Online Learning with Multiple Operator-valued Kernels

We consider the problem of learning a vector-valued function f in an online learning setting. The function f is assumed to lie in a reproducing Hilbert space of operator-valued kernels. We describe two online algorithms for learning f while taking into account the output structure. A first contribution is an algorithm, ONORMA, that extends the standard kernel-based online learning algorithm NORMA from scalar-valued to operator-valued setting. We report a cumulative error bound that holds both for classification and regression. We then define a second algorithm, MONORMA, which addresses the limitation of pre-defining the output structure in ONORMA by learning sequentially a linear combination of operator-valued kernels. Our experiments show that the proposed algorithms achieve good performance results with low computational cost

M-Power Regularized Least Squares Regression

Regularization is used to find a solution that both fits the data and is sufficiently smooth, and thereby is very effective for designing and refining learning algorithms. But the influence of its exponent remains poorly understood. In particular, it is unclear how the exponent of the reproducing kernel Hilbert space~(RKHS) regularization term affects the accuracy and the efficiency of kernel-based learning algorithms. Here we consider regularized least squares regression (RLSR) with an RKHS regularization raised to the power of m, where m is a variable real exponent. We design an efficient algorithm for solving the associated minimization problem, we provide a theoretical analysis of its stability, and we compare its advantage with respect to computational complexity, speed of convergence and prediction accuracy to the classical kernel ridge regression algorithm where the regularization exponent m is fixed at 2. Our results show that the m-power RLSR problem can be solved efficiently, and support the suggestion that one can use a regularization term that grows significantly slower than the standard quadratic growth in the RKHS norm

Stationary Mixing Bandits

We study the bandit problem where arms are associated with stationary phi-mixing processes and where rewards are therefore dependent: the question that arises from this setting is that of recovering some independence by ignoring the value of some rewards. As we shall see, the bandit problem we tackle requires us to address the exploration/exploitation/independence trade-off. To do so, we provide a UCB strategy together with a general regret analysis for the case where the size of the independence blocks (the ignored rewards) is fixed and we go a step beyond by providing an algorithm that is able to compute the size of the independence blocks from the data. Finally, we give an analysis of our bandit problem in the restless case, i.e., in the situation where the time counters for all mixing processes simultaneously evolve

Decoy Bandits Dueling on a Poset

We adress the problem of dueling bandits defined on partially ordered sets, or posets. In this setting, arms may not be comparable, and there may be several (incomparable) optimal arms. We propose an algorithm, UnchainedBandits, that efficiently finds the set of optimal arms of any poset even when pairs of comparable arms cannot be distinguished from pairs of incomparable arms, with a set of minimal assumptions. This algorithm relies on the concept of decoys, which stems from social psychology. For the easier case where the incomparability information may be accessible, we propose a second algorithm, SlicingBandits, which takes advantage of this information and achieves a very significant gain of performance compared to UnchainedBandits. We provide theoretical guarantees and experimental evaluation for both algorithms

Equivalence of the Fleming-Viot and Look-down models of Muller's ratchet

We consider Muller's ratchet Fleming-Viot model with compensatory mutations, which is an infinite system of SDE used to study the accumulation of deleterious mutations in asexual population including mutations and selection. We construct a specific look-down model, and we prove that it is equivalent to the previous Muller's ratchet model

Equivalence of Learning Algorithms

The purpose of this paper is to introduce a concept of equivalence between machine learning algorithms. We define two notions of algorithmic equivalence, namely, weak and strong equivalence. These notions are of paramount importance for identifying when learning prop erties from one learning algorithm can be transferred to another. Using regularized kernel machines as a case study, we illustrate the importance of the introduced equivalence concept by analyzing the relation between kernel ridge regression (KRR) and m-power regularized least squares regression (M-RLSR) algorithms

Bandits Dueling on Partially Ordered Sets

International audienceWe address the problem of dueling bandits defined on partially ordered sets, or posets. In this setting, arms may not be comparable, and there may be several (incomparable) optimal arms. We propose an algorithm, UnchainedBandits, that efficiently finds the set of optimal arms —the Pareto front— of any poset even when pairs of comparable arms cannot be a priori distinguished from pairs of incomparable arms, with a set of minimal assumptions. This means that Un-chainedBandits does not require information about comparability and can be used with limited knowledge of the poset. To achieve this, the algorithm relies on the concept of decoys, which stems from social psychology. We also provide theoretical guarantees on both the regret incurred and the number of comparison required by UnchainedBandits, and we report compelling empirical results

MESSI: Maximum Entropy Semi-Supervised Inverse Reinforcement Learning

International audienceA 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 semi-supervised 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

APCNN: Tackling Cclass imbalance in relation extraction through aggregated piecewise convolutional neural networks

One of the major difficulties in applying distant supervision to relation extraction is class imbalance, as the distribution of relations appearing in text is heavily skewed. This is particularly damaging for the multi-instance variant of relation extraction. In this work, we introduce a new model called Aggregated Piecewise Convolutional Neural Networks, or APCNN, to address this problem. APCNN relies on the combination of two neural networks, a novel objective function as well as oversampling techniques to tackle class imbalance. We empirically compare APCNN to state-of-the-art approaches and show that it outperforms previous multi-instance approaches on two standard datasets