Related papers: Improved Impossible Tuning and Lipschitz-Adaptive …
This paper introduces a new problem-dependent regret measure for online convex optimization with smooth losses. The notion, which we call the $G^\star$ regret, depends on the cumulative squared gradient norm evaluated at the decision in…
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…
This paper considers distributed online optimization with time-varying coupled inequality constraints. The global objective function is composed of local convex cost and regularization functions and the coupled constraint function is the…
In this paper, we study fundamental problems of maximizing DR-submodular continuous functions that have real-world applications in the domain of machine learning, economics, operations research and communication systems. It captures a…
We consider the dynamic resource allocation problem where the decision space is finite-dimensional, yet the solution must satisfy a large or even infinite number of constraints revealed via streaming data or oracle feedback. We model this…
We consider the online control problem with an unknown linear dynamical system in the presence of adversarial perturbations and adversarial convex loss functions. Although the problem is widely studied in model-based control, it remains…
The performance of online convex optimization algorithms in a dynamic environment is often expressed in terms of the dynamic regret, which measures the decision maker's performance against a sequence of time-varying comparators. In the…
In this paper, we study online convex optimization in dynamic environments, and aim to bound the dynamic regret with respect to any sequence of comparators. Existing work have shown that online gradient descent enjoys an…
Bandit convex optimization (BCO) is a fundamental online learning framework with partial feedback, where the learner observes only the loss incurred at the chosen decision point in each round. In this work, we investigate whether optimistic…
We present a reduction from reinforcement learning (RL) to no-regret online learning based on the saddle-point formulation of RL, by which "any" online algorithm with sublinear regret can generate policies with provable performance…
This paper considers the stability of online learning algorithms and its implications for learnability (bounded regret). We introduce a novel quantity called {\em forward regret} that intuitively measures how good an online learning…
Optimization in the presence of sharp (non-Lipschitz), unpredictable (w.r.t. time and amount) changes is a challenging and largely unexplored problem of great significance. We consider the class of piecewise Lipschitz functions, which is…
Online learning and model reference adaptive control have many interesting intersections. One area where they differ however is in how the algorithms are analyzed and what objective or metric is used to discriminate "good" algorithms from…
This paper addresses an online convex optimization problem where the cost function at each step depends on a history of past decisions (i.e., memory), and the decision maker has access to limited predictions of future cost values within a…
We revisit the question of reducing online learning to approximate optimization of the offline problem. In this setting, we give two algorithms with near-optimal performance in the full information setting: they guarantee optimal regret and…
The Matrix Multiplicative Weight Update (MMWU) is a seminal online learning algorithm with numerous applications. Applied to the matrix version of the Learning from Expert Advice (LEA) problem on the $d$-dimensional spectraplex, it is well…
We study numerical optimisation algorithms that use zeroth-order information to minimise time-varying geodesically-convex cost functions on Riemannian manifolds. In the Euclidean setting, zeroth-order algorithms have received a lot of…
We propose a novel adaptive, accelerated algorithm for the stochastic constrained convex optimization setting. Our method, which is inspired by the Mirror-Prox method, \emph{simultaneously} achieves the optimal rates for smooth/non-smooth…
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…
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…