Related papers: Minimax-optimal and Locally-adaptive Online Nonpar…
We study online adversarial regression with convex losses against a rich class of continuous yet highly irregular prediction rules, modeled by Besov spaces $B\_{pq}^s$ with general parameters $1 \leq p,q \leq \infty$ and smoothness $s >…
One of the main strengths of online algorithms is their ability to adapt to arbitrary data sequences. This is especially important in nonparametric settings, where performance is measured against rich classes of comparator functions that…
Despite tremendous advancements of machine learning models and algorithms in various application domains, they are known to be vulnerable to subtle, natural or intentionally crafted perturbations in future input data, known as adversarial…
We introduce a new online convex optimization algorithm that adaptively chooses its regularization function based on the loss functions observed so far. This is in contrast to previous algorithms that use a fixed regularization function…
We consider online learning when the time horizon is unknown. We apply a minimax analysis, beginning with the fixed horizon case, and then moving on to two unknown-horizon settings, one that assumes the horizon is chosen randomly according…
We study online convex optimization under stochastic sub-gradient observation faults, where we introduce adaptive algorithms with minimax optimal regret guarantees. We specifically study scenarios where our sub-gradient observations can be…
This paper establishes minimax rates for online regression with arbitrary classes of functions and general losses. We show that below a certain threshold for the complexity of the function class, the minimax rates depend on both the…
Recent literature on online learning has focused on developing adaptive algorithms that take advantage of a regularity of the sequence of observations, yet retain worst-case performance guarantees. A complementary direction is to develop…
We study fast rates of convergence in the setting of nonparametric online regression, namely where regret is defined with respect to an arbitrary function class which has bounded complexity. Our contributions are two-fold: - In the…
We study Online Convex Optimization in the unbounded setting where neither predictions nor gradient are constrained. The goal is to simultaneously adapt to both the sequence of gradients and the comparator. We first develop parameter-free…
We consider the problem of online nonparametric regression with arbitrary deterministic sequences. Using ideas from the chaining technique, we design an algorithm that achieves a Dudley-type regret bound similar to the one obtained in a…
In this paper, we analyze the problem of online convex optimization in different settings, including different feedback types (full-information/semi-bandit/bandit/etc) in either stochastic or non-stochastic setting and different notions of…
We investigate online convex optimization in non-stationary environments and choose dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible…
We establish optimal rates for online regression for arbitrary classes of regression functions in terms of the sequential entropy introduced in (Rakhlin, Sridharan, Tewari, 2010). The optimal rates are shown to exhibit a phase transition…
Practical online learning tasks are often naturally defined on unconstrained domains, where optimal algorithms for general convex losses are characterized by the notion of comparator adaptivity. In this paper, we design such algorithms in…
We consider the problem of controlling an unknown linear dynamical system under adversarially changing convex costs and full feedback of both the state and cost function. We present the first computationally-efficient algorithm that attains…
The goal of a learner in standard online learning is to maintain an average loss close to the loss of the best-performing single function in some class. In many real-world problems, such as rating or ranking items, there is no single best…
We develop a modified online mirror descent framework that is suitable for building adaptive and parameter-free algorithms in unbounded domains. We leverage this technique to develop the first unconstrained online linear optimization…
In this paper, we address tracking of a time-varying parameter with unknown dynamics. We formalize the problem as an instance of online optimization in a dynamic setting. Using online gradient descent, we propose a method that sequentially…
In the convex optimization approach to online regret minimization, many methods have been developed to guarantee a $O(\sqrt{T})$ bound on regret for subdifferentiable convex loss functions with bounded subgradients, by using a reduction to…