Length Of Horizon Research Articles

When Demands Evolve Larger and Noisier: Learning and Earning in a Growing Environment

Many emerging businesses and services encounter growing environments where the stochastic demand gradually increases. The increases are often not only in the expectation of the demand but also in the variance. Because of the growing environments, sequential decision making problems raise additional challenges when model parameters are unknown and need to be dynamically learned from sequentially observed data. In this work, we use a single-product dynamic pricing problem to illustrate how the non-stationary growing environment influences policy design and policy performance such as regret. We prove matching upper and lower bounds on regret and design near-optimal pricing policies. We then demonstrate how the growth rate of demand variance affects the best achievable policy performance as well as the near-optimal policy design. In the analysis, we also prove that that whether the seller knows the length of time horizon in advance or not render different optimal regret orders.

Model-based feed-forward control for time-varying systems with an example for SRF cavities

To derive feed-forward signals the impulse response matrix has to be inverted. While for time-invariant systems this matrix has a Toeplitz structure, this is not the case for time-variant systems. Thus, the derivation of the inverse scales cubically with the length of the signal horizon. This paper presents an efficient way to calculate the inverse impulse response matrix based on the description as linear fractional transformation. With this the calculation effort scales only linearly with the horizon. The feed-forward signal generation is applied in this paper for superconducting accelerating structures. The superconducting accelerating cavities are operated in pulsed mode. Each cavity is fed by a 1.3GHz radio frequency signal with high power. Model-based feed-forward control is essential here to relief the feedback controller and with this to minimize the power consumption and therefore heating of different components. To derive a model-based feed-forward signal, first, a reasonable reference signal is to be chosen, which is done here based on physical properties of the cavities, then the efficient inversion of the impulse response matrix is applied. Experimentally results from the European X-ray free-electron laser are presented.

Explicit spline-based continuous-time MPC: a study on design and performance

This paper presents a continuous-time model predictive control scheme based on B-spline functions used for signals and model approximation. The proposed controller offers two interesting advantages. First, it formulates the control signal as a continuous polynomial spline function, the nature of which is determined by its control polygon that is subject of optimization. Second, all continuous constraints assumed over prediction horizon are consistently transformed into constraints imposed on a finite number of elements of this control polygon. Using parametric quadratic programming we further show how to obtain an explicit representation of the proposed controller, which is known for its efficient online implementation. The featured simulation study demonstrates that by a suitable choice of number and position of knots of the spline function over the prediction horizon it is possible to substantially reduce the number of critical regions of the explicit controller while preserving control performance, and to mitigate the direct correlation between number of regions and chosen length of prediction horizon.

Complexity minimisation of suboptimal MPC without terminal constraints

This paper generalises stability analysis of Nonlinear Model Predictive Control without terminal constraints to incorporate possible suboptimality of MPC solutions and develops a framework for minimisation of computational efforts associated with obtaining such a solution. The framework is applied to primal-dual interior-point solvers by choosing the length of the prediction horizon together with a degree of suboptimality of the solution in a way that reduces algorithmic complexity while satisfying certain stability and performance guarantees. The framework ensures an optimal choice for the prediction horizon in order to minimise computational complexity if applied to linear or convex quadratic MPC problems, and acts as a good indicator to this end in the more general case of nonlinear systems. This is illustrated in a numerical case study, where we apply the proposed framework to a nonholonomic robot.

Optimal Control and Inverse Optimal Control with Continuous Updating for Human Behavior Modeling

The theory of optimal control has received considerable attention to model motion behavior or decision making of humans. Most approaches are based on a fixed (or infinite) time horizon which implies that all information is available at the beginning of the time interval. Nevertheless, it is reasonable to believe that the human uses information defined by a continuously moving information horizon at each time instant and adapts accordingly. Therefore, in this paper, we propose an optimal feedback control approach based on the paradigm of continuous updating. The model parameters which define individual human behavior consist of the cost function parameters and the length of the information horizon, which can be identified via a corresponding inverse optimal control approach. We show the applicability of the approach with simulations of a potential application example of human behavior identification from the point of view of a driving assistance system.

Short-Term Photovoltaic Power Forecasting Using an LSTM Neural Network and Synthetic Weather Forecast

In this paper, a forecasting algorithm is proposed to predict photovoltaic (PV) power generation using a long short term memory (LSTM) neural network (NN). A synthetic weather forecast is created for the targeted PV plant location by integrating the statistical knowledge of historical solar irradiance data with the publicly available type of sky forecast of the host city. To achieve this, a ${K}$ -means algorithm is used to classify the historical irradiance data into dynamic type of sky groups that vary from hour to hour in the same season. In other words, the types of sky are defined for each hour uniquely using different levels of irradiance based on the hour of the day and the season. This can mitigate the performance limitations of using fixed type of sky categories by translating them into dynamic and numerical irradiance forecast using historical irradiance data. The proposed synthetic weather forecast is proved to embed the statistical features of the historical weather data, which results in a significant improvement in the forecasting accuracy. The performance of the proposed model is investigated using different intraday horizon lengths in different seasons. It is shown that using the synthetic irradiance forecast can achieve up to 33% improvement in accuracy in comparison to that when an hourly categorical type of sky forecast is used, and up to 44.6% in comparison to that when a daily type of sky forecast is used. This highlights the significance of utilizing the proposed synthetic forecast, and promote a more efficient utilization of the publicly available type of sky forecast to achieve a more reliable PV generation prediction. Moreover, the superiority of the LSTM NN with the proposed features is verified by investigating other machine learning engines, namely the recurrent neural network (RNN), the generalized regression neural network (GRNN) and the extreme learning machine (ELM).

Exponential Decay in the Sensitivity Analysis of Nonlinear Dynamic Programming

In this paper, we study the sensitivity of discrete-time dynamic programs with nonlinear dynamics and objective to perturbations in the initial conditions and reference parameters. Under uniform controllability and boundedness assumptions for the problem data, we prove that the directional derivative of the optimal state and control at time $k$, $x^*_k$, and $u^*_k$, with respect to the reference signal at time $i$, $d_i$, will have exponential decay in terms of $|k-i|$ with a decay rate $\rho$ independent of the temporal horizon length. The key technical step is to prove that a version of the convexification approach proposed by Verschueren et al. can be applied to the KKT conditions and results in a convex quadratic program with uniformly bounded data. In turn, Riccati techniques can be further employed to obtain the sensitivity result, borne from the observation that the directional derivatives are solutions of quadratic programs with structure similar to the KKT conditions themselves. We validate our findings with numerical experiments on a small nonlinear, nonconvex, dynamic program.

Conventional and Explicit Approaches for Simultaneous Moving Horizon Estimation and Model Predictive Control: A Comparative Evaluation

Model Predictive Control (MPC) has been applied across a wide range of engineering applications including process industries. MPC requires complete knowledge of states at the current instant which can either be measured directly or estimated using a state estimator. Of late, Moving Horizon Estimation (MHE) has been widely used as a state estimator owing to its ability to handle constraints. Both MPC and MHE involve solving an optimization problem at each sampling instant which can prove computationally burdensome for fast systems. Multi-parametric programming based explicit approaches have been proposed in literature as a possible approach for solving the online optimization problems in a computationally efficient manner. In the current work, feasibility of the explicit approaches simultaneously for both MPC and MHE is investigated using simulation as well as experimental studies on a quadruple tank setup. The computational efforts required for this simultaneous implementation of the explicit approaches for MPC and MHE are compared with the conventional optimization approach. Results indicate feasibility of multi-parametric implementation for lower horizon lengths.

Political Security in Authoritarian Systems with a Resource Rent Economy: a Result of the „Social Contract” and High Resource Prices?

Most researchers believe that states which are rich in natural resources are more able to maintain political stability in comparison to countries without such an access to exceptional profits. However, some rent resource autocracies are unanimously considered fragile, and their ability to extract maximum rents does not always contribute to political and economic security during price fluctuations. Based on the idea that the state’s ability to extract resources imposes on it certain ob- ligations, the research question touches upon the quality of governance as a supposed core factor, which mediates the resource dependence and political security in terms of stateness and the ability to fulfil the “social contract.” The latter is described as implementation of political decisions, provision of public goods and services. However, the quality of governance is substantially different in various autocratic systems. Using casestudy and descriptive statistics, the authors try to reveal the context and ascertain which factors trigger the horizon length of autocrats` political strategies during rising and falling resource prices. The authors affirm that resource dependence negatively affects political security less due to an absence of economic growth during price breaks, and more due to the struggle of political elites for the redistribution of resources, absence of disciplinary mechanisms, weak representation and accountability systems, and poor enabling environments as a basis for quality of resource management. The authors conclude that political security in autocratic resource economies is achieved through the coexistence of political will and triggers, conducive to specifying the length of the planning horizon.

Optimal Exploration–Exploitation in a Multi-armed Bandit Problem with Non-stationary Rewards

In a multi-armed bandit problem, a gambler needs to choose at each round one of K arms, each characterized by an unknown reward distribution. The objective is to maximize cumulative expected earnings over a planning horizon of length T, and performance is measured in terms of regret relative to a (static) oracle that knows the identity of the best arm a priori. This problem has been studied extensively when the reward distributions do not change over time, and uncertainty essentially amounts to identifying the optimal arm. We complement this literature by developing a flexible non-parametric model for temporal uncertainty in the rewards. The extent of temporal uncertainty is measured via the cumulative mean change in the rewards over the horizon, a metric we refer to as temporal variation, and regret is measured relative to a (dynamic) oracle that plays the point-wise optimal action at each period. Assuming that nature can choose any sequence of mean rewards such that their temporal variation does not exceed V (a temporal uncertainty budget), we characterize the complexity of this problem via the minimax regret, which depends on V (the hardness of the problem), the horizon length T, and the number of arms K.

A Robust Prognostic Indicator for Renewable Energy Technologies: A Novel Error Correction Grey Prediction Model

This paper proposes a novel error correction grey prediction model for degradation prediction of renewable energy storages. The proposed approach uses an error correction factor ψ to eliminate the inherent error of the original grey model (GM), and at the same time retain the original simplicity and fast prototyping. In addition, due to the uncertainty and complexity of failure mechanisms, a trigonometric residual modification is considered in order to well-describe the influence of operating conditions or cyclic fluctuation on the renewable energy storages. Two experimental case studies, including lithium-ion battery and fuel cell aging tests, are performed to validate the performance of the proposed method. In particular, the accuracy of the proposed method is investigated for different prediction horizon lengths, in order to further demonstrate its effectiveness and robustness. It is worth mentioning that the proposed method can ensure the accuracy of the remaining useful life estimation in the case of long-term forecasting, and thus, the maintenance management and corrective action of renewable energy storages can be scheduled earlier, leading to more effective cost minimization and risk mitigation.

RESEARCH OF MULTIPLE INVESTMENT STRATEGIES USING A SHORT AND LONG POSITION


 
 
 The construction of an optimal portfolio of securities is one of the main tasks of managing the financial system, in which individual assets are only a component part. However, each asset also requires a separate study.I gave the article building an investment portfolio with a zero strategy, comprising borrowing some assets and buying other assets for the same amount. The study comprised choosing the length of the historical horizon, the ranking criterion and the portfolio structure that ensured the maximum investor income.
 
 

Exponentially Convergent Receding Horizon Strategy for Constrained Optimal Control

Receding horizon control has been a widespread method in industrial control engineering as well as an extensively studied subject in control theory. In this work, we consider a lag L receding horizon strategy that applies the initial L optimal controls from each quadratic program to each receding horizon. We investigate a discrete-time and time-varying linear-quadratic optimal control problem that includes a nonzero reference trajectory and constraints on both state and control. We prove that, under boundedness and controllability conditions, the solution obtained by the receding horizon strategy converges to the solution of the full problem interval exponentially fast in the length of the receding horizon for some lag L. The exponential rate of convergence provides a systematic way of choosing the receding horizon length given a desired accuracy level. We illustrate our theoretical findings using a small, synthetic production cost model with real demand data.

Constrained model predictive control of a vehicle suspension using Laguerre polynomials

In this paper, a fast constrained model predictive control algorithm was designed for the active suspension of a half-car model to increase the controller bandwidth so that high frequency displacement disturbance coming from the road can be rejected. To this end, a quasi-LTI model of a semi-active suspension model was controlled by a model predictive controller with orthogonal Laguerre polynomials. With the use of Laguerre polynomials, it has been shown that the optimization parameter set could be made minimal, and thereby it has been shown that on-line optimization takes less time. With numerical simulations, it has been shown that the time complexity of a model predictive control having Laguerre polynomials is linear in the length of prediction horizon, whereas time complexity of a regular model predictive control is quadratic in the length of prediction horizon. Since it has been shown that time complexity of the constrained model predictive controller with orthogonal Laguerre polynomial is reduced, it is possible to extend the prediction horizon to large values. Further, constraints on the input signal and the state vector were also discussed within this context.

On the Disclosure of Promotion Value in Platforms with Learning Sellers

We consider a platform facilitating trade between sellers and buyers with the objective of maximizing consumer surplus. Even though in many such marketplaces prices are set by revenue-maximizing sellers, platforms can influence prices through (i) price-dependent promotion policies that can increase demand for a product by featuring it in a prominent position on the webpage and (ii) the information revealed to sellers about the value of being promoted. Identifying effective joint information design and promotion policies is a challenging dynamic problem as sellers can sequentially learn the promotion value from sales observations and update prices accordingly. We introduce the notion of confounding promotion policies, which are designed to prevent a Bayesian seller from learning the promotion value (at the expense of the short-run loss of diverting consumers from the best product offering). Leveraging these policies, we characterize the maximum long-run average consumer surplus that is achievable through joint information design and promotion policies when the seller sets prices myopically. We then establish a Bayesian Nash equilibrium by showing that the seller's best response to the platform's optimal policy is to price myopically at every history. Moreover, the equilibrium we identify is platform-optimal within the class of horizon-maximin equilibria, in which strategies are not predicated on precise knowledge of the horizon length, and are designed to maximize payoff over the worst-case horizon. Our analysis allows one to identify practical long-run average optimal platform policies in a broad range of demand models.

Minimax strategy in approximate model predictive control

It is known that a model predictive control law for a linear dynamical system with a linear or quadratic cost function can be explicitly computed as a piece-wise affine function. However, the number of regions required grows rapidly with the horizon length, the number of states and constraints limiting the deployment of explicit solutions to relatively small MPC problems, and motivating approximate solutions requiring less storage for online implementation. Unfortunately, the offline computation required to generate the approximate solution can be very high using many existing algorithms. In this paper, we propose a new procedure to generate the approximate solution based on barycentric interpolation whilst retaining a (less conservative) certification of the controller. This novel certification procedure requires solving a number of small-scale multiparametric linear programs together with convex optimization problems. During the online implementation of the approximate MPC, only a small linear program has to be solved to evaluate the control law. The efficacy of the proposed approach is demonstrated through both simulation and also in application to a canonical cart–pole stabilization problem.

PCN157 COST-EFFECTIVENESS ANALYSIS OF NIVOLUMAB + IPILIMUMAB VERSUS SUNITINIB IN THE FIRST-LINE TREATMENT OF ADVANCED OR METASTATIC INTERMEDIATE- OR POOR-RISK RENAL CELL CARCINOMA IN SPAIN

Nivolumab plus ipilimumab (nivolumab+ipilimumab) is the first immuno-oncology combination that has shown significant, long-term overall survival (OS) benefit for the first-line treatment of adult patients with intermediate- or poor-risk advanced renal cell carcinoma (1L RCC) compared with standard of care (sunitinib). This study assessed the cost-effectiveness of nivolumab+ipilimumab versus sunitinib in 1L RCC patients in Spain. A three-state partitioned survival model was developed (progression-free, progressed disease and death) with a lifetime horizon (40 years) and one-week cycle length. Progression-free survival, OS, time to treatment discontinuation, adverse event and treatment-specific utility data (EQ-5D-3L) was obtained from CheckMate-214 (NCT02231749; 30 months minimum follow-up). Spanish costs for adverse events and drug acquisition were obtained from Isla (2017) and CGCOF, respectively. Costs for drug administration, monitoring and subsequent therapies were taken from ESALUD (2018) ; associated resource use was based on CheckMate-214 and obtained through clinical expert input. An annual discount of 3.0% was applied to both costs and outcomes. Outcomes of interest were total costs, life years (LYs), quality-adjusted life-years (QALYs), and the incremental cost-utility ratio (ICUR). Furthermore, deterministic and probabilistic sensitivity analyses (DSA and PSA) were assessed for robustness of the results. Nivolumab+ipilimumab was associated with higher QALYs versus sunitinib (4.86 versus 3.54, respectively) at increased total cost (€142,450 versus €104,085, respectively). This resulted in an ICUR of €29,146/QALY versus sunitinib. Based on the DSA, the key ICUR drivers were the proportion of patients receiving treatment after sunitinib and the maximum treatment duration for nivolumab+ipilimumab. The model’s robustness was further confirmed by the PSA; nivolumab+ipilimumab had a 54% and 95% probability of being cost-effective at willingness-to-pay thresholds of €30,000/QALY and €50,000/QALY, respectively. Driven by the increased and sustained OS benefit demonstrated in CheckMate-214, nivolumab+ipilimumab is a cost-effective treatment when compared to sunitinib for 1L RCC patients in Spain, considering a willingness-to-pay of €30,000/QALY.

FINRA 529 Plan Share Class Initiative encourages firms to self-report violations

Purpose To explain FINRA’s new 529 Plan Share Class Initiative, which encourages broker-dealers to self-report violations. Design/methodology/approach This article provides an overview of 529 plans, the various fee structures of the underlying investment funds, and guidance that broker-dealers should tailor their recommendations to the needs of the individual customer. The article discusses FINRA’s initiative for broker-dealers to self-report if they have violations in this area. It describes various supervisory failures brokerage firms may experience in connection with recommending 529 plans, eligibility for the self-reporting initiative and benefits of self-reporting. Findings This FINRA initiative provides an opportunity for firms to reflect on their supervisory systems and provide restitution to harmed customers. It also provides relevant fee-based investment information to customers. Practical implications 529 plans are valuable tax-advantaged tools to encourage saving for the future educational expenses of a designated beneficiary. If brokerage firms lack reasonable supervisory procedures to recommend appropriate investments based on the length of the investment horizon, this FINRA initiative provides a unique and limited opportunity for firms to assess their supervisory systems and procedures governing 529 Plan share-class recommendations, to identify and remediate any defects, and to compensate any investors harmed by supervisory failures, while possibly avoiding fines for such conduct. Originality/value Expert guidance from experienced financial services regulatory and public finance lawyers.

Replenishment and denomination mix of automated teller machines with dynamic forecast demands

In the inventory management of automated teller machines (ATMs) many activities affect the total costs, such as forecasting, replenishments and the denomination mix used. The denomination mix is the combination of bills used to fulfill a customer’s demand. We investigate whether allowing the denomination mix to vary over time based on the forecast withdrawals at an ATM reduces actual operating costs of an ATM. To verify this, we propose a time-varying denomination mix strategy, which is validated by benchmarking it against the case of a bank’s denomination mix strategy. The bank’s predetermined strategy typically consists of a least note strategy or a one-smallest strategy. In all strategies we simultaneously optimize denomination mixes and replenishment decisions. We define the problem and solution strategies as mixed integer programming formulations and solve them via a rolling horizon algorithm using different frequencies of denomination mix updates, rolling horizon lengths, numbers of ATMs, cost parameters, and forecast qualities. By implementing the time-varying denomination mix, we show that the operational costs of managing an ATM can be reduced by 21% or €153.77 per ATM per month on average, which can represent over €10 million per year in the Netherlands only.

Assessment of an Improved Finite Control Set Model Predictive Current Controller for Automotive Propulsion Applications

This paper presents an investigation on finite control set model predictive current control, validated experimentally with a rear axle electrical drive unit used in automotive applications. An improved problem formulation is suggested which lowers the computational turnaround time of the solver with approximately $\text{40}\%$ for an horizon length of $N=4$ . Apart from the computational requirement aspects, the assessment focuses on inverter efficiency, phase current total demand distortion, and acoustic performance. The proposed solution is evaluated against a standard double proportional and integrator (PI) field-oriented current controller with pulsewidth modulation. It is shown that the proposed solution is feasible, the associated optimization problem at hand can be solved in real time, while exploiting the attractiveness of the proposed improvements. In summary, it is concluded that the inverter efficiency can be improved without deteriorating neither the phase current harmonics nor the acoustic performance.