Related papers: Nearly Optimal Algorithms for Level Set Estimation

We study gap-dependent performance guarantees for nearly minimax-optimal algorithms in reinforcement learning with linear function approximation. While prior works have established gap-dependent regret bounds in this setting, existing…

We study the adversarial kernel bandit problem, in which the loss at each round is induced by an arbitrary bounded element of a reproducing kernel Hilbert space (RKHS). We propose an exponential-weights algorithm built on a regularized…

Adaptive bandwidth selection is a fundamental challenge in nonparametric regression. This paper introduces a new bandwidth selection procedure inspired by the optimality criteria for $\ell_0$-penalized regression. Although similar in spirit…

In this paper, we consider the problem of black-box optimization with noisy feedback revealed in batches, where the unknown function to optimize has a bounded norm in some Reproducing Kernel Hilbert Space (RKHS). We refer to this as the…

In this work we consider active local learning: given a query point $x$, and active access to an unlabeled training set $S$, output the prediction $h(x)$ of a near-optimal $h \in H$ using significantly fewer labels than would be needed to…

Traditional machine learning models, particularly neural networks, are rooted in finite-dimensional parameter spaces and nonlinear function approximations. This report explores an alternative formulation where learning tasks are expressed…

We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. The theory in this paper covers in particular…

In this paper, we consider the infinite-dimensional integration problem on weighted reproducing kernel Hilbert spaces with norms induced by an underlying function space decomposition of ANOVA-type. The weights model the relative importance…

We investigate the problem of best policy identification in discounted linear Markov Decision Processes in the fixed confidence setting under a generative model. We first derive an instance-specific lower bound on the expected number of…

Linear fixed point equations in Hilbert spaces arise in a variety of settings, including reinforcement learning, and computational methods for solving differential and integral equations. We study methods that use a collection of random…

Federated learning must address heterogeneity, strict communication and computation limits, and privacy while ensuring performance. We propose an operator-theoretic framework that maps the $L^2$-optimal solution into a reproducing kernel…

We study offline Reinforcement Learning in large infinite-horizon discounted Markov Decision Processes (MDPs) when the reward and transition models are linearly realizable under a known feature map. Starting from the classic linear-program…

Most commonly used \emph{adaptive} algorithms for univariate real-valued function approximation and global minimization lack theoretical guarantees. Our new locally adaptive algorithms are guaranteed to provide answers that satisfy a…

Reinforcement learning from human feedback (RLHF) has been widely adopted to align language models (LMs) with human preference. Prior RLHF works typically take a bandit formulation, which, though intuitive, ignores the sequential nature of…

Peak estimation of hybrid systems aims to upper bound extreme values of a state function along trajectories, where this state function could be different in each subsystem. This finite-dimensional but nonconvex problem may be lifted into an…

We propose online algorithms for sequential learning in the contextual multi-armed bandit setting. Our approach is to partition the context space and then optimally combine all of the possible mappings between the partition regions and the…

The approximate degree of a Boolean function $f(x_{1},x_{2},\ldots,x_{n})$ is the minimum degree of a real polynomial that approximates $f$ pointwise within $1/3$. Upper bounds on approximate degree have a variety of applications in…

We consider linear stochastic bandits where the set of actions is an ellipsoid. We provide the first known minimax optimal algorithm for this problem. We first derive a novel information-theoretic lower bound on the regret of any algorithm,…

We introduce the concept of strong high-order approximate minimizers for nonconvex optimization problems. These apply in both standard smooth and composite non-smooth settings, and additionally allow convex or inexpensive constraints. An…

We study the best approximation problem: \[ \displaystyle \min_{\alpha\in \mathbb R^m}\max_{1\leq i\leq n}\left|y_i -\sum_{j=1}^m \alpha_j \Gamma_j ({\bf x}_i) \right|. \] Here: $\Gamma:=\left\{\Gamma_1,...,\Gamma_m\right\}$ is a list of…