risk sensitive and risk neutral multiarmed bandits for the multiarmed bandit the classic result is probabilistic each state of each bandit markov chain with rewards has an index that is determined by an optimal stopping time for that state s bandit and expected discounted income is maximized by playing at each epoch a bandit whose current state has the largest index our approach is analytic not probabilistic it uses pairwise comparison in place of stopping times a simple recursion assigns to each state of each bandit a utility and an amplification of future utility that depend solely on the data for that state s bandit these utilities and amplifications determine whether or not one state dominates another we show that it is optimal to play at each epoch any bandit whose current state is not dominated by the current states of the other bandits we obtain this result by a coherent analysis that encompasses three models one with risk averse exponential utility one with risk seeking exponential utility and one with linear utility and either stopping or discounting we also show that the risk seeking case and a model of nash nash p 1980 a generalized bandit problem j roy statist soc b42 165 169 are equivalent to each other

finite growth representations of conformal lie algebras that contain a virasoro subalgebra in the present paper we classify all finite growth representations of all infinite rank conformal subalgebras of gcn that contain a virasoro subalgebra

transformation groups for soliton equations iv a new hierarchy of soliton equations of kp type abstract a new approach to soliton equations based on functions or hirota s dependent variables vertex operators and the clifford algebra of free fermions is applied to study a new hierarchy of kadomtsev petviashvili type equations the bkp hierarchy the infinite dimensional orthogonal group acts on the space of bkp functions the sawada kotera equation is obtained as a reduction of bkp its infinitesimal transformations constitute the euclidean lie algebra a2 2

robust mean field linear quadratic gaussian games with unknown l 2 disturbance this paper considers a class of mean field linear quadratic gaussian games with model uncertainty the drift term in the dynamics of the agents contains a common unknown function we take a robust

on actor critic algorithms in this article we propose and analyze a class of actor critic algorithms these are two time scale algorithms in which the critic uses temporal difference learning with a linearly parameterized approximation architecture and the actor is updated in an approximate gradient direction based on information provided by the critic we show that the features for the critic should ideally span a subspace prescribed by the choice of parameterization of the actor we study actor critic algorithms for markov decision processes with polish state and action spaces we state and prove two results regarding their convergence

discounted robust stochastic games and an application to queueing control this paper presents a robust optimization model for n person finite state action stochastic games with incomplete information we consider nonzero sum discounted stochastic games in which none of the players knows the true data of a game and each player adopts a robust optimization approach to address the uncertainty we call these games discounted robust stochastic games such games allow us to use simple uncertainty sets for the unknown data and eliminate the need to have an a priori probability distribution over a set of games we prove the existence of equilibrium points and propose an explicit mathematical programming formulation for an equilibrium calculation we illustrate the use of discounted robust stochastic games in a single server queueing control problem

index policies for stochastic search in a forest with an application to r d project management this paper concerns a stochastic search problem in a forest as motivation consider the issue of investing in a research and development project each activity that could be undertaken in the project is represented as an edge in a forest each edge has a cost of being attempted and a probability of success an edge can be attempted if each of its predecessors has been attempted and if each of those attempts has succeeded the overall project succeeds if a path is found from a stem to a leaf of the forest all of whose edges are successful overall success yields an economic benefit the problem is to find an investment strategy that maximizes expected utility either with a linear or an exponential utility function this problem will be shown to have a simple solution each edge will be assigned an index such that expected utility is maximized by attempting at each opportunity an edge whose index is most positive terminating the search when no edges remain whose indices are positive these indices are nested in a way that makes them quick to compute

spin and wedge representations of infinite dimensional lie algebras and groups abstract we suggest a purely algebraic construction of the spin representation of an infinite dimensional orthogonal lie algebra sections 1 and 2 and a corresponding group section 4 from this we deduce a construction of all level one highest weight representations of orthogonal affine lie algebras in terms of creation and annihilation operators on an infinite dimensional grassmann algebra section 3 we also give a similar construction of the level one representations of the general linear affine lie algebra in an infinite dimensional wedge space along these lines we construct the corresponding representations of the universal central extension of the group sln k t t 1 in spaces of sections of line bundles over infinite dimensional homogeneous spaces section 5

on the classification of subalgebras of cendn and gcn the problem of classification of infinite subalgebras of cendn and of gcn that acts irreducibly on c n is discussed in this paper

constrained clustering as an optimization method a deterministic annealing approach to clustering is derived on the basis of the principle of maximum entropy this approach is independent of the initial state and produces natural hierarchical clustering solutions by going through a sequence of phase transitions it is modified for a larger class of optimization problems by adding constraints to the free energy the concept of constrained clustering is explained and three examples are are given in which it is used to introduce deterministic annealing the previous clustering method is improved by adding cluster mass variables and a total mass constraint the traveling salesman problem is reformulated as constrained clustering yielding the elastic net en approach to the problem more insight is gained by identifying a second lagrange multiplier that is related to the tour length and can also be used to control the annealing process the open path constraint formulation is shown to relate to dimensionality reduction by self organization in unsupervised learning a similar annealing procedure is applicable in this case as well

representations of a symplectic type subalgebra of w n in this paper we classify the irreducible quasifinite highest weight modules over the symplectic type lie subalgebra of the lie algebra of all regular differential operators on circle that kill constants we also realize them in terms of the representations theory of the complex lie algebra gl m of infinite matrices with a finite number of non zero diagonals with entries in the algebra of truncated polynomials and the corresponding subalgebras of type c

structural properties of optimal transmission policies over a randomly varying channel we consider the problem of transmitting packets over a randomly varying point to point channel with the objective of minimizing the expected power consumption subject to a constraint on the average packet delay by casting it as a constrained markov decision process in discrete time with time averaged costs we prove structural results about the dependence of the optimal policy on buffer occupancy number of packet arrivals in the previous slot and the channel fading state for both i i d and markov arrivals and channel fading the techniques we use to establish such results convexity stochastic dominance decreasing differences are among the standard ones for the purpose our main contribution however is the passage to the average cost case a notoriously difficult problem for which rather limited results are available the novel proof techniques used here are likely to have utility in other stochastic control problems well beyond their immediate application considered here

the price of robustness a robust approach to solving linear optimization problems with uncertain data was proposed in the early 1970s and has recently been extensively studied and extended under this approach we are willing to accept a suboptimal solution for the nominal values of the data in order to ensure that the solution remains feasible and near optimal when the data changes a concern with such an approach is that it might be too conservative in this paper we propose an approach that attempts to make this trade off more attractive that is we investigate ways to decrease what we call the price of robustness in particular we flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations an attractive aspect of our method is that the new robust formulation is also a linear optimization problem thus we naturally extend our methods to discrete optimization problems in a tractable way we report numerical results for a portfolio optimization problem a knapsack problem and a problem from the net lib library

robust control of markov decision processes with uncertain transition matrices optimal solutions to markov decision problems may be very sensitive with respect to the state transition probabilities in many practical problems the estimation of these probabilities is far from accurate hence estimation errors are limiting factors in applying markov decision processes to real world problems we consider a robust control problem for a finite state finite action markov decision process where uncertainty on the transition matrices is described in terms of possibly nonconvex sets we show that perfect duality holds for this problem and that as a consequence it can be solved with a variant of the classical dynamic programming algorithm the robust dynamic programming algorithm we show that a particular choice of the uncertainty sets involving likelihood regions or entropy bounds leads to both a statistically accurate representation of uncertainty and a complexity of the robust recursion that is almost the same as that of the classical recursion hence robustness can be added at practically no extra computing cost we derive similar results for other uncertainty sets including one with a finite number of possible values for the transition matrices we describe in a practical path planning example the benefits of using a robust strategy instead of the classical optimal strategy even if the uncertainty level is only crudely guessed the robust strategy yields a much better worst case expected travel time

robust dynamic programming in this paper we propose a robust formulation for discrete time dynamic programming dp the objective of the robust formulation is to systematically mitigate the sensitivity of the dp optimal policy to ambiguity in the underlying transition probabilities the ambiguity is modeled by associating a set of conditional measures with each state action pair consequently in the robust formulation each policy has a set of measures associated with it we prove that when this set of measures has a certain rectangularity property all of the main results for finite and infinite horizon dp extend to natural robust counterparts we discuss techniques from nilim and el ghaoui 17 for constructing suitable sets of conditional measures that allow one to efficiently solve for the optimal robust policy we also show that robust dp is equivalent to stochastic zero sum games with perfect information

finite growth representations of infinite lie conformal algebras we classify all finite growth representations of all infinite rank subalgebras of the lie conformal algebra gc1 that contain a virasoro subalgebra

stochastic scheduling with release dates and due dates we consider stochastic scheduling problems in which the processing times of jobs are independent exponentially distributed random variables the release dates are random variables with an arbitrary joint distribution and the due dates are random variables with a joint distribution that satisfies certain conditions our development establishes simple policies that minimize such criteria as the expected weighted sum of completion times and the expected weighted number of late jobs these results contrast markedly with the deterministic counterparts of these models for which no polynomial time algorithms are known

qhwm of the orthogonal type lie subalgebra of the lie algebra of matrix differential operators on the circle in this paper we classify the irreducible quasifinite highest weight modules of the orthogonal lie subalgebra of the lie algebra of matrix differential operators on the circle we also realize them in terms of the representation theory of the complex lie algebra gl m of infinite matrices with a finite number of nonzero diagonals with entries in the algebra of truncated polynomials and the corresponding subalgebras of type b and d

quasifinite highest weight modules over the lie algebra of matrix differential operators on the circle we classify positive energy representations with finite degeneracies of the lie algebraw1 and construct them in terms of representation theory of the lie algebra hat gl infty r m of infinites matrices with finite number of non zero diagonals over the algebrar m t tm 1 the unitary ones are classified as well similar results are obtained for the sin algebras

robust convex optimization we study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set u yet the constraints must hold for all possible values of the data from u the ensuing optimization problem is called robust optimization in this paper we lay the foundation of robust convex optimization in the main part of the paper we show that if u is an ellipsoidal uncertainty set then for some of the most important generic convex optimization problems linear programming quadratically constrained programming semidefinite programming and others the corresponding robust convex program is either exactly or approximately a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods

on optimal policies for production inventory systems with compound poisson demand and setup costs in this paper we consider a single item one machine production inventory system with compound poisson demand the production facility may be on or off while on the production rate is constant and while off the production rate is zero system costs consist of switching costs and inventory and backlogging costs we provide conditions when s s policies are optimal under the long run average expected cost criterion these conditions are met in particular but not necessarily when the inventory costs are convex the developed method in the proof is easy to apply to more general cases moreover the method allows us to compute optimal policies very efficiently

robust game theory we present a distribution free model of incomplete information games both with and without private information in which the players use a robust optimization approach to contend with payoff uncertainty our robust game model relaxes the assumptions of harsanyi s bayesian game model and provides an alternative distribution free equilibrium concept which we call robust optimization equilibrium to that of the ex post equilibrium we prove that the robust optimization equilibria of an incomplete information game subsume the ex post equilibria of the game and are unlike the latter guaranteed to exist when the game is finite and has bounded payoff uncertainty set for arbitrary robust finite games with bounded polyhedral payoff uncertainty sets we show that we can compute a robust optimization equilibrium by methods analogous to those for identifying a nash equilibrium of a finite game with complete information in addition we present computational results

optimal linear representations of images for object recognition although linear representations are frequently used in image analysis their performances are seldom optimal in specific applications this paper proposes a stochastic gradient algorithm for finding optimal linear representations of images for use in appearance based object recognition using the nearest neighbor classifier a recognition performance function is specified and linear representations that maximize this performance are sought for solving this optimization problem on a grassmann manifold a stochastic gradient algorithm utilizing intrinsic flows is introduced several experimental results are presented to demonstrate this algorithm

stochastic games with a single controller and incomplete information we study stochastic games with incomplete information on one side in which the transition is controlled by one of the players we prove that if the informed player also controls the transitions the game has a value whereas if the uninformed player controls the transitions the max min value as well as the min max value exist but they may differ we discuss the structure of the optimal strategies and provide extensions to the case of incom plete information on both sides

a fast fixed point algorithm for independent component analysis we introduce a novel fast algorithm for independent component analysis which can be used for blind source separation and feature extraction we show how a neural network learning rule can be transformed into a fixedpoint iteration which provides an algorithm that is very simple does not depend on any user defined parameters and is fast to converge to the most accurate solution allowed by the data the algorithm finds one at a time all nongaussian independent components regardless of their probability distributions the computations can be performed in either batch mode or a semiadaptive manner the convergence of the algorithm is rigorously proved and the convergence speed is shown to be cubic some comparisons to gradient based algorithms are made showing that the new algorithm is usually 10 to 100 times faster sometimes giving the solution in just a few iterations

forward recursion for markov decision processes with skip free to the right transitions part i theory and algorithm we consider a markovian decision process with countable state space states 0 1 2 which is skip free to the right a transition from i to j is impossible if j i 1 in this type of system it is easy to calculate by forward recursion the maximal total expected reward going from state 0 to state i the same can be done of course for the case where a constant g is subtracted from the one period reward function g revised reward let wgi be the maximal total expected g revised reward going from state 0 to state i we show that wg satisfies the average reward optimality equation if wg satisfies a growth condition then g g the maximal average reward for all other g the function wg increases or decreases so fast that this cannot be the case thus in principle the solution wg can be used to check if g g which suggests a method for approximating g and an associated average return optimal policy we develop an efficient algorithm based on this idea in a companion paper we shall show how the algorithm or modifications of it can be applied to some special cases such as control of arrivals to a queue control of the service rate and controlled random walks

an information theoretic approach to spectral variability similarity and discrimination for hyperspectral image analysis a hyperspectral image can be considered as an image cube where the third dimension is the spectral domain represented by hundreds of spectral wavelengths as a result a hyperspectral image pixel is actually a column vector with dimension equal to the number of spectral bands and contains valuable spectral information that can be used to account for pixel variability similarity and discrimination we present a new hyperspectral measure the spectral information measure sim to describe spectral variability and two criteria spectral information divergence and spectral discriminatory probability for spectral similarity and discrimination respectively the spectral information measure is an information theoretic measure which treats each pixel as a random variable using its spectral signature histogram as the desired probability distribution spectral information divergence sid compares the similarity between two pixels by measuring the probabilistic discrepancy between two corresponding spectral signatures the spectral discriminatory probability calculates spectral probabilities of a spectral database library relative to a pixel to be identified so as to achieve material identification in order to compare the discriminatory power of one spectral measure relative to another a criterion is also introduced for performance evaluation which is based on the power of discriminating one pixel from another relative to a reference pixel the experimental results demonstrate that the new hyperspectral measure can characterize spectral variability more effectively than the commonly used spectral angle mapper sam

communication over fading channels with delay constraints we consider a user communicating over a fading channel with perfect channel state information data are assumed to arrive from some higher layer application and are stored in a buffer until transmitted we study adapting the user s transmission rate and power based on the channel state information as well as the buffer occupancy the objectives are to regulate both the long term average transmission power and the average buffer delay incurred by the traffic two models for this situation are discussed one corresponding to fixed length variable rate codewords and one corresponding to variable length codewords the tradeoff between the average delay and the average transmission power required for reliable communication is analyzed a dynamic programming formulation is given to find all pareto optimal power delay operating points we then quantify the behavior of this tradeoff in the regime of asymptotically large delay in this regime we characterize simple buffer control policies which exhibit optimal characteristics connections to the delay limited capacity and the expected capacity of fading channels are also discussed

asymptotic bounds on the power delay tradeoff for fading point to point links from geometric bounds on the stationary distribution of the queue length the optimal power delay tradeoff is studied for a time slotted independently and identically distributed fading point to point link with perfect channel state information at both transmitter and receiver and with random packet arrivals to the transmitter queue it is assumed that the transmitter can control the number of packets served by controlling the transmit power in the slot the optimal tradeoff between average power and average delay is analyzed for stationary and monotone transmitter policies for such policies an asymptotic lower bound on the minimum average delay of the packets is obtained when average transmitter power approaches the minimum average power required for transmitter queue stability the asymptotic lower bound on the minimum average delay is obtained from geometric upper bounds on the stationary distribution of the queue length this approach which uses geometric upper bounds also leads to an intuitive explanation of the asymptotic behavior of average delay the asymptotic lower bounds along with previously known asymptotic upper bounds are used to identify three new cases where the order of the asymptotic behavior differs from that obtained from a previously considered approximate model in which the transmit power is a strictly convex function of real valued service batch size for every fade state

fuzzy wavelet polynomial neural networks analysis and design in this study we propose a concept of fuzzy wavelet polynomial neural networks fwpnns based on concepts and constructs of polynomial neural networks and fuzzy wavelet neurons fwns these networks exhibit a rule based architecture while each rule in the fwn consists of the premise part and consequence part the premise part is realized by using c means clustering method while the consequence part is realized by means of wavelet functions whose parameters are estimated with the aid of the least square method in some sense the fwpnn can be regarded as a generalized fuzzy wavelet neural network fwnn unlike gaussian membership functions that are commonly utilized to implement the premise part of the rules in typical fwnns c means method is employed here to overcome a possible curse of dimensionality polynomial neural networks pnns are used to express the nonlinearity of a complex system furthermore the particle swarm optimization is used to optimize the design parameters of the proposed network based on the pnns and fwnns the proposed fwpnns take advantages of these two neural networks it exhibits the abilities to describe high order nonlinear relations between input and output variables and it is beneficial to describe models impacted by uncertainty the proposed fwpnns are applied for time series prediction and regression problems e g control of dynamic plants several well known modeling benchmarks including regression and time series are considered to evaluate the performance of the proposed fwpnns a comparative analysis shows that the proposed fwpnns result in better performance when comparing with some previous models reported in the literature

fast and robust fixed point algorithms for independent component analysis independent component analysis ica is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible we use a combination of two different approaches for linear ica comon s information theoretic approach and the projection pursuit approach using maximum entropy approximations of differential entropy we introduce a family of new contrast functions for ica these contrast functions enable both the estimation of the whole decomposition by minimizing mutual information and estimation of individual independent components as projection pursuit directions the statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model and it is shown how to choose contrast functions that are robust and or of minimum variance finally we introduce simple fixed point algorithms for practical optimization of the contrast functions

accurate estimation of ica weight matrix by implicit constraint imposition using lie group this paper presents a new stochastic algorithm to optimize the independence criterion mutual information among multivariate data using local global and hybrid optimizers in conjunction with techniques involving a lie group and its corresponding lie algebra for implicit imposition of the orthonormality constraint among the estimated sources the major advantage of the proposed algorithm is the increased accuracy with which the weight matrix in the independent component analysis ica model is estimated compared to conventional schemes when the local optimizer with lie group techniques and the fast fixed point fastica algorithm were experimented by inputting the same set of random vectors the former method superseded the conventional one by producing accurate weight matrix estimates in a majority of the test cases importantly in our approach the use of a lie group to ldquolockrdquo the weight matrix estimates onto the constraint surface enabled easy realization of the hybrid optimizers to yield near global optimum solutions consistently in most of the test cases compared to well known global optimizers the inherent computational overhead in the hybrid optimizers was lowered by preprocessing the input data and periodically integrating the local optimizers with the global one the proposed algorithms were applied to six dimensional multispectral satellite image data to emphasize their usefulness in terms of accurate ica weight matrix estimation

zeta values and differential operators on the circle abstract the fock representation of the virasoro lie algebra is extended to a larger graded lie subalgebra of the algebra of differential operators on the circle the central cocycle is related to values of the riemann zeta function at odd negative integers the corresponding generating function is related to eisenstein series for sl 2 z an analogous result is obtained for values of l series associated to even dirichlet characters using differential operators of infinite order

markov decision processes with imprecise transition probabilities we present new numerical algorithms and bounds for the infinite horizon discrete stage finite state and action markov decision process with imprecise transition probabilities we assume that the transition probability mass vector for each state and action is described by a finite number of linear inequalities this model of imprecision appears to be well suited for describing statistically determined confidence limits and or natural language statements of likelihood the numerical procedures for calculating an optimal max min strategy are based on successive approximations reward revision and modified policy iteration the bounds that are determined are at least as tight as currently available bounds for the case where the transition probabilities are precise

games with incomplete information played by bayesian players i iii this article originally appeared in management science november 1967 volume 14 number 3 pp 159 182 published by the institute of management sciences the paper develops a new theory for the analysis of games with incomplete information where the players are uncertain about some important parameters of the game situation such as the payoff functions the strategies available to various players the information other players have about the game etc however each player has a subjective probability distribution over the alternative possibilities in most of the paper it is assumed that these probability distributions entertained by the different players are mutually consistent in the sense that they can be regarded as conditional probability distributions derived from a certain basic probability distribution over the parameters unknown to the various players but later the theory is extended also to cases where the different players subjective probability distributions fail to satisfy this consistency assumption in cases where the consistency assumption holds the original game can be replaced by a game where nature first conducts a lottery in accordance with the basic probability distribution and the outcome of this lottery will decide which particular subgame will be played i e what the actual values of the relevant parameters will be in the game yet each player will receive only partial information about the outcome of the lottery and about the values of these parameters however every player will know the basic probability distribution governing the lottery thus technically the resulting game will be a game with complete information it is called the bayes equivalent of the original game part i of the paper describes the basic model and discusses various intuitive interpretations for the latter part ii shows that the nash equilibrium points of the bayes equivalent game yield bayesian equilibrium points for the original game finally part iii considers the main properties of the basic probability distribution

bounded parameter markov decision process in this paper we introduce the notion of a em bounded parameter markov decision process as a generalization of the traditional em exact mdp a bounded parameter mdp is a set of exact mdps specified by giving upper and lower bounds on transition probabilities and rewards all the mdps in the set share the same state and action space bounded parameter mdps can be used to represent variation or uncertainty concerning the parameters of sequential decision problems bounded parameter mdps can also be used in aggregation schemes to represent the variation in the transition probabilities for different base states aggregated together in the same aggregate state we introduce em interval value functions as a natural extension of traditional value functions an interval value function assigns a closed real interval to each state representing the assertion that the value of that state falls within that interval an interval value function can be used to bound the performance of a policy over the set of exact mdps associated with a given bounded parameter mdp we describe an iterative dynamic programming algorithm called em interval policy evaluation which computes an interval value function for a given bounded parameter mdp and specified policy interval policy evaluation on a policy policy computes the most restrictive interval value function that is sound i e that bounds the value function for policy in every exact mdp in the set defined by the bounded parameter mdp a simple modification of interval policy evaluation results in a variant of value iteration bellman57 that we call em interval value iteration which computes a policy for an bounded parameter mdp that is optimal in a well defined sense

approximation algorithms for restless bandit problems the restless bandit problem is one of the most well studied generalizations of the celebrated stochastic multi armed bandit mab problem in decision theory in its ultimate generality the restless bandit problem is known to be pspace hard to approximate to any nontrivial factor and little progress has been made on this problem despite its significance in modeling activity allocation under uncertainty in this article we consider the feedback mab problem where the reward obtained by playing each of n independent arms varies according to an underlying on off markov process whose exact state is only revealed when the arm is played the goal is to design a policy for playing the arms in order to maximize the infinite horizon time average expected reward this problem is also an instance of a partially observable markov decision process pomdp and is widely studied in wireless scheduling and unmanned aerial vehicle uav routing unlike the stochastic mab problem the feedback mab problem does not admit to greedy index based optimal policies we develop a novel duality based algorithmic technique that yields a surprisingly simple and intuitive 2 approximate greedy policy to this problem we show that both in terms of approximation factor and computational efficiency our policy is closely related to the whittle index which is widely used for its simplicity and efficiency of computation subsequently we define a multi state generalization that we term monotone bandits which remains subclass of the restless bandit problem we show that our policy remains a 2 approximation in this setting and further our technique is robust enough to incorporate various side constraints such as blocking plays switching costs and even models where determining the state of an arm is a separate operation from playing it our technique is also of independent interest for other restless bandit problems and we provide an example in nonpreemptive machine replenishment interestingly in this case our policy provides a constant factor guarantee whereas the whittle index is provably polynomially worse by presenting the first o 1 approximations for nontrivial instances of restless bandits as well as of pomdps our work initiates the study of approximation algorithms in both these contexts

descent algorithms on oblique manifold for source adaptive ica contrast a riemannian manifold optimization strategy is proposed to facilitate the relaxation of the orthonormality constraint in a more natural way in the course of performing independent component analysis ica that employs a mutual information based source adaptive contrast function despite the extensive development of manifold techniques catering to the orthonormality constraint only a limited number of works have been dedicated to oblique manifold ob algorithms to intrinsically handle the normality constraint which has been empirically shown to be superior to other riemannian and euclidean approaches imposing the normality constraint implicitly in line with the ica definition essentially guarantees a substantial improvement in the solution accuracy by way of increased degrees of freedom while searching for an optimal unmixing ica matrix in contrast with the orthonormality constraint designs of the steepest descent conjugate gradient with hager zhang or a hybrid update parameter quasi newton and cost effective quasi newton methods intended for ob are presented in this paper their performance is validated using natural images and systematically compared with the popular state of the art approaches in order to assess the performance effects of the choice of algorithm and the use of a riemannian rather than euclidean framework we surmount the computational challenge associated with the direct estimation of the source densities using the improved fast gauss transform in the evaluation of the contrast function and its gradient the proposed ob schemes may find applications in the offline image signal analysis wherein on one hand the computational overhead can be tolerated and on the other the solution quality holds paramount interest

character and determinant formulae of quasifinite representation of thew1 algebra we diagonalize the hilbert space of some subclass of the quasifinite module of thew1 algebra states are classified according to their eigenvalues for infinitely many commuting charges and the young diagrams the parameter dependence of their norms is explicitly derived the full character formulae of the degenerate representations are given as summation of the bilinear combinations of the schur polynomials

evaluating strategies for markov decision processes in parallel the authors work on the use of gittins indices in the evaluation of strategies for families of alternative bandit processes has found many applications among these are procedures for sensitivity analysis in stochastic scheduling this theoretical paper aims at developing results which will form the basis of an approach to strategy evaluation for a class of processes of greater complexity these are markov decision processes in parallel satisfying a condition first enunciated by whittle the theory of gittins indices forms the basis of the analysis

index policies and a novel performance space structure for a class of generalised branching bandit problems our object of study is a new class of controlled stochastic systems called generalised branching bandits which include discounted branching bandits and generalised bandit problems as special cases these models allow us to study queueing scheduling and project scheduling problems in which the reward earned from processing a particular job is influenced by other job types present in the system our mode of analysis is the achievable region approach what is novel here is that the full system may be partitioned into two subsystems each of which satisfies its own set of conservation laws and has its own highly structured performance space an optimal policy for the full system is constructed from two sets of gittins indices derived from the conservation laws governing the two subsystems

submodular returns and greedy heuristics for queueing scheduling problems we consider a range of controlled stochastic systems satisfying conservation laws together with a reducibility property that says that appropriate laws continue to hold when access to the system is restricted to a subset of all possible demand job customer types we show that for linear objectives the optimum system wide performance is a nondecreasing submodular or supermodular function of the subset chosen and that these properties are inherited from the geometry of the performance space concerned these results are of considerable interest in their own right but they also motivate the use of greedy heuristics for the solution of a range of job selection and scheduling problems which have hitherto seemed intractable computational experience suggests that such heuristics perform very well

two armed restless bandits with imperfect information stochastic control and indexability we present a two armed bandit model of decision making under uncertainty where the expected return to investing in the risky arm increases when choosing that arm and decreases when choosing the safe arm these dynamics are natural in applications such as human capital development job search and occupational choice using new insights from stochastic control along with a monotonicity condition on the payoff dynamics we show that optimal strategies in our model are stopping rules that can be characterized by an index which formally coincides with gittins index our result implies the indexability of a new class of restless bandit models

quasifinite representations of classical lie subalgebras of w1 we show that there are precisely two up to conjugation anti involutions of the algebra of differential operators on the circle preserving the principal gradation we classify the irreducible quasifinite highest weight representations of the central extension d of the lie subalgebra of this algebra fixed by and find the unitary ones we realize them in terms of highest weight representations of the central extension of the lie algebra of infinite matrices with finitely many non zero diagonals over the algebra c u um 1 and its classical lie subalgebras ofb canddtypes character formulas forpositive primitiverepresentations of d including all the unitary ones are obtained we also realize a class of primitive representations of d in terms of free fields and establish a number of duality results between these primitive representations and finite dimensional irreducible representations of finite dimensional lie groups and supergroups we show that the vacuum modulevcof d carries a vertex algebra structure and establish a relationship betweenvcforc 12z and w algebras

self stabilized gradient algorithms for blind source separation with orthogonality constraints developments in self stabilized algorithms for gradient adaptation of orthonormal matrices have resulted in simple but powerful principal and minor subspace analysis methods we extend these ideas to develop algorithms for instantaneous prewhitened blind separation of homogeneous signal mixtures our algorithms are proven to be self stabilizing to the stiefel manifold of orthonormal matrices such that the rows of the adaptive demixing matrix do not need to be periodically reorthonormalized several algorithm forms are developed including those that are equivariant with respect to the prewhitened mixing matrix simulations verify the excellent numerical properties of the proposed methods for the blind source separation task

subalgebras of w 1 infinity and their quasifinite representations we propose a series of new subalgebras of the w1 infinity algebra parametrized by polynomials p omega and study their quasifinite representations we also investigate the relation between such subalgebras and the gl infinity algebra as an example we investigate the winfinity algebra which corresponds to the case p omega w presenting its free field realizations and kac determinants at lower levels

stochastic scheduling with priority classes we consider controlled stochastic systems in which multiple job types customers projects jobs etc may require processing by one or more servers the job types are all members of priority classes and admissible controls must respect the constraints imposed by these for systems which when unconstrained satisfy generalised conservation laws we obtain the performance space and show that linear objectives are optimised by admissible controls which choose job types within each priority class according to a set of gittins indices various degrees of decomposition of the problem are described and illustrated in the special case of discounted and undiscounted branching bandits the theory is developed further to yield index based suboptimality bounds for general policies

optimal control of two interacting service stations optimal controls described by switching curves in the two dimensional state space are shown to exist for the optimal control of a markov network with two service stations and linear cost the controls govern routing and service priorities finite horizon and long run average cost problems are considered and value iteration is a key tool nonconvex value functions are shown to exist for slightly more general networks nonconvex value functions are also shown to arise for a simple single station control problem in which the instantaneous cost is convex but not monotone nevertheless optimality of threshold policies is established for the single station problem the proof is based on a novel use of stochastic coupling and policy iteration

quasifinite highest weight modules over the lie algebra of differential operators on the circle we classify positive energy representations with finite degeneracies of the lie algebraw 1 and construct them in terms of representation theory of the lie algebra hat gl infty r m of infinites matrices with finite number of non zero diagonals over the algebrar m t t m 1 the unitary ones are classified as well similar results are obtained for the sin algebras

flow control using the theory of zero sum markov games considers the problem of dynamic flow control of arriving packets into an infinite buffer the service rate may depend on the state of the system may change in time and is unknown to the controller the goal of the controller is to design an efficient policy which guarantees the best performance under the worst service conditions the cost is composed of a holding cost a cost of rejecting customers packets and a cost that depends on the quality of the service the problem is studied in the framework of zero sum markov games and a value iteration algorithm is used to solve it it is shown that there exists an optimal stationary policy such that the decisions depend only on the actual number of customers in the queue it is of a threshold type and it uses randomization in at most one state

monotonic and insensitive optimal policies for control of queues with undiscounted costs we consider the problem of controlling the service and or arrival rates in queues with the objective of minimizing the total expected cost to reach state zero we present a unified simple method for proving that an optimal policy is monotonic in the number of customers in the system applications to average cost minimization over an infinite horizon are given both exponential and nonexponential models are considered the essential characteristic is a left skip free transition structure and a nondecreasing not necessarily convex holding cost function some of our results are insensitive to service time distributions