Continuous state-space Markov Decision Processes (MDPs) are notoriously difficult to solve.

We present a novel message passing algorithm for approximating the MAP problem in graphical models. The algorithm is similar in structure to max-product but unlike max-product it always converges, and can be proven to find the exact MAP solution in various settings. The algorithm is derived via block coordinate descent in a dual of the LP relaxation of MAP, but does not require any tunable parameters such as step size or tree weights. We also describe a generalization of the method to cluster based potentials. The new method is tested on synthetic and real-world problems, and compares favorably with previous approaches.

The classical hypothesis, that bottom-up saliency is a center-surround process, is combined with a more recent hypothesis that all saliency decisions are optimal in a decision-theoretic sense. The combined hypothesis is denoted as discriminant center-surround saliency, and the corresponding optimal saliency architecture is derived. This architecture equates the saliency of each image location to the discriminant power of a set of features with respect to the classification problem that opposes stimuli at center and surround, at that location. It is shown that the resulting saliency detector makes accurate quantitative predictions for various aspects of the psychophysics of human saliency, including non-linear properties beyond the reach of previous saliency models. Furthermore, it is shown that discriminant center-surround saliency can be easily generalized to various stimulus modalities (such as color, orientation and motion), and provides optimal solutions for many other saliency problems of interest for computer vision. Optimal solutions, under this hypothesis, are derived for a number of the former (including static natural images, dense motion fields, and even dynamic textures), and applied to a number of the latter (the prediction of human eye fixations, motion-based saliency in the presence of ego-motion, and motion-based saliency in the presence of highly dynamic backgrounds). In result, discriminant saliency is shown to predict eye fixations better than previous models, and produce background subtraction algorithms that outperform the state-of-the-art in computer vision.

Using multiple regularization hyperparameters is an effective method for managing model complexity in problems where input features have varying amounts of noise. While algorithms for choosing multiple hyperparameters are often used in neural networks and support vector machines, they are not common in structured prediction tasks, such as sequence labeling or parsing. In this paper, we consider the problem of learning regularization hyperparameters for log-linear models, a class of probabilistic models for structured prediction tasks which includes conditional random fields (CRFs). Using an implicit differentiation trick, we derive an efficient gradient-based method for learning Gaussian regularization priors with multiple hyperparameters. In both simulations and the real-world task of computational RNA secondary structure prediction, we find that multiple hyperparameter learning provides a significant boost in accuracy compared to models learned using only a single regularization hyperparameter.

We present sharp rates of convergence (with respect to additive regret) for both the full information setting (where the cost function is revealed at the end of each round) and the bandit setting (where only the scalar cost incurred is revealed). In particular, this paper is concerned with the price of bandit information, by which we mean the ratio of the best achievable regret in the bandit setting to that in the full-information setting.

Experiments on a collected data have demonstrated the merits of our approach.

We present four new reinforcement learning algorithms based on actor-critic and natural-gradient ideas, and provide their convergence proofs. Actor-critic reinforcement learningmethods are online approximations to policy iteration in which the value-function parameters are estimated using temporal difference learning and the policy parameters are updated by stochastic gradient descent. Methods based on policy gradients in this way are of special interest because of their compatibility withfunction approximation methods, which are needed to handle large or infinite state spaces. The use of temporal difference learning in this way is of interest because in many applications it dramatically reduces the variance of the gradient estimates. The use of the natural gradient is of interest because it can produce better conditioned parameterizations and has been shown to further reduce variancein some cases. Our results extend prior two-timescale convergence results for actor-critic methods by Konda and Tsitsiklis by using temporal difference learningin the actor and by incorporating natural gradients, and they extend prior empirical studies of natural actor-critic methods by Peters, Vijayakumar and Schaal by providing the first convergence proofs and the first fully incremental algorithms.

Maximum entropy analysis of binary variables provides an elegant way for studying therole of pairwise correlations in neural populations. Unfortunately, these approaches suffer from their poor scalability to high dimensions. In sensory coding, however,high-dimensional data is ubiquitous. Here, we introduce a new approach using a near-maximum entropy model, that makes this type of analysis feasiblefor very high-dimensional data--the model parameters can be derived in closed form and sampling is easy. Therefore, our NearMaxEnt approach can serve as a tool for testing predictions from a pairwise maximum entropy model not only for low-dimensional marginals, but also for high dimensional measurements of more than thousand units. We demonstrate its usefulness by studying natural images with dichotomized pixel intensities. Our results indicate that the statistics of such higher-dimensional measurements exhibit additional structure that are not predicted by pairwise correlations, despite the fact that pairwise correlations explain thelower-dimensional marginal statistics surprisingly well up to the limit of dimensionality where estimation of the full joint distribution is feasible.

Computational models of visual cortex, and in particular those based on sparse coding, have enjoyed much recent attention. Despite this currency, the question of how sparse or how over-complete a sparse representation should be, has gone without principled answer. Here, we use Bayesian model-selection methods to address these questions for a sparse-coding model based on a Student-t prior. Having validated our methods on toy data, we find that natural images are indeed best modelled by extremely sparse distributions; although for the Student-t prior, the associated optimal basis size is only modestly overcomplete.

Recent experimental studies have focused on the specialization of different neural structures for different types of instrumental behavior. Recent theoretical work has provided normative accounts for why there should be more than one control system, and how the output of different controllers can be integrated. Two particlar controllershave been identified, one associated with a forward model and the prefrontal cortex and a second associated with computationally simpler, habitual, actor-criticmethods and part of the striatum. We argue here for the normative appropriateness of an additional, but so far marginalized control system, associated withepisodic memory, and involving the hippocampus and medial temporal cortices. We analyze in depth a class of simple environments to show that episodic control should be useful in a range of cases characterized by complexity and inferential noise,and most particularly at the very early stages of learning, long before habitization has set in. We interpret data on the transfer of control from the hippocampus to the striatum in the light of this hypothesis.