Stochastic Cost Functions Research Articles

Online Distributed Algorithms for Online Noncooperative Games With Stochastic Cost Functions: High Probability Bound of Regrets

Online Distributed Algorithms for Online Noncooperative Games With Stochastic Cost Functions: High Probability Bound of Regrets

Moment based model predictive control for linear systems: Additive perturbations case

AbstractIn this article, we present a novel linear model predictive control (MPC) strategy for controlling uncertain dynamical systems. The moment based MPC strategy is based on the (centralized) moments of the stochastic cost and constraint functions. We show that moment based MPC formulations yield computationally tractable predictive control problems, due to the explicit analytic expressions of the moments and linearity in the dynamics. This article considers (i) the output regulation MPC configuration, where the output is steered towards a reference and state vector is not correctly accessible to the controller at the decision instants; (ii) the moment based MPC formulation with uncertainties that are non‐Gaussian random variables, and (iii) bound and polytopic constraints in the uncertain MPC problem subject to either Gaussian disturbances or uncertainties with symmetric distributions. We demonstrate the effectiveness of the proposed MPC technique on simulation examples such as a double integrator system and a quadruple tank system.

Stochastic Delay Cost Functions to Estimate Delay Propagation Under Uncertainty

We provide a mathematical formulation of flight-specific delay cost functions that enables a detailed tactical consideration of how a given flight delay will interact with all downstream constraints in the respective aircraft rotation. These functions are reformulated into stochastic delay cost functions to respect conditional probabilities and increasing uncertainty related to more distant operational constraints. Conditional probabilities are learned from historical operations data, such that typical delay propagation patterns can support the flight prioritization process as a part of tactical airline schedule recovery. A case study compares the impact of deterministic and stochastic cost functions on optimal recovery decisions during an airport constraint. We find that deterministic functions systematically overestimate potential disruption costs as well as optimal schedule recovery costs in high delay situations. Thus, an optimisation based on stochastic costs outperforms the deterministic approach by up to 15%, as it reveals ‘hidden’ downstream recovery potentials. This results in different slot allocations and in fewer passengers missing their connections.

Distributed Learning in Non-Convex Environments—Part I: Agreement at a Linear Rate

Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments. Most available works on distributed non-convex optimization problems focus on the deterministic setting where exact gradients are available at each agent. In this work and its Part II, we consider stochastic cost functions, where exact gradients are replaced by stochastic approximations and the resulting gradient noise persistently seeps into the dynamics of the algorithm. We establish that the diffusion learning strategy continues to yield meaningful estimates non-convex scenarios in the sense that the iterates by the individual agents will cluster in a small region around the network centroid. We use this insight to motivate a short-term model for network evolution over a finite-horizon. In Part II of this work, we leverage this model to establish descent of the diffusion strategy through saddle points in O(1/μ) steps, where μ denotes the step-size, and the return of approximately second-order stationary points in a polynomial number of iterations.

English

The study analyzed economic capacity utilization rates in the sugar industry for the period 1970 to 2010 in Nigeria. Secondary data obtained from sugar firms; Central Bank of Nigeria; National Bureau of Statistics and the Federal Ministry of Finance were used in the study. Stochastic Cobb-Douglas cost functions for the sugar industry were estimated from which indices of economic capacity utilization rates were obtained. Trend in the economic capacity utilization rate showed undulated pattern with an average index of 60.30% and excess economic capacity of 39.70%. Multiple-regression of various forms based on the ordinary least squares technique was used to determine factors that influence the performance indicators in the industry. Empirical results revealed that economic capacity utilization rates in the sugar industry was influenced by the inflation rate, per capita real GDP, energy consumption of the industry, federal government expenditure on the sugar industry and the period of liberalization. The result of the regression and descriptive analyses revealed that the sugar industry in Nigeria was constrained by insufficient production inputs. Policy measures aimed at reduction or maintaining a steady or less fluctuated inflation rate in the country, expansionary aggregate demand, increase funding to agencies that have direct dealings with the sugar production and adequate provision of electricity to the industry as well as the adoption of the liberalization industrial policy on sugar industry were recommended. Key word: Sugar, industry, capacity, utilization, economic, Nigeria.

An Efficiency Analysis for Turkish Banking Sector

Banking sector, as in many countries, has the largest share in the financial market in Turkey. Increasing competition conditions has forced banks to work more effectively, especially after the liberalization process in the 1980’s. Within this framework, the aim of this dissertation is to investigate the cost and profit efficiency of the commercial banks operating in Turkey. The dissertation is organized as follows. Firstly, the concept of efficiency is clarified and then the efficiency measurement methods are introduced. Secondly, the historical development of the Turkish banking sector, to related years, are presented. Finally, in the framework of the intermediation approach, panel data belonging to 32 commercial banks operating between the years 2003–2007 is used and the efficiency scores of banks are calculated by estimating the stochastic translog cost and profit functions. The main reason for choosing this period is the studies about this period are not enough and external shocks like crises didn’t occur after the transition to inflation accounting since 2003. As a result of the study, it is evident that the small-scale and foreign banks in the Turkish banking sector operate more efficient than other banks in terms of both profit and cost. Especially, the low efficiency level of state banks is associated with the size of banks and managerial skills.

Information Technology and Productivity Changes in the Banking Industry

This paper analyses the effects of investment in information technologies (IT) in the financial sector using micro‐data from a panel of 600 Italian banks over the period 1989–2000. Stochastic cost and profit functions are estimated allowing for individual banks’ displacements from the best practice frontier and for non‐neutral technological change. The results show that both cost and profit frontier shifts are strongly correlated with IT capital accumulation. Banks adopting IT capital‐intensive techniques are also more efficient. On the whole, over the past decade IT capital‐deepening contribution to total factor productivity growth of the Italian banking industry can be estimated in a range between 1.3 and 1.8 per cent per year.

Single-Machine Scheduling with Exponential Processing Times and General Stochastic Cost Functions

We study a single-machine stochastic scheduling problem with n jobs, in which each job has a random processing time and a general stochastic cost function which may include a random due date and weight. The processing times are exponentially distributed, whereas the stochastic cost functions and the due dates may follow any distributions. The objective is to minimize the expected sum of the cost functions. We prove that a sequence in an order based on the product of the rate of processing time with the expected cost function is optimal, and under certain conditions, a sequence with the weighted shortest expected processing time first (WSEPT) structure is optimal. We show that this generalizes previous known results to more general situations. Examples of applications to practical problems are also discussed.

Risk efficient juvenile haddock production systems: An ex‐ante recursive stochastic approach

The risk efficient live feed system for juvenile haddock production is derived through recursive ex‐ante stochastic cost estimation. Four alternative feeding technologies are simulated to capture the economic costs associated with live feed and juvenile production and scale economies are investigated by simulating three production levels. Using Monte Carlo simulation techniques, multivariate stochastic cost functions are derived in a time‐dependent recursive production model. With the current technologies and price levels, land‐based juvenile haddock production is viable. The marginal impact, in terms of cost‐savings, to additional research on optimal feeding periods will be minimal. On the other hand, the high opportunity cost of capital used in aquaculture production, due to numerous perceived risk premia, may pose a more immediate constraint for capital formation and industry development.

Information Technology and Productivity Changes in the Banking Industry

This paper analyzes the effects of investment in information technologies (IT) in the financial sector using micro-data from a panel of 600 Italian banks over the period 1989-2000. Stochastic cost and profit functions are estimated allowing for individual banks' displacements from the best practice frontier and for non-neutral technological change. The results show that both cost and profit frontier shifts are strongly correlated with IT capital accumulation. Banks adopting IT capital intensive techniques are also more efficient. On the whole, over the past decade IT capital deepening contribution to total factor productivity growth of the Italian banking industry can be estimated in a range between 1.3% and 1.8% per year.

Stochastic Operating Characteristics and Cost Functions of Electrostatic Precipitators

Stochastic Operating Characteristics and Cost Functions of Electrostatic Precipitators