相关论文: Online Learning of Smooth Functions

We consider the fundamental problem of prediction with expert advice where the experts are "optimizable": there is a black-box optimization oracle that can be used to compute, in constant time, the leading expert in retrospect at any point…

We consider differentially private algorithms for reinforcement learning in continuous spaces, such that neighboring reward functions are indistinguishable. This protects the reward information from being exploited by methods such as…

In this paper, we consider an online optimization problem over $T$ rounds where at each step $t\in[T]$, the algorithm chooses an action $x_t$ from the fixed convex and compact domain set $\mathcal{K}$. A utility function $f_t(\cdot)$ is…

$Q$-learning is the most fundamental model-free reinforcement learning algorithm. Deployment of $Q$-learning requires approximation of the state-action value function (also known as the $Q$-function). In this work, we provide online random…

Many numerical methods for recovering ODE solutions from data rely on approximating the solutions using basis functions or kernel functions under a least square criterion. The accuracy of this approach hinges on the smoothness of the…

This paper concerns three classes of real-valued functions on intervals, operator monotone functions, operator convex functions, and strongly operator convex functions. Strongly operator convex functions were previously treated in [3] and…

The article is devoted to the investigation of smoothness of functions $f(x_1,...,x_m)$ of variables $x_1,...,x_m$ in infinite fields with non-trivial multiplicative ultra-norms, where $m\ge 2$. Theorems about classes of smoothness $C^n$ or…

To obtain a near-optimal policy with fewer interactions in Reinforcement Learning (RL), a promising approach involves the combination of offline RL, which enhances sample efficiency by leveraging offline datasets, and online RL, which…

In this paper, we present an improved analysis for dynamic regret of strongly convex and smooth functions. Specifically, we investigate the Online Multiple Gradient Descent (OMGD) algorithm proposed by Zhang et al. (2017). The original…

We generalize the notion of average Lipschitz smoothness proposed by Ashlagi et al. (COLT 2021) by extending it to H\"older smoothness. This measure of the "effective smoothness" of a function is sensitive to the underlying distribution and…

Offline reinforcement learning (RL) provides a promising direction to exploit massive amount of offline data for complex decision-making tasks. Due to the distribution shift issue, current offline RL algorithms are generally designed to be…

We initiate an investigation of learning tasks in a setting where the learner is given access to two competing provers, only one of which is honest. Specifically, we consider the power of such learners in assessing purported properties of…

This paper presents a new method to learn online policies in continuous state, continuous action, model-free Markov decision processes, with two properties that are crucial for practical applications. First, the policies are implementable…

In this paper, we study oracle-efficient algorithms for beyond worst-case analysis of online learning. We focus on two settings. First, the smoothed analysis setting of [RST11,HRS22] where an adversary is constrained to generating samples…

Offline reinforcement learning (RL) enables policy learning from static data but often suffers from poor coverage of the state-action space and distributional shift problems. This problem can be addressed by allowing limited online…

We study online classification under smoothed adversaries. In this setting, at each time point, the adversary draws an example from a distribution that has a bounded density with respect to a fixed base measure, which is known apriori to…

Semi-Supervised Learning (SSL) seeks to leverage large amounts of non-annotated data along with the smallest amount possible of annotated data in order to achieve the same level of performance as if all data were annotated. A fruitful…

We provide a lower bound showing that the $O(1/k)$ convergence rate of the NoLips method (a.k.a. Bregman Gradient) is optimal for the class of functions satisfying the $h$-smoothness assumption. This assumption, also known as relative…

This paper introduces a projected functional gradient descent algorithm (P-FGD) for training nonparametric additive quantile regression models in online settings. This algorithm extends the functional stochastic gradient descent framework…

Smoothed online learning has emerged as a popular framework to mitigate the substantial loss in statistical and computational complexity that arises when one moves from classical to adversarial learning. Unfortunately, for some spaces, it…