal decision making. This equivalence does not hold anymore if also allowing pre-garbling, i. e. for the so-called Shannon-order (see Rauh et al., 2017). We show that the equivalence Fails in general even if the set of decision makers is reduced. This is overcome by the introduction of convexified Shannon-usefulness as a preference relation of decision makers over channels. We prove that convexified Shannon-order and convexified Shannon-usefulness are equivalent.
We use decision theory to confront uncertainty that is sufficiently broad to incorporate "models as approximations." We presume the existence of a featured collection of what we call "structured models" that have explicit substantive motivations. The decision maker confronts uncertainty through the lens of these models, but also views these models as simplifications, and hence, as misspecified. We extend the max-min analysis under model ambiguity to incorporate the uncertainty induced by acknowledging that the models used in decision-making are simplified approximations. Formally, we provide a…
Perfectly rational decision-makers maximize expected utility, but crucially ignore the resource costs incurred when determining optimal actions. Here we propose an information-theoretic formalization of bounded rational decision-making where decision-makers trade off expected utility and information processing costs. Such bounded rational decision-makers can be thought of as thermodynamic machines that undergo physical state changes when they compute. Their behavior is governed by a free energy functional that trades off changes in internal energy-as a proxy for utility-and entropic changes re…
University of Pennsylvania（宾夕法尼亚大学）；Princeton University（普林斯顿大学）
With an eye towards human-centered automation, we contribute to the development of a systematic means to infer features of human decision-making from behavioral data. Motivated by the common use of softmax selection in models of human decision-making, we study the maximum likelihood parameter estimation problem for softmax decision-making models with linear objective functions. We present conditions under which the likelihood function is convex. These allow us to provide sufficient conditions for convergence of the resulting maximum likelihood estimator and to construct its asymptotic distribu…
Double Fuzzy Probabilistic Interval Linguistic Term Set and a Dynamic Fuzzy Decision Making Model based on Markov Process with tts Application in Multiple Criteria Group Decision Making
