Utility Optimization Problem Research Articles

Recursive utility optimization problem described by forward–backward stochastic differential inclusions

The main result of the paper deals with the existence of a solution of a recursive utility optimization problem described by systems of the forward–backward stochastic differential inclusion of the form: X t − X s ∈ ∫ s t F ( τ , X τ ) d τ + ∫ s t ( G ∘ X ) d B τ and Y t ∈ E [ H ( X T ) + ∫ t T Φ ( τ , X τ , Y τ ) d τ | F t ] , considered in the author paper [Kisielewicz. Weak compactness of weak solutions to forward–backward stochastic differential inclusions. Stoch Anal Appl. 2024;42(2):306–326], where the existence of weak solutions and weak compactness in distribution of the set W ( F , H , Φ , G , μ ) of all its weak solutions have been proved.

Partial offloading in device-to-device-assisted MEC network: A utility optimization approach

In order to meet the growing demand for faster and more efficient communication and computing in internet of things networks, the device-to-device (D2D)-assisted multi-access edge computing (MEC) network has emerged as a promising solution. However, most existing literature overlooks the monetary cost associated with computing and communication resources when it comes to computation offloading. Motivated by this, we first formulate a novel utility function which is defined as the tradeoff between the benefit of the delay reduction via partial offloading and the cost of the purchased computing and communication resources. Then, we propose the partial offloading-based utility optimization (POUO) algorithm to solve the utility optimization problem. Afterward, we determine the resource allocation policy and offloading ratios while taking into account the constraints of the utility optimization problem. In addition, the offloading pairing decision in the device-to-edge server (D2E) offloading mode is modeled as a knapsack problem and solved using a greedy algorithm. For D2D offloading mode, we transform the offloading pairing decision into an assignment problem and apply the Hungarian algorithm to solve it. Finally, we validate and evaluate the proposed POUO algorithm across a range of system parameters. Simulation results show that the POUO algorithm improves the completed tasks ratio, the total utility, and the average delay.

Portfolio selection and job switching with CARA utility

We investigate an optimal consumption and portfolio selection problem with a job switching option. The agent with CARA utility can choose between two types of jobs: one with high labor income but high disutility from labor, and the other with low labor income and low disutility from labor. We use the dual/martingale approach to obtain closed-form solutions to the agent’s lifetime utility optimization problem. We also obtain some numerical implications.

Incentive Mechanism for Differentially Private Federated Learning in Industrial Internet of Things

Federated learning (FL) is a newly emerging distributed machine learning paradigm, whereby a server can coordinate multiple clients to jointly train a learning model by using their private datasets. Many researches focus on designing incentive mechanisms in FL, but most of them cannot allow that clients flexibly determine privacy budgets by themselves. In this article, we propose a privacy-preserving incentive mechanism (NICE) based on differential privacy (DP) and Stackelberg game for FL systems in industrial Internet of Things. First, we design a flexible privacy-preserving mechanism for NICE, in which clients can add a Laplace noise into the loss function according to a customized privacy budget. Under this mechanism, we design two incentive utility functions for the server and clients. Next, we model the utility optimization problems as a two-stage Stackelberg game by seeing the server as a leader and the clients as followers. Finally, we derive an optimal Stackelberg equilibrium solution for both the stages of the whole game. Based on this solution, NICE can make the server and all clients achieve their maximum utilities simultaneously. In addition, we conduct extensive simulations on real-world datasets to demonstrate the significant performance of the proposed mechanism.

Mean-field backward stochastic differential equations and applications

In this paper we study the linear mean-field backward stochastic differential equations (mean-field BSDE) of the form (0.1) d Y ( t ) = − [ α 1 ( t ) Y ( t ) + β 1 ( t ) Z ( t ) + ∫ R 0 η 1 ( t , ζ ) K ( t , ζ ) ν ( d ζ ) + α 2 ( t ) E [ Y ( t ) ] + β 2 ( t ) E [ Z ( t ) ] + ∫ R 0 η 2 ( t , ζ ) E [ K ( t , ζ ) ] ν ( d ζ ) + γ ( t ) ] d t + Z ( t ) d B ( t ) + ∫ R 0 K ( t , ζ ) N ̃ ( d t , d ζ ) , t ∈ 0 , T , Y ( T ) = ξ . where ( Y , Z , K ) is the unknown solution triplet, B is a Brownian motion, N ̃ is a compensated Poisson random measure, independent of B . We prove the existence and uniqueness of the solution triplet ( Y , Z , K ) of such systems. Then we give an explicit formula for the first component Y ( t ) by using partial Malliavin derivatives. To illustrate our result we apply them to study a mean-field recursive utility optimization problem in finance.

Releasing Differentially Private Trajectories with Optimized Data Utility

The ubiquity of GPS-enabled devices has resulted in an abundance of data about individual trajectories. Releasing trajectories enables a range of data analysis tasks, such as urban planning, but it also poses a risk in compromising individual location privacy. To tackle this issue, a number of location privacy protection algorithms are proposed. However, existing works are primarily concerned with maintaining the trajectory data geographic utility and neglect the semantic utility. Thus, many data analysis tasks relying on utility, e.g., semantic annotation, suffer from poor performance. Furthermore, the released trajectories are vulnerable to location inference attacks and de-anonymization attacks due to insufficient privacy guarantee. In this paper, to design a location privacy protection algorithm for releasing an offline trajectory dataset to potentially untrusted analyzers, we propose a utility-optimized and differentially private trajectory synthesizer (UDPT) with two novel features. First, UDPT simultaneously preserves both geographical utility and semantic utility by solving a data utility optimization problem with a genetic algorithm. Second, UDPT provides a formal and provable guarantee against privacy attacks by synthesizing obfuscated trajectories in a differentially private manner. Extensive experimental evaluations on real-world datasets demonstrate UDPT’s outperformance against state-of-the-art works in terms of data utility and privacy.

An Optimized Load Balancing Using Firefly Algorithm in Flying Ad-Hoc Network

In flying ad hoc networks (FANETs), load balancing is a vital issue. Numerous conventional routing protocols that have been created are ineffective at load balancing. The different scope of its applications has given it wide applicability, as well as the necessity for location assessment accuracy. Subsequently, implementing traffic congestion control based on the current connection status is difficult. To successfully tackle the above problem, we frame the traffic congestion control algorithm as a network utility optimization problem that takes different parameters of the network into account. For the location calculation of unknown nodes, the suggested approach distributes the computational load among flying nodes. Furthermore, the technique has been optimized in a FANET utilizing the firefly algorithm along with the traffic congestion control algorithm. The unknown nodes are located using the optimized backbone. Because the computational load is divided efficiently among the flying nodes, the simulation results show that our technique considerably enhances the network longevity and balanced traffic.

Optimal Asset Allocation Subject to Withdrawal Risk and Solvency Constraints

This paper investigates the optimal asset allocation of a financial institution whose customers are free to withdraw their capital-guaranteed financial contracts at any time. In accounting for the asset-liability mismatch risk of the institution, we present a general utility optimization problem in a discrete-time setting and provide a dynamic programming principle for the optimal investment strategies. Furthermore, we consider an explicit context, including liquidity risk, interest rate, and credit intensity fluctuations, and show by numerical results that the optimal strategy improves both the solvency and asset returns of the institution compared to a standard institutional investor’s asset allocation.

A Game Theory Based CTU-Level Bit Allocation Scheme for HEVC Region of Interest Coding.

In this article, a new CTU-level bit allocation scheme aimed at subjectively optimized video coding for video conferencing applications is presented, in which the non-cooperative Stackelberg game is used for formulating and solving the bit allocation problem during the encoding process. Videos are divided into the Region of interests (ROI) which attracts people more and the non-ROI. The two regions are defined as the players in the game, where the ROI is the leader who takes the priority in strategy making and the non-ROI follows the leader's strategy. Based on the formulated game, the bit allocation problem can be expressed as a utility optimization problem. By solving the corresponding utility optimization problem, the bit allocation strategy between the ROI and the non-ROI will be established. Then the bits will be allocated to each CTU by a Newton-method-based algorithm for encoding, in which a trade-off between the ROI's quality and the overall quality can be achieved. Both the objective and subjective experimental results show that our proposed bit allocation method can improve the quality of ROI significantly with an acceptable overall quality degradation, leading to a better visual experience.

Jamsa: A Utility Optimal Contextual Online Learning Framework for Anti-Jamming Wireless Scheduling Under Reactive Jamming Attack

Reactive jamming attack, enabled by programmable software defined radio, has become a serious threat to the ubiquitous wireless systems. Wireless scheduling under reactive jamming attack is important yet challenging. In this article, we consider the utility optimal scheduling problem for multi-hop wireless networks under reactive jamming attack. We propose pilot-aided channel probing , defensive power allocations, and jamming-aware route-selection mechanisms to counteract reactive jamming. By incorporating the link-level packet delivery ratio (PDR), we devise effective online learning approaches to improve network performance over time. The constantly sought optimal scheduling policy on the conflict graph is found to be between the well-known “experts” setting and the “Multi-armed bandits (MAB)” setting. More importantly, the PDRs treated as “expert advices” (contextual information) to recommend optimal schedules online over time makes the scheduling an intrinsic combinatorial contextual MAB (CMAB) problem. The utility optimal scheduling problem is formulated as a stochastic optimization framework to minimize the incurred regret. We define two rigorous reactive jamming attack models. An anti-jamming protocol is then proposed with provable utility and regret guarantees. We conduct both synthetic and real experiments to validate our theory. Experimental results show that our algorithm achieves 35%∼97% and 79%∼138% improvements of network delay and 23%∼58% and 67%∼108% improvement of network throughput over other state-of-the-art approaches for oblivious jamming and adaptive jamming, respectively. These results indicate that our framework could sustain high throughput under powerful reactive jamming attacks.

Access Point Association in Uplink Two-Hop Cellular IoT Networks With Data Aggregators

Node clustering and data aggregation help extend the coverage of cellular networks and increase the number of supported devices, while meeting the various service quality requirements and reducing energy consumption, making them suitable for enabling the future massive cellular Internet-of-Things (IoT) applications. Consequently, we propose to overlay the cellular network with a layer of data aggregators (DAs) to act as relays. DAs use cellular backhauling, and thus, the network provides both single- and two-hop routes; however, DAs share radio resources with single-hop devices, creating a dependency between the two routes. Thus, the proper design of the DA-enabled network becomes critical for cost effectiveness and efficient radio resource utilization. In this article, we formulate a joint access point association, resources utilization, and energy-efficient communication optimization problem that takes into account various networking factors, such as the number of devices, the number of DAs, the number of available resource units, interference, the transmission power limitation of the devices, DA transmission performance, and channel conditions. The objective is to show the usefulness of data aggregation and shed light on the importance of network design when the number of devices is massive. We propose a coalition game theory-based algorithm PAUSE to transform the optimization problem into a simpler form that can be successfully solved in polynomial time. Different network scenarios are simulated to showcase the effectiveness of PAUSE and to draw observations on cost-effective network design with DAs.

Randomized Channel Sparsifying Hybrid Precoding for FDD Massive MIMO Systems

We propose a novel randomized channel sparsifying hybrid precoding (RCSHP) design to reduce the signaling overhead of channel estimation and the hardware cost and power consumption at the base station (BS), in order to fully harvest benefits of frequency division duplex (FDD) massive multiple-input multiple-output (MIMO) systems. RCSHP allows time-sharing among multiple analog precoders, each serving a compatible user group. The analog precoder is adapted to the channel statistics to properly sparsify the channel for the associated user group, such that the resulting effective channel (product of channel and analog precoder) not only has enough spatial degrees of freedom (DoF) to serve this group of users, but also can be accurately estimated under the limited pilot budget. The digital precoder is adapted to the effective channel based on the duality theory to facilitate the power allocation and exploit the spatial multiplexing gain. We formulate the joint optimization of the time-sharing factors and the associated sets of analog precoders and power allocations as a general utility optimization problem, which considers the impact of effective channel estimation error on the system performance. Then we propose an efficient stochastic successive convex approximation algorithm to provably obtain Karush-Kuhn-Tucker (KKT) points of this problem.

Joint user association and power allocation for massive MIMO HetNets with imperfect CSI

Since Massive multiple-input and multiple-output (MIMO) and heterogeneous networks (HetNets) have significantly improvement in spectrum efficiency, Massive MIMO enabled HetNets have emerged as a promising technique for the fifth-generation cellular networks. Most previous studies focus on energy-efficient resource allocation of Massive MIMO HetNets by assuming perfect channel state information (CSI). In this paper, we investigate the α-fairness network utility optimization problem of joint user association and power allocation for a downlink Massive MIMO HetNet with imperfect CSI. By utilizing zero-forcing beamforming, we show a new closed-form lower bound expression on the ergodic achievable rate. Furthermore, we formulate the optimization problem as a mixed-integer nonlinear programming problem, which is non-convex and NP-hard, to achieve the maximization of α-fairness network utility. Consequently, a joint iterative algorithm with respect to user association and power allocation is developed by decomposing the original problem and relaxing the constraints. Simulation results show that our proposed algorithm can yield much better network utility performance than the other algorithms.

On the singular risk-sensitive stochastic maximum principle

We consider a risk-sensitive stochastic control problem of a nonlinear system in which the variable control has two components, the first being absolutely continuous and the second is singular. The author generalizes the result obtained in risk neutral into risk-sensitive performance cost. The auxiliary process has been introduced to solve the problem of risk sensitive. The relationship between the expected exponential utility and the quadratic backward stochastic differential equation has been given and proved. Actually, I have proved in details two results, the first is necessary optimality condition, while the second is sufficient optimality condition for risk sensitive performance cost. Two examples to carried out to illustrate our main results of risk-sensitive control problem under nonlinear stochastic dynamics with exponential quadratic cost function with numerical investigation, while the second will be in the exponential utility optimization problem.

A Classification Approach to General S-Shaped Utility Optimization with Principals' Constraints

We study a problem in the principal-agent model of two general S-shaped utilities without explicit expressions, where the two parties have different reference points. The problem is featured with a principal's participating incentive compatible constraint, which particularly stands in the context of asset management with motivation to safeguard the benefit of the principal. After a thorough investigation, it turns out to be a complicated double S-shaped utility optimization problem. We propose a new classification approach to study the optimal final asset allocation. First, it is classified into two cases: (a) One-side-loss case in which either both parties suffer liquidation, or one gains and the other loses, or both make profit. (b) Option case in which either both parties suffer liquidation or both make profit. Further, we demonstrate an asymptotic classification of the optimal asset allocation that the single utility maximization of the principal is the limit of the option case, while that of the agent is the limit of the one-side-loss case. More importantly, we find a division reservation utility which the optimal asset allocation belongs to the option case beyond and to the one-side-loss case below. Thus, the key factor resulting in different risk choices is the size of the reservation utility. As an application, we numerically visualize these results with a specific participating contract, which illustrates some novel mechanisms in asset management.

A Principal-Agent Problem of General S-Shaped Utilities With Different Reference Points

We study a problem in the principal-agent model of two general S-shaped utilities without explicit expressions, where the two parties have different reference points. The problem is featured with a principal's participating incentive compatible constraint, which particularly stands in the context of asset management with motivation to safeguard the benefit of the principal. After a thorough investigation, it turns out to be a complicated double S-shaped utility optimization problem. We propose a new classification approach to study the optimal final asset allocation. First, it is classified into two cases: (a) One-side-loss case in which either both parties suffer liquidation, or one gains and the other loses, or both make profit. (b) Option case in which either both parties suffer liquidation or both make profit. Further, we demonstrate an asymptotic classification of the optimal asset allocation that the single utility maximization of the principal is the limit of the option case, while that of the agent is the limit of the one-side-loss case. More importantly, we find a division reservation utility which the optimal asset allocation belongs to the option case beyond and to the one-side-loss case below. Thus, the key factor resulting in different risk choices is the size of the reservation utility. As an application, we numerically visualize these results with a specific participating contract, which illustrates some novel mechanisms in asset management.

Utility Analysis of Radio Access Network Slicing

The utility optimization problem of radio access network-slicing aided mobile systems is formulated considering both throughput and delay demands from a mobile network operator's perspective, whilst relying on stochastic geometry and Lyapunov optimization. Then a joint virtual resource optimization algorithm is proposed to dynamically allocate both virtual spectral and the power resources. Our numerical results support both the high-throughput slice and the low-delay slice and quantify the associated throughput vs. delay trade-off. Moreover, we compare the proposed algorithm with the benchmark one, which ensures better utility.

Water wave optimization for combinatorial optimization: Design strategies and applications

Although the community of nature-inspired computing has witnessed a wide variety of metaheuristics, it often requires considerable effort to adapt them to different combinatorial optimization problems (COPs), and few studies have been devoted to reducing this burden. This paper proposes a systematic approach that consists of a set of basic steps and strategies for adapting water wave optimization (WWO), a simple and generic metaheuristic, to concrete heuristic algorithms for different COPs. Taking advantages of the generic algorithmic framework, designers can only focus on adapting the prorogation operator and the wavelength calculation method according to the combinatorial properties of the given problem, and thus easily derive efficient problem-solving algorithms. We illustrate and test our approach on the flow-shop scheduling problem (FSP), the single-objective multidimensional knapsack problem (MKP), and the multi-objective MKP, and then present an application to a machine utilization optimization problem for a large manufacturing enterprise. The results demonstrate that our approach can derive concrete algorithms that are competitive to the state-of-the-arts. Our approach also provides insights into the adaptation of other metaheuristics and the development of new metaheuristics for COPs.

Connections Between Spectral Properties of Asymptotic Mappings and Solutions to Wireless Network Problems

In this study we establish connections between asymptotic functions and properties of solutions to important problems in wireless networks. We start by introducing a class of self-mappings (called asymptotic mappings) constructed with asymptotic functions, and we show that spectral properties of these mappings explain the behavior of solutions to some maxmin utility optimization problems. For example, in a common family of max-min utility power control problems, we prove that the optimal utility as a function of the power available to transmitters is approximately linear in the low power regime. However, as we move away from this regime, there exists a transition point, easily computed from the spectral radius of an asymptotic mapping, from which gains in utility become increasingly marginal. From these results we derive analogous properties of the transmit energy efficiency. In this study we also generalize and unify existing approaches for feasibility analysis in wireless networks. Feasibility problems often reduce to determining the existence of the fixed point of a standard interference mapping, and we show that the spectral radius of an asymptotic mapping provides a necessary and sufficient condition for the existence of such a fixed point. We further present a result that determines whether the fixed point satisfies a constraint given in terms of a monotone norm.

Joint Channel Assignment and Stochastic Energy Management for RF-Powered OFDMA WSNs

As an emerging energy replenishment technique, radio-frequency (RF) energy transfer has been considered as a promising solution to power the low-end wireless sensor networks (WSNs). However, in RF-powered orthogonal frequency-division multiple accessing (OFDMA) WSNs, both the energy provisioning and data transmission are easily impacted by the highly dynamic and unpredictable wireless channels, making channel assignment and energy management closely coupled. Furthermore, due to the lack of priori knowledge of stochastic channel conditions, network performance optimization becomes more challenging. In this paper, we investigate joint channel assignment and stochastic energy management to optimize the long-term network utility in RF-powered OFDMA WSNs, by jointly considering the stochasticity in RF energy harvesting rates and channel fading. We formulate the network utility optimization problem (NUOP) as a mixed-integer non-linear stochastic optimization problem. By leveraging Lyapunov optimization to decouple NUOP into two subproblems and address them separately, we propose an online algorithm, named JAMA, to adaptively adjust the sampling rates, data transmission power, transmission rate, and channel assignment according to the ever-changing channel conditions, while guarantee the network stability and sustainability. In addition, theoretical performance analysis is provided to prove that JAMA can achieve near-optimal network utility and satisfy the network stability and sustainability constraints. Extensive simulation results based on the experimental data of an RF-powered WSN testbed verify the effectiveness and efficiency of JAMA and evaluate the impacts of system parameters on network performance.