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Despite the recent progress towards efficient multiple kernel learning (MKL), the structured output case remains an open research front. Current approaches involve repeatedly solving a batch learning problem, which makes them inadequate for…
The problem of sample complexity of online reinforcement learning is often studied in the literature without taking into account any partial knowledge about the system dynamics that could potentially accelerate the learning process. In this…
This paper investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by \emph{general}, we mean that many stationary stochastic processes can be included. We show that…
An informal observation, made by several authors, is that the adaptive design of a Markov transition kernel has the flavour of a reinforcement learning task. Yet, to-date it has remained unclear how to actually exploit modern reinforcement…
In this work, we investigate the generalization properties of random feature methods. Our analysis extends prior results for Tikhonov regularization to a broad class of spectral regularization techniques and further generalizes the setting…
Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically…
Online federated learning (OFL) becomes an emerging learning framework, in which edge nodes perform online learning with continuous streaming local data and a server constructs a global model from the aggregated local models. Online…
Dynamic multilayer networks arise in many applications where multiple types of relations among a common set of nodes evolve over time. Existing approaches often assume temporal independence, focus on single-layer networks or impose…
In this paper we propose a model to study the appropriation of knowledge of one student in a non-collaborative online class. We formulate a stochastic model based on the quality of the teacher's class and the affinity of the student to…
We present methods for online linear optimization that take advantage of benign (as opposed to worst-case) sequences. Specifically if the sequence encountered by the learner is described well by a known "predictable process", the algorithms…
We uncover a fairly general principle in online learning: If regret can be (approximately) expressed as a function of certain "sufficient statistics" for the data sequence, then there exists a special Burkholder function that 1) can be used…
Financial time series are characterised by their nonstationarity and autocorrelation. Even if these time series are differenced, technically ensuring their stationarity, they experience regular covariate shifts and concept drifts. Against…
Most of the existing works for reinforcement learning (RL) with general function approximation (FA) focus on understanding the statistical complexity or regret bounds. However, the computation complexity of such approaches is far from being…
A class of examples is constructed to show that for strictly stationary Markov chains that are reversible, the simultaneous mixing rates for the $\rho$-mixing and strong mixing ($\alpha$-mixing) conditions can be fairly arbitrary, within…
In this work, we analyze the generalization ability of distributed online learning algorithms under stationary and non-stationary environments. We derive bounds for the excess-risk attained by each node in a connected network of learners…
In this paper, we study the problem of early stopping for iterative learning algorithms in a reproducing kernel Hilbert space (RKHS) in the nonparametric regression framework. In particular, we work with the gradient descent and (iterative)…
This paper aims at the algorithmic/theoretical core of reinforcement learning (RL) by introducing the novel class of proximal Bellman mappings. These mappings are defined in reproducing kernel Hilbert spaces (RKHSs), to benefit from the…
Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…
Multiscale Models are known to be successful in uncovering and analyzing the structures in data at different resolutions. In the current work we propose a feature driven Reproducing Kernel Hilbert space (RKHS), for which the associated…
Imitation of expert behaviour is a highly desirable and safe approach to the problem of sequential decision making. We provide an easy-to-implement, novel algorithm for imitation learning under a strict data paradigm, in which the agent…