Related papers: Sublinear Regret with Barzilai-Borwein Step Sizes

In this paper we propose a framework for solving constrained online convex optimization problem. Our motivation stems from the observation that most algorithms proposed for online convex optimization require a projection onto the convex set…

Regret minimization is a powerful tool for solving large-scale extensive-form games. State-of-the-art methods rely on minimizing regret locally at each decision point. In this work we derive a new framework for regret minimization on…

A stochastic combinatorial semi-bandit is an online learning problem where at each step a learning agent chooses a subset of ground items subject to constraints, and then observes stochastic weights of these items and receives their sum as…

Regret minimization has proved to be a versatile tool for tree-form sequential decision making and extensive-form games. In large two-player zero-sum imperfect-information games, modern extensions of counterfactual regret minimization (CFR)…

This work focuses on dynamic regret of online convex optimization that compares the performance of online learning to a clairvoyant who knows the sequence of loss functions in advance and hence selects the minimizer of the loss function at…

Bayesian optimisation (BO) is a well-known efficient algorithm for finding the global optimum of expensive, black-box functions. The current practical BO algorithms have regret bounds ranging from $\mathcal{O}(\frac{logN}{\sqrt{N}})$ to…

This paper investigates online composite optimization in dynamic environments, where each objective or loss function contains a time-varying nondifferentiable regularizer. To resolve it, an online proximal gradient algorithm is studied for…

Algorithm selection is typically based on models of algorithm performance, learned during a separate offline training sequence, which can be prohibitively expensive. In recent work, we adopted an online approach, in which a performance…

This paper studies multi-stage systems with end-to-end bandit feedback. In such systems, each job needs to go through multiple stages, each managed by a different agent, before generating an outcome. Each agent can only control its own…

We consider the problem of online adaptive control of the linear quadratic regulator, where the true system parameters are unknown. We prove new upper and lower bounds demonstrating that the optimal regret scales as…

Bayesian optimization is a principled optimization strategy for a black-box objective function. It shows its effectiveness in a wide variety of real-world applications such as scientific discovery and experimental design. In general, the…

We consider model selection in stochastic bandit and reinforcement learning problems. Given a set of base learning algorithms, an effective model selection strategy adapts to the best learning algorithm in an online fashion. We show that by…

The Barzilai-Borwein (BB) steplengths play great roles in practical gradient methods for solving unconstrained optimization problems. Motivated by the observation that the two well-known BB steplengths correspond to the ordinary and the…

We study a widely used Bayesian optimization method, Gaussian process Thompson sampling (GP-TS), under the assumption that the objective function is a sample path from a GP. Compared with the GP upper confidence bound (GP-UCB) with…

We present an adaptive online gradient descent algorithm to solve online convex optimization problems with long-term constraints , which are constraints that need to be satisfied when accumulated over a finite number of rounds T , but can…

In online learning the performance of an algorithm is typically compared to the performance of a fixed function from some class, with a quantity called regret. Forster proposed a last-step min-max algorithm which was somewhat simpler than…

We develop parameter-free algorithms for unconstrained online learning with regret guarantees that scale with the gradient variation $V_T(u) = \sum_{t=2}^T \|\nabla f_t(u)-\nabla f_{t-1}(u)\|^2$. For $L$-smooth convex loss, we provide…

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 address the online linear optimization problem with bandit feedback. Our contribution is twofold. First, we provide an algorithm (based on exponential weights) with a regret of order $\sqrt{d n \log N}$ for any finite action set with $N$…

This paper studies online optimization from a high-level unified theoretical perspective. We not only generalize both Optimistic-DA and Optimistic-MD in normed vector space, but also unify their analysis methods for dynamic regret. Regret…