Spectral dimensionality reduction methods have recently emerged as powerful tools for various applications in pattern recognition, data mining and computer vision. These methods use information contained in the eigenvectors of a data affinity (i.e, item-item similarity) matrix to reveal the low dimensional structure of the high dimensional data. One of the limitations of various spectral dimensionality reduction methods is their high computational complexity. They all need to construct a data affinity matrix and compute the top eigenvectors. This leads to O(n2) computational complexity, where n is the number of samples. Moreover, when the data are highly non-linear distributed, some linear methods have to be performed in a reproducing kernel Hilbert space (leads to the corresponding kernel methods) to learn an effective non-linear mapping. The computational complexity of these kernel methods is O(n3). In this paper, we propose a novel nonlinear dimensionality reduction algorithm, called Compressed Spectral Regression, with O(n) computational complexity. Extensive experiments on data clustering demonstrate the effectiveness and efficiency of the proposed approach.

Reinforcement learning describes how a learning agent can achieve optimal behaviour based on interactions with its environment and reward feedback. A limiting factor in reinforcement learning as employed in artificial intelligence is the need for an often prohibitively large number of environment samples before the agent reaches a desirable level of performance. Learning from demonstration is an approach that provides the agent with demonstrations by a supposed expert, from which it should derive suitable behaviour. Yet, one of the challenges of learning from demonstration is that no guarantees can be provided for the quality of the demonstrations, and thus the learned behavior. In this paper, we investigate the intersection of these two approaches, leveraging the theoretical guarantees provided by reinforcement learning, and using expert demonstrations to speed up this learning by biasing exploration through a process called reward shaping. This approach allows us to leverage human input without making an erroneous assumption regarding demonstration optimality. We show experimentally that this approach requires significantly fewer demonstrations, is more robust against suboptimality of demonstrations, and achieves much faster learning than the recently developed HAT algorithm.

Online multi-task learning is an important capability for lifelong learning agents, enabling them to acquire models for diverse tasks over time and rapidly learn new tasks by building upon prior experience. However, recent progress toward lifelong reinforcement learning (RL) has been limited to learning from within a single task domain. For truly versatile lifelong learning, the agent must be able to autonomously transfer knowledge between different task domains. A few methods for cross-domain transfer have been developed, but these methods are computationally inefficient for scenarios where the agent must learn tasks consecutively. In this paper, we develop the first cross-domain lifelong RL framework. Our approach efficiently optimizes a shared repository of transferable knowledge and learns projection matrices that specialize that knowledge to different task domains. We provide rigorous theoretical guarantees on the stability of this approach, and empirically evaluate its performance on diverse dynamical systems. Our results show that the proposed method can learn effectively from interleaved task domains and rapidly acquire high performance in new domains.

Count-based estimators are a fundamental building block of a number of powerful sequential prediction algorithms, including Context Tree Weighting and Prediction by Partial Matching. Keeping exact counts, however, typically results in a high memory overhead. In particular, when dealing with large alphabets the memory requirements of count-based estimators often become prohibitive. In this paper we propose three novel ideas for approximating count-based estimators using bounded memory. Our first contribution, of independent interest, is an extension of reservoir sampling for sampling distinct symbols from a stream of unknown length, which we call K-distinct reservoir sampling. We combine this sampling scheme with a state-of-the-art count-based estimator for memoryless sources, the Sparse Adaptive Dirichlet (SAD) estimator. The resulting algorithm, the Budget SAD, naturally guarantees a limit on its memory usage. We finally demonstrate the broader use of K-distinct reservoir sampling in nonparametric estimation by using it to restrict the branching factor of the Context Tree Weighting algorithm. We demonstrate the usefulness of our algorithms with empirical results on two sequential, large-alphabet prediction problems.

When a transition probability matrix is represented as the product of two stochastic matrices, swapping the factors of the multiplication yields another transition matrix that retains some fundamental characteristics of the original. Since the new matrix can be much smaller than its precursor, replacing the former for the latter can lead to significant savings in terms of computational effort. This strategy, dubbed the "stochastic-factorization trick," can be used to compute the stationary distribution of a Markov chain, to determine the fundamental matrix of an absorbing chain, and to compute a decision policy via dynamic programming or reinforcement learning. In this paper we show that the stochastic-factorization trick can also provide benefits in terms of the number of samples needed to estimate a transition matrix. We introduce a probabilistic interpretation of a stochastic factorization and build on the resulting model to develop an algorithm to compute the factorization directly from data. If the transition matrix can be well approximated by a low-order stochastic factorization, estimating its factors instead of the original matrix reduces significantly the number of parameters to be estimated. Thus, when compared to estimating the transition matrix directly via maximum likelihood, the proposed method is able to compute approximations of roughly the same quality using less data. We illustrate the effectiveness of the proposed algorithm by using it to help a reinforcement learning agent learn how to play the game of blackjack.

In this paper, we develop a novel graph kernel by aligning the Jensen-Shannon (JS) representations of vertices. We commence by describing how to compute the JS representation of a vertex by measuring the JS divergence (JSD) between the corresponding $-layer depth-based (DB) representations developed. By aligning JS representations of vertices, we identify the correspondence between the vertices of two graphs and this allows us to construct a matching-based graph kernel. Unlike existing R-convolution kernels that roughly record the isomorphism information between any pair of substructures under a type of graph decomposition, the new kernel can be seen as an aligned subgraph kernel that incorporates explicit local correspondences of substructures i.e., the local information graphs) into the process of kernelization through the JS representation alignment. The new kernel thus addresses the drawback of neglecting the relative locations between substructures that arises in the R-convolution kernels. Experiments demonstrate that our kernel can easily outperform state-of-the-art graph kernels in terms of the classification accuracies.

A popular approach to apprenticeship learning (AL) is to formulate it as an inverse reinforcement learning (IRL) problem. The MaxEnt-IRL algorithm successfully integrates the maximum entropy principle into IRL and unlike its predecessors, it resolves the ambiguity arising from the fact that a possibly large number of policies could match the expert's behavior. In this paper, we study an AL setting in which in addition to the expert's trajectories,a number of unsupervised trajectories is available. We introduce MESSI,a novel algorithm that combines MaxEnt-IRL with principles coming from semisupervised learning. In particular, MESSI integrates the unsupervised data into the MaxEnt-IRL framework using a pairwise penalty on trajectories. Empirical results in a highway driving and grid-world problems indicate that MESSI is able to take advantage of the unsupervised trajectories and improve the performance of MaxEnt-IRL.

Nearly all algorithms for learning an unknown regular language, in particular the popular L* algorithm, yield deterministic finite automata. It was recently shown that the ideas of L* can be extended to yield non-deterministic automata, and that the respective learning algorithm, NL*, outperforms L* on randomly generated regular expressions. We conjectured that this is due to the existential nature of regular expressions, and NL* might not outperform L* on languages with a universal nature. In this paper we introduce UL* — a learning algorithm for universal automata (the dual of non-deterministic automata); and AL* — a learning algorithm for alternating automata (which generalize both universal and non-deterministic automata). Our empirical results illustrate the advantages and trade-offs among L*, NL*, UL* and AL*.

Classic entrenchment-based contraction is not applicable to many useful logics, such as description logics. This is because the semantic construction refers to arbitrary disjunctions of formulas, while many logics do not fully support disjunction. In this paper, we present a new entrenchment-based contraction which does not rely on any logical connectives except conjunction. This contraction is applicable to all fragments of first-order logic that support conjunction. We provide a representation theorem for the contraction which shows that it satisfies all the AGM postulates except for the controversial Recovery Postulate, and is a natural generalisation of entrenchment-based contraction.

In this paper, we study the expressive power of first-order disjunctive logic programming (DLP) and normal logic programming (NLP) under the stable model semantics. We show that, unlike the propositional case, first-order DLP is strictly more expressive than NLP. This result still holds even if auxiliary predicates are allowed, assuming that NP not equals to coNP. On the other side, we propose a partial translation from first-order DLP to NLP via unfolding and shifting, which suggests a sound yet incomplete approach to implement DLP via NLP solvers. We also identify some NLP definable subclasses, and conjecture to exactly capture NLP definability by unfolding and shifting.