Design of an optimal auction for sponsored search auctions

In this paper we first describe a framework to model the sponsored search auction on the web as a mechanism design problem. Using this framework, we design a novel auction which we call the OPT (optimal) auction. The OPT mechanism maximizes the search engine's expected revenue while achieving Bayesian incentive compatibility and individual rationality of the advertisers. We show that the OPT mechanism is superior to two of the most commonly used mechanisms for sponsored search namely (1) GSP (Generalized Second Price) and (2) VCG (Vickrey-Clarke-Groves). We then show an important revenue equivalence result that the expected revenue earned by the search engine is the same for all the three mechanisms provided the advertisers are symmetric and the number of sponsored slots is strictly less than the number of advertisers.

Mechanism design for cost optimal PAC learning in the presence of strategic noisy annotators

We consider the problem of Probably Ap-proximate Correct (PAC) learning of a bi-nary classifier from noisy labeled exam-ples acquired from multiple annotators(each characterized by a respective clas-sification noise rate). First, we consider the complete information scenario, where the learner knows the noise rates of all the annotators. For this scenario, we derive sample complexity bound for the Mini-mum Disagreement Algorithm (MDA) on the number of labeled examples to be ob-tained from each annotator. Next, we consider the incomplete information sce-nario, where each annotator is strategic and holds the respective noise rate as a private information. For this scenario, we design a cost optimal procurement auc-tion mechanism along the lines of Myer-son’s optimal auction design framework in a non-trivial manner. This mechanism satisfies incentive compatibility property,thereby facilitating the learner to elicit true noise rates of all the annotators.

An Optimal Mechanism for Sponsored Search Auctions on the Web and Comparison With Other Mechanisms

In this paper, we first describe a framework to model the sponsored search auction on the web as a mechanism design problem. Using this framework, we describe two well-known mechanisms for sponsored search auction-Generalized Second Price (GSP) and Vickrey-Clarke-Groves (VCG). We then derive a new mechanism for sponsored search auction which we call optimal (OPT) mechanism. The OPT mechanism maximizes the search engine's expected revenue, while achieving Bayesian incentive compatibility and individual rationality of the advertisers. We then undertake a detailed comparative study of the mechanisms GSP, VCG, and OPT. We compute and compare the expected revenue earned by the search engine under the three mechanisms when the advertisers are symmetric and some special conditions are satisfied. We also compare the three mechanisms in terms of incentive compatibility, individual rationality, and computational complexity. Note to Practitioners-The advertiser-supported web site is one of the successful business models in the emerging web landscape. When an Internet user enters a keyword (i.e., a search phrase) into a search engine, the user gets back a page with results, containing the links most relevant to the query and also sponsored links, (also called paid advertisement links). When a sponsored link is clicked, the user is directed to the corresponding advertiser's web page. The advertiser pays the search engine in some appropriate manner for sending the user to its web page. Against every search performed by any user on any keyword, the search engine faces the problem of matching a set of advertisers to the sponsored slots. In addition, the search engine also needs to decide on a price to be charged to each advertiser. Due to increasing demands for Internet advertising space, most search engines currently use auction mechanisms for this purpose. These are called sponsored search auctions. A significant percentage of the revenue of Internet giants such as Google, Yahoo!, MSN, etc., comes from sponsored search auctions. In this paper, we study two auction mechanisms, GSP and VCG, which are quite popular in the sponsored auction context, and pursue the objective of designing a mechanism that is superior to these two mechanisms. In particular, we propose a new mechanism which we call the OPT mechanism. This mechanism maximizes the search engine's expected revenue subject to achieving Bayesian incentive compatibility and individual rationality. Bayesian incentive compatibility guarantees that it is optimal for each advertiser to bid his/her true value provided that all other agents also bid their respective true values. Individual rationality ensures that the agents participate voluntarily in the auction since they are assured of gaining a non-negative payoff by doing so.

An auction algorithm for procuring wireless channel in a heterogenous wireless network

In this paper, we develop a novel auction algorithm for procuring wireless channel by a wireless node in a heterogeneous wireless network. We assume that the service providers of the heterogeneous wireless network are selfish and non-cooperative in the sense that they are only interested in maximizing their own utilities. The wireless user needs to procure wireless channels to execute multiple tasks. To solve the problem of the wireless user, we propose a reverse optimal (REVOPT) auction and derive an expression for the expected payment by the wireless user. The proposed auction mechanism REVOPT satisfies important game theoretic properties such as Bayesian incentive compatibility and individual rationality.

Optimal allocation of carbon credits to emitting agents in a carbon economy

Reduction of carbon emissions is of paramount importance in the context of global warming. Countries and global companies are now engaged in understanding systematic ways of achieving well defined emission targets. In fact, carbon credits have become significant and strategic instruments of finance for countries and global companies. In this paper, we formulate and suggest a solution to the carbon allocation problem, which involves determining a cost minimizing allocation of carbon credits among different emitting agents. We address this challenge in the context of a global company which is faced with the challenge of determining an allocation of carbon credit caps among its divisions in a cost effective way. The problem is formulated as a reverse auction problem where the company plays the role of a buyer or carbon planning authority and the different divisions within the company are the emitting agents that specify cost curves for carbon credit reductions. Two natural variants of the problem: (a) with unlimited budget and (b) with limited budget are considered. Suitable assumptions are made on the cost curves and in each of the two cases we show that the resulting problem formulation is a knapsack problem that can be solved optimally using a greedy heuristic. The solution of the allocation problem provides critical decision support to global companies engaged seriously in green programs.

Optimal barrier subdivision for Kramers' escape rate

We examine the effect of subdividing the potential barrier along the reaction coordinate on Kramers' escape rate for a model potential. Using the known supersymmetric potential approach, we show the existence of an optimal number of subdivisions that maximizes the rate.

Optimal scheduling of hydro-thermal power systems under shortage

The problem of optimal scheduling of the generation of a hydro-thermal power system that is faced with a shortage of energy is studied. The deterministic version of the problem is first analyzed, and the results are then extended to cases where the loads and the hydro inflows are random variables.

Optimal hydrothermal load flow: Formulation and a successive approximation solution for fixed head systems

This paper deals with the optimal load flow problem in a fixed-head hydrothermal electric power system. Equality constraints on the volume of water available for active power generation at the hydro plants as well as inequality constraints on the reactive power generation at the voltage controlled buses are imposed. Conditions for optimal load flow are derived and a successive approximation algorithm for solving the optimal generation schedule is developed. Computer implementation of the algorithm is discussed, and the results obtained from the computer solution of test systems are presented.

A hierarchical system of learning automata that can learn die globally optimal path

Systems of learning automata have been studied by various researchers to evolve useful strategies for decision making under uncertainity. Considered in this paper are a class of hierarchical systems of learning automata where the system gets responses from its environment at each level of the hierarchy. A classification of such sequential learning tasks based on the complexity of the learning problem is presented. It is shown that none of the existing algorithms can perform in the most general type of hierarchical problem. An algorithm for learning the globally optimal path in this general setting is presented, and its convergence is established. This algorithm needs information transfer from the lower levels to the higher levels. Using the methodology of estimator algorithms, this model can be generalized to accommodate other kinds of hierarchical learning tasks.

Optimal Parameter Trajectory Estimation in Parameterized SDEs: An Algorithmic Procedure

We consider the problem of estimating the optimal parameter trajectory over a finite time interval in a parameterized stochastic differential equation (SDE), and propose a simulation-based algorithm for this purpose. Towards this end, we consider a discretization of the SDE over finite time instants and reformulate the problem as one of finding an optimal parameter at each of these instants. A stochastic approximation algorithm based on the smoothed functional technique is adapted to this setting for finding the optimal parameter trajectory. A proof of convergence of the algorithm is presented and results of numerical experiments over two different settings are shown. The algorithm is seen to exhibit good performance. We also present extensions of our framework to the case of finding optimal parameterized feedback policies for controlled SDE and present numerical results in this scenario as well.

Bi-criteria single machine scheduling problem with a learning effect: Aneja-Nair method to obtain the set of optimal sequences

In this paper, we consider the bi-criteria single machine scheduling problem of n jobs with a learning effect. The two objectives considered are the total completion time (TC) and total absolute differences in completion times (TADC). The objective is to find a sequence that performs well with respect to both the objectives: the total completion time and the total absolute differences in completion times. In an earlier study, a method of solving bi-criteria transportation problem is presented. In this paper, we use the methodology of solvin bi-criteria transportation problem, to our bi-criteria single machine scheduling problem with a learning effect, and obtain the set of optimal sequences,. Numerical examples are presented for illustrating the applicability and ease of understanding.

Comment: Eigenvalue sensitivity method for optimal stabilisation of linear systems

In a letter RauA proposed a new method for designing statefeedback controllers using eigenvalue sensitivity matrices. However, there appears to be a conceptual mistake in the procedure, or else it is unduly restricted in its applicability. In particular the equation — BR~lBTK = A/.I, in which K is a positive-definite symmetric matrix.

D-MG Tradeoff and Optimal Codes for a Class of AF and DF Cooperative Communication Protocols

Cooperative relay communication in a fading channel environment under the orthogonal amplify-and-forward (OAF), nonorthogonal and orthogonal selection decode-and-forward (NSDF and OSDF) protocols is considered here. The diversity-multiplexing gain tradeoff (DMT) of the three protocols is determined and DMT-optimal distributed space-time (ST) code constructions are provided. The codes constructed are sphere decodable and in some instances incur minimum possible delay. Included in our results is the perhaps surprising finding that the orthogonal and the nonorthogonal amplify-and-forward (NAF) protocols have identical DMT when the time durations of the broadcast and cooperative phases are optimally chosen to suit the respective protocol. Moreover our code construction for the OAF protocol incurs less delay. Two variants of the NSDF protocol are considered: fixed-NSDF and variable-NSDF protocol. In the variable-NSDF protocol, the fraction of time occupied by the broadcast phase is allowed to vary with multiplexing gain. The variable-NSDF protocol is shown to improve on the DMT of the best previously known static protocol when the number of relays is greater than two. Also included is a DMT optimal code construction for the NAF protocol.

Learning Optimal Discriminant Functions through a Cooperative Game of Automata

The problem of learning correct decision rules to minimize the probability of misclassification is a long-standing problem of supervised learning in pattern recognition. The problem of learning such optimal discriminant functions is considered for the class of problems where the statistical properties of the pattern classes are completely unknown. The problem is posed as a game with common payoff played by a team of mutually cooperating learning automata. This essentially results in a probabilistic search through the space of classifiers. The approach is inherently capable of learning discriminant functions that are nonlinear in their parameters also. A learning algorithm is presented for the team and convergence is established. It is proved that the team can obtain the optimal classifier to an arbitrary approximation. Simulation results with a few examples are presented where the team learns the optimal classifier.

An Optimal g-Guidance Scheme for Satellite Launch Vehicles

A closed-loop steering logic based on an optimal (2-guidance is developed here. The guidance system drives the satellite launch vehicle along a two- or three- dimensional trajectory for placing the payload into a specified circular orbit. The modified g-guidance algorithm makes use of the optimal required velocity vector, which minimizes the total impulse needed for an equivalent two-impluse transfer from the present state to the final orbit. The required velocity vector is defined as velocity of the vehicle on the hypothetical transfer orbit immediately after the application of the first impulse. For this optimal transfer orbit, a simple and elegant expression for the Q-matrix is derived. A working principle for the guidance algorithm in terms of the major and minor cycles, and also for the generation of the steering command, is outlined.