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.

Competition between actions is based on the motivating characteristics of their consequent states in this sense.

It has been noted by several authors that Belief Propagation can can also give impressive results for graphs that are not trees [2]. The Cluster Variation Method (CVM), is a method that has been developed in the physics community for approximate inference in the Ising model [3]. The CVM approximates the joint probability distribution by a number of (overlapping) marginal distributions (clusters). The quality of the approximation is determined by the size and number of clusters. When the clusters consist of only two variables, the method is known as the Bethe approximation.

We combine the replica approach from statistical physics with a variational approach to analyze learning curves analytically. We apply the method to Gaussian process regression. As a main result we derive approximative relations between empirical error measures, the generalization error and the posterior variance.

We present new simulation results, in which a computational model of interacting visual neurons simultaneously predicts the modulation of spatial vision thresholds by focal visual attention, for five dual-task human psychophysics experiments. This new study complements our previous findings that attention activates a winnertake-all competition among early visual neurons within one cortical hypercolumn. This "intensified competition" hypothesis assumed that attention equally affects all neurons, and yielded two singleunit predictions: an increase in gain and a sharpening of tuning with attention. While both effects have been separately observed in electrophysiology, no single-unit study has yet shown them simultaneously. Hence, we here explore whether our model could still predict our data if attention might only modulate neuronal gain, but do so non-uniformly across neurons and tasks. Specifically, we investigate whether modulating the gain of only the neurons that are loudest, best-tuned, or most informative about the stimulus, or of all neurons equally but in a task-dependent manner, may account for the data. We find that none of these hypotheses yields predictions as plausible as the intensified competition hypothesis, hence providing additional support for our original findings.

Assume that we model a complex decision-making problem under uncertainty by a finite MDP. Because of the limited resources used, the parameters of the MDP (transition probabilities and rewards) are uncertain: we assume that we only know a belief state over their possible values. IT we select the most probable values of the parameters, we can build a MDP and solve it to deduce the corresponding optimal policy. However, because of the uncertainty over the true parameters, this policy may not be the one that maximizes the expected cumulative rewards of the true (but partially unknown) decision-making problem. We can nevertheless use sampling techniques to estimate the expected loss of using this policy.

We propose a new approach to reinforcement learning which combines least squares function approximation with policy iteration. Our method is model-free and completely off policy. We are motivated by the least squares temporal difference learning algorithm (LSTD), which is known for its efficient use of sample experiences compared to pure temporal difference algorithms. LSTD is ideal for prediction problems, however it heretofore has not had a straightforward application to control problems. Moreover, approximations learned by LSTD are strongly influenced by the visitation distribution over states.

We provide a natural gradient method that represents the steepest descent direction based on the underlying structure of the parameter space. Although gradient methods cannot make large changes in the values of the parameters, we show that the natural gradient is moving toward choosing a greedy optimal action rather than just a better action. These greedy optimal actions are those that would be chosen under one improvement step of policy iteration with approximate, compatible value functions, as defined by Sutton et al. [9]. We then show drastic performance improvements in simple MDPs and in the more challenging MDP of Tetris. 1 Introduction There has been a growing interest in direct policy-gradient methods for approximate planning in large Markov decision problems (MDPs). Unfortunately, the standard gradient descent rule is noncovariant.

We consider the use of two additive control variate methods to reduce the variance of performance gradient estimates in reinforcement learning problems. The first approach we consider is the baseline method, in which a function of the current state is added to the discounted value estimate. We relate the performance of these methods, which use sample paths, to the variance of estimates based on iid data. We derive the baseline function that minimizes this variance, and we show that the variance for any baseline is the sum of the optimal variance and a weighted squared distance to the optimal baseline. We show that the widely used average discounted value baseline (where the reward is replaced by the difference between the reward and its expectation) is suboptimal.

The first is the widely used optimistic Q-learning, which initializes the Q-values to large initial values and then follows a greedy policy with respect to the Q-values. We show that setting the initial value sufficiently large guarantees the converges to an E optimal policy. The second is a new and novel algorithm incremental Q-learning, which gradually promotes the values of actions that are not taken. We show that incremental Q-learning converges, in the limit, to the optimal policy. Our incremental Q-learning algorithm can be viewed as derandomization of the E-greedy Q-learning. 1 Introduction One of the challenges of Reinforcement Learning is learning in an unknown environment.