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Building highly non-linear and non-parametric models is central to several state-of-the-art machine learning systems. Kernel methods form an important class of techniques that induce a reproducing kernel Hilbert space (RKHS) for inferring…
In distributed optimization, the practical problem-solving performance is essentially sensitive to algorithm selection, parameter setting, problem type and data pattern. Thus, it is often laborious to acquire a highly efficient method for a…
Distributionally robust offline reinforcement learning (RL) aims to find a policy that performs the best under the worst environment within an uncertainty set using an offline dataset collected from a nominal model. While recent advances in…
We consider Markov Decision Problems defined over continuous state and action spaces, where an autonomous agent seeks to learn a map from its states to actions so as to maximize its long-term discounted accumulation of rewards. We address…
Selecting an appropriate kernel is a central challenge in kernel-based spectral methods. In \emph{Kernelized Diffusion Maps} (KDM), the kernel determines the accuracy of the RKHS estimator of a diffusion-type operator and hence the quality…
Sequential Bayesian filters in non-linear dynamic systems require the recursive estimation of the predictive and posterior distributions. This paper introduces a Bayesian filter called the adaptive kernel Kalman filter (AKKF). With this…
The Bellman equation and its continuous form, the Hamilton-Jacobi-Bellman equation, are ubiquitous in reinforcement learning and control theory. However, these equations become intractable for high-dimensional or nonlinear systems. This…
This paper studies the continuous-time reinforcement learning (RL) for optimal switching problems across multiple regimes. We consider a type of exploratory formulation under entropy regularization where the agent randomizes both the timing…
In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on…
In this paper, we focus on the problem of inferring the underlying reward function of an expert given demonstrations, which is often referred to as inverse reinforcement learning (IRL). In particular, we propose a model-free density-based…
We consider multi-agent stochastic optimization problems over reproducing kernel Hilbert spaces (RKHS). In this setting, a network of interconnected agents aims to learn decision functions, i.e., nonlinear statistical models, that are…
We address the problem of {\it adaptivity} in the framework of reproducing kernel Hilbert space (RKHS) regression. More precisely, we analyze estimators arising from a linear regularization scheme $g_\lam$. In practical applications, an…
Ensuring reliability in modern software systems requires rigorous pre-production testing across highly heterogeneous and evolving environments. Because exhaustive evaluation is infeasible, practitioners must decide how to allocate limited…
The notion of reproducing kernel Hilbert space (RKHS) has emerged in system identification during the past decade. In the resulting framework, the impulse response estimation problem is formulated as a regularized optimization defined on an…
Reinforcement Learning (RL) remains a central optimisation framework in machine learning. Although RL agents can converge to optimal solutions, the definition of ``optimality'' depends on the environment's statistical properties. The…
Kernel Adaptive Filtering (KAF) are mathematically principled methods which search for a function in a Reproducing Kernel Hilbert Space. While they work well for tasks such as time series prediction and system identification they are…
We consider a context-dependent Reinforcement Learning (RL) setting, which is characterized by: a) an unknown finite number of not directly observable contexts; b) abrupt (discontinuous) context changes occurring during an episode; and c)…
This paper investigates a general regularization framework for unsupervised domain adaptation in vector-valued regression under the covariate shift assumption, utilizing vector-valued reproducing kernel Hilbert spaces (vRKHS). Covariate…
We introduce Limited Rollout Beam Search (LRBS), a beam search strategy for deep reinforcement learning (DRL) based combinatorial optimization improvement heuristics. Utilizing pre-trained models on the Euclidean Traveling Salesperson…
We develop a mathematical framework to address a broad class of metric and preference learning problems within a Hilbert space. We obtain a novel representer theorem for the simultaneous task of metric and preference learning. Our key…