Related papers: Online Learning of Smooth Functions

Online learning is a model of machine learning where the learner is trained on sequential feedback. We investigate worst-case error for the online learning of real functions that have certain smoothness constraints. Suppose that…

We investigate the generalization of the mistake-bound model to continuous real-valued single variable functions. Let $\mathcal{F}_q$ be the class of absolutely continuous functions $f: [0, 1] \rightarrow \mathbb{R}$ with $||f'||_q \le 1$,…

We study adversarial online learning of real-valued functions on $\mathbb{R}$. In each round the learner is queried at $x_t\in\mathbb{R}$, predicts $\hat y_t$, and then observes the true value $f(x_t)$; performance is measured by cumulative…

We study the problem of finding an $\epsilon$-first-order stationary point (FOSP) of a smooth function, given access only to gradient information. The best-known gradient query complexity for this task, assuming both the gradient and…

Smoothness is known to be crucial for acceleration in offline optimization, and for gradient-variation regret minimization in online learning. Interestingly, these two problems are actually closely connected -- accelerated optimization can…

Regularized online learning is widely used in machine learning applications. In online learning, performing exact minimization ($i.e.,$ implicit update) is known to be beneficial to the numerical stability and structure of solution. In this…

We study online linear optimization with matrix variables constrained by the operator norm, a setting where the geometry renders designing data-dependent and efficient adaptive algorithms challenging. The best-known adaptive regret bounds…

Offline reinforcement learning, which aims at optimizing sequential decision-making strategies with historical data, has been extensively applied in real-life applications. State-Of-The-Art algorithms usually leverage powerful function…

Practical and pervasive needs for robustness and privacy in algorithms have inspired the design of online adversarial and differentially private learning algorithms. The primary quantity that characterizes learnability in these settings is…

We study online optimization of smoothed piecewise constant functions over the domain [0, 1). This is motivated by the problem of adaptively picking parameters of learning algorithms as in the recently introduced framework by Gupta and…

We study a family of potential functions for online learning. We show that if the potential function has strictly positive derivatives of order 1-4 then the min-max optimal strategy for the adversary is Brownian motion. Using that fact we…

Online learning is the process of answering a sequence of questions based on the correct answers to the previous questions. It is studied in many research areas such as game theory, information theory and machine learning. There are two…

Much of modern learning theory has been split between two regimes: the classical offline setting, where data arrive independently, and the online setting, where data arrive adversarially. While the former model is often both computationally…

In the last several years, the intimate connection between convex optimization and learning problems, in both statistical and sequential frameworks, has shifted the focus of algorithmic machine learning to examine this interplay. In…

The forward-forward algorithm presents a new method of training neural networks by updating weights during an inference, performing parameter updates for each layer individually. This immediately reduces memory requirements during training…

Offline safe reinforcement learning (RL) seeks reward-maximizing policies from static datasets under strict safety constraints. Existing methods often rely on soft expected-cost objectives or iterative generative inference, which can be…

We consider the problems of \emph{learning} and \emph{testing} real-valued convex functions over Gaussian space. Despite the extensive study of function convexity across mathematics, statistics, and computer science, its learnability and…

Modern applications in sensitive domains such as biometrics and medicine frequently require the use of non-decomposable loss functions such as precision@k, F-measure etc. Compared to point loss functions such as hinge-loss, these offer much…

We propose a new algorithm that finds an $\varepsilon$-approximate fixed point of a smooth function from the $n$-dimensional $\ell_2$ unit ball to itself. We use the general framework of finding approximate solutions to a variational…

Due to the drastic gap in complexity between sequential and batch statistical learning, recent work has studied a smoothed sequential learning setting, where Nature is constrained to select contexts with density bounded by 1/{\sigma} with…