This paper extends our earlier analysis on approximate linear programming asan approach to approximating the cost-to-go function in a discounted-cost dynamic program [6]. In this paper, we consider the average-cost criterion and a version of approximate linear programming that generates approximations to the optimal average cost and differential cost function. We demonstrate that a naive version of approximate linear programming prioritizes approximation of the optimal average cost and that this may not be well-aligned with the objective of deriving a policy with low average cost. For that, the algorithm should aim at producing a good approximation of the differential cost function. We propose a twophase variantof approximate linear programming that allows for external control of the relative accuracy of the approximation of the differential cost function over different portions of the state space via state-relevance weights. Performance bounds suggest that the new algorithm is compatible withthe objective of optimizing performance and provide guidance on appropriate choices for state-relevance weights.

We developed a robust control policy design method in high-dimensional state space by using differential dynamic programming with a minimax criterion. As an example, we applied our method to a simulated five link biped robot. The results show lower joint torques from the optimal control policycompared to a hand-tuned PD servo controller. Results also show that the simulated biped robot can successfully walk with unknown disturbances that cause controllers generated by standard differential dynamic programmingand the hand-tuned PD servo to fail. Learning to compensate for modeling error and previously unknown disturbances in conjunction with robust control design is also demonstrated.

Segmentation and recognition have long been treated as two separate processes. Wepropose a mechanism based on spectral graph partitioning that readily combine the two processes into one. A part-based recognition systemdetects object patches, supplies their partial segmentations as well as knowledge about the spatial configurations of the object. The goal of patch grouping is to find a set of patches that conform best to the object configuration, while the goal of pixel grouping is to find a set of pixels that have the best low-level feature similarity. Through pixel-patch interactions andbetween-patch competition encoded in the solution space, these two processes are realized in one joint optimization problem. The globally optimal partition is obtained by solving a constrained eigenvalue problem. We demonstrate that the resulting object segmentation eliminates falsepositives for the part detection, while overcoming occlusion and weak contours for the low-level edge detection.

In this paper we consider formulations of multi-class problems based on a generalized notion of a margin and using output coding. This includes, but is not restricted to, standard multi-class SVM formulations. Differently frommany previous approaches we learn the code as well as the embedding function. We illustrate how this can lead to a formulation that allows for solving a wider range of problems with for instance many classes or even "missing classes". To keep our optimization problems tractable we propose an algorithm capable of solving them using twoclass classifiers,similar in spirit to Boosting.

We investigate data based procedures for selecting the kernel when learning withSupport Vector Machines. We provide generalization error bounds by estimating the Rademacher complexities of the corresponding function classes. In particular we obtain a complexity bound for function classes induced by kernels with given eigenvectors, i.e., we allow to vary the spectrum and keep the eigenvectors fix. This bound is only a logarithmic factorbigger than the complexity of the function class induced by a single kernel. However, optimizing the margin over such classes leads to overfitting. We thus propose a suitable way of constraining the class. We use an efficient algorithm to solve the resulting optimization problem, present preliminary experimental results, and compare them to an alignment-based approach.

An essential step in understanding the function of sensory nervous systems isto characterize as accurately as possible the stimulus-response function (SRF) of the neurons that relay and process sensory information. Oneincreasingly common experimental approach is to present a rapidly varying complex stimulus to the animal while recording the responses ofone or more neurons, and then to directly estimate a functional transformation of the input that accounts for the neuronal firing. The estimation techniques usually employed, such as Wiener filtering or other correlation-based estimation of the Wiener or Volterra kernels, are equivalent to maximum likelihood estimation in a Gaussian-output-noise regression model. We explore the use of Bayesian evidence-optimization techniques to condition these estimates. We show that by learning hyperparameters thatcontrol the smoothness and sparsity of the transfer function it is possible to improve dramatically the quality of SRF estimates, as measured by their success in predicting responses to novel input.

This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This representation often allows an exponential reduction in the representation size of structured MDPs, but the complexity of exact solution algorithms for such MDPs can grow exponentially in the representation size. In this paper, we present two approximate solution algorithms that exploit structure in factored MDPs. Both use an approximate value function represented as a linear combination of basis functions, where each basis function involves only a small subset of the domain variables. A key contribution of this paper is that it shows how the basic operations of both algorithms can be performed efficiently in closed form, by exploiting both additive and context-specific structure in a factored MDP. A central element of our algorithms is a novel linear program decomposition technique, analogous to variable elimination in Bayesian networks, which reduces an exponentially large LP to a provably equivalent, polynomial-sized one. One algorithm uses approximate linear programming, and the second approximate dynamic programming. Our dynamic programming algorithm is novel in that it uses an approximation based on max-norm, a technique that more directly minimizes the terms that appear in error bounds for approximate MDP algorithms. We provide experimental results on problems with over 10^40 states, demonstrating a promising indication of the scalability of our approach, and compare our algorithm to an existing state-of-the-art approach, showing, in some problems, exponential gains in computation time.

This paper presents an evolutionary algorithm with a new goal-sequence domination scheme for better decision support in multi-objective optimization. The approach allows the inclusion of advanced hard/soft priority and constraint information on each objective component, and is capable of incorporating multiple specifications with overlapping or non-overlapping objective functions via logical "OR" and "AND" connectives to drive the search towards multiple regions of trade-off. In addition, we propose a dynamic sharing scheme that is simple and adaptively estimated according to the on-line population distribution without needing any a priori parameter setting. Each feature in the proposed algorithm is examined to show its respective contribution, and the performance of the algorithm is compared with other evolutionary optimization methods. It is shown that the proposed algorithm has performed well in the diversity of evolutionary search and uniform distribution of non-dominated individuals along the final trade-offs, without significant computational effort. The algorithm is also applied to the design optimization of a practical servo control system for hard disk drives with a single voice-coil-motor actuator. Results of the evolutionary designed servo control system show a superior closed-loop performance compared to classical PID or RPT approaches.

We propose a framework based on a parametric quadratic programming (QP) technique to solve the support vector machine (SVM) training problem. This framework, can be specialized to obtain two SVM optimization methods. The first solves the fixed bias problem, while the second starts with an optimal solution for a fixed bias problem and adjusts the bias until the optimal value is found. The later method can be applied in conjunction with any other existing technique which obtains a fixed bias solution. Moreover, the second method can also be used independently to solve the complete SVM training problem. A combination of these two methods is more flexible than each individual method and, among other things, produces an incremental algorithm which exactly solve the 1-Norm Soft Margin SVM optimization problem. Applying Selective Sampling techniques may further boost convergence.

The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of large-scale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. Theapproach "fits" a linear combination of pre-selected basis functions to the dynamic programming cost-to- go function. We develop bounds on the approximation error and present experimental resultsin the domain of queueing network control, providing empirical support for the methodology.