There is much evidence that humans and other animals utilize a combination of model-based and model-free RL methods. Although it has been proposed that these systems may dominate according to their relative statistical efficiency in different circumstances, there is little specific evidence -- especially in humans -- as to the details of this trade-off. Accordingly, we examine the relative performance of different RL approaches under situations in which the statistics of reward are differentially noisy and volatile. Using theory and simulation, we show that model-free TD learning is relatively most disadvantaged in cases of high volatility and low noise. We present data from a decision-making experiment manipulating these parameters, showing that humans shift learning strategies in accord with these predictions. The statistical circumstances favoring model-based RL are also those that promote a high learning rate, which helps explain why, in psychology, the distinction between these strategies is traditionally conceived in terms of rule-based vs. incremental learning.

Computing a good strategy in a large extensive form game often demands an extraordinary amount of computer memory, necessitating the use of abstraction to reduce the game size. Typically, strategies from abstract games perform better in the real game as the granularity of abstraction is increased. This paper investigates two techniques for stitching a base strategy in a coarse abstraction of the full game tree, to expert strategies in fine abstractions of smaller subtrees. We provide a general framework for creating static experts, an approach that generalizes some previous strategy stitching efforts. In addition, we show that static experts can create strong agents for both 2-player and 3-player Leduc and Limit Texas Hold'em poker, and that a specific class of static experts can be preferred among a number of alternatives. Furthermore, we describe a poker agent that used static experts and won the 3-player events of the 2010 Annual Computer Poker Competition.

We describe a simple algorithm that runs in time poly(n,1/gamma,1/eps) and learns an unknown n-dimensional gamma-margin halfspace to accuracy 1-eps in the presence of malicious noise, when the noise rate is allowed to be as high as Theta(eps gamma sqrt(log(1/gamma))). Previous efficient algorithms could only learn to accuracy eps in the presence of malicious noise of rate at most Theta(eps gamma). Our algorithm does not work by optimizing a convex loss function. We show that no algorithm for learning gamma-margin halfspaces that minimizes a convex proxy for misclassification error can tolerate malicious noise at a rate greater than Theta(eps gamma); this may partially explain why previous algorithms could not achieve the higher noise tolerance of our new algorithm.

When used to learn high dimensional parametric probabilistic models, the clas- sical maximum likelihood (ML) learning often suffers from computational in- tractability, which motivates the active developments of non-ML learning meth- ods. Yet, because of their divergent motivations and forms, the objective func- tions of many non-ML learning methods are seemingly unrelated, and there lacks a unified framework to understand them. In this work, based on an information geometric view of parametric learning, we introduce a general non-ML learning principle termed as minimum KL contraction, where we seek optimal parameters that minimizes the contraction of the KL divergence between the two distributions after they are transformed with a KL contraction operator. We then show that the objective functions of several important or recently developed non-ML learn- ing methods, including contrastive divergence [12], noise-contrastive estimation [11], partial likelihood [7], non-local contrastive objectives [31], score match- ing [14], pseudo-likelihood [3], maximum conditional likelihood [17], maximum mutual information [2], maximum marginal likelihood [9], and conditional and marginal composite likelihood [24], can be unified under the minimum KL con- traction framework with different choices of the KL contraction operators.

We propose an algorithm called Sparse Manifold Clustering and Embedding (SMCE) for simultaneous clustering and dimensionality reduction of data lying in multiple nonlinear manifolds. Similar to most dimensionality reduction methods, SMCE finds a small neighborhood around each data point and connects each point to its neighbors with appropriate weights. The key difference is that SMCE finds both the neighbors and the weights automatically. This is done by solving a sparse optimization problem, which encourages selecting nearby points that lie in the same manifold and approximately span a low-dimensional affine subspace. The optimal solution encodes information that can be used for clustering and dimensionality reduction using spectral clustering and embedding. Moreover, the size of the optimal neighborhood of a data point, which can be different for different points, provides an estimate of the dimension of the manifold to which the point belongs. Experiments demonstrate that our method can effectively handle multiple manifolds that are very close to each other, manifolds with non-uniform sampling and holes, as well as estimate the intrinsic dimensions of the manifolds.

In this paper we consider general rank minimization problems with rank appearing ineither objective function or constraint. We first show that a class of matrix optimization problems can be solved as lower dimensional vector optimization problems. As a consequence, we establish that a class of rank minimization problems haveclosed form solutions. Using this result, we then propose penalty decomposition methodsfor general rank minimization problems. The convergence results of the PD methods have been shown in the longer version of the paper [19]. Finally, we test the performance of our methods by applying them to matrix completion and nearest low-rank correlation matrix problems. The computational results demonstrate that our methods generally outperform the existing methods in terms of solution quality and/or speed.

Many clustering techniques aim at optimizing empirical criteria that are of the form of a U-statistic of degree two. Given a measure of dissimilarity between pairs of observations, the goal is to minimize the within cluster point scatter over a class of partitions of the feature space. It is the purpose of this paper to define a general statistical framework, relying on the theory of U-processes, for studying the performance of such clustering methods. In this setup, under adequate assumptions on the complexity of the subsets forming the partition candidates, the excess of clustering risk is proved to be of the order O(1/\sqrt{n}). Based on recent results related to the tail behavior of degenerate U-processes, it is also shown how to establish tighter rate bounds. Model selection issues, related to the number of clusters forming the data partition in particular, are also considered.

We present a probabilistic algorithm for nonlinear inverse reinforcement learning. The goal of inverse reinforcement learning is to learn the reward function in a Markov decision process from expert demonstrations. While most prior inverse reinforcement learning algorithms represent the reward as a linear combination of a set of features, we use Gaussian processes to learn the reward as a nonlinear function, while also determining the relevance of each feature to the expert's policy. Our probabilistic algorithm allows complex behaviors to be captured from suboptimal stochastic demonstrations, while automatically balancing the simplicity of the learned reward structure against its consistency with the observed actions.

Multi-instance learning (MIL) considers input as bags of instances, in which labels areassigned to the bags. MIL is useful in many real-world applications. For example, in image categorization semantic meanings (labels) of an image mostly arise from its regions (instances) instead of the entire image (bag). Existing MIL methods typically build their models using the Bag-to-Bag (B2B) distance, which are often computationally expensive and may not truly reflect the semantic similarities. Totackle this, in this paper we approach MIL problems from a new perspective using the Class-to-Bag (C2B) distance, which directly assesses the relationships between the classes and the bags.

Traditionally, semantics has been seen as a feature of human language. The advent of the information era has led to its widespread redefinition as an information feature. Contrary to this praxis, I define semantics as a special kind of information. Revitalizing the ideas of Bar-Hillel and Carnap I have recreated and reestablished (on totally new grounds) the notion of semantics as the notion of Semantic Information. I have proposed a new definition of information (as a description, a linguistic text, a piece of a story or a tale) and a clear segregation between two different types of information - physical and semantic information. I hope, I have clearly explained the (usually obscured and mysterious) interrelations between data and physical information as well as the relation between physical information and semantic information. Consequently, usually indefinable notions of "information", "knowledge", "memory", "learning" and "semantics" have also received their suitable illumination and explanation.