Related papers: Efficient Lipschitzian Global Optimization of H\"o…
A gradient-free deterministic method is developed to solve global optimization problems for Lipschitz continuous functions defined in arbitrary path-wise connected compact sets in Euclidean spaces. The method can be regarded as granular…
We study online prediction where regret of the algorithm is measured against a benchmark defined via evolving constraints. This framework captures online prediction on graphs, as well as other prediction problems with combinatorial…
The global optimization have the very extensive applications in econometrics, science and engineering. However, the global optimization for non-convex objective functions is particularly difficult since most of the existing global…
Bayesian optimization is a powerful global optimization technique for expensive black-box functions. One of its shortcomings is that it requires auxiliary optimization of an acquisition function at each iteration. This auxiliary…
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…
Some of the most compelling applications of online convex optimization, including online prediction and classification, are unconstrained: the natural feasible set is R^n. Existing algorithms fail to achieve sub-linear regret in this…
To deal with changing environments, a new performance measure -- adaptive regret, defined as the maximum static regret over any interval, was proposed in online learning. Under the setting of online convex optimization, several algorithms…
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…
In online convex optimization, some efficient algorithms have been designed for each of the individual classes of objective functions, e.g., convex, strongly convex, and exp-concave. However, existing regret analyses, including those of…
We consider the minimisation problem of submodular functions and investigate the application of a zeroth-order method to this problem. The method is based on exploiting a Gaussian smoothing random oracle to estimate the smoothed function…
The problem of minimizing the maximum of $N$ convex, Lipschitz functions plays significant roles in optimization and machine learning. It has a series of results, with the most recent one requiring $O(N\epsilon^{-2/3} + \epsilon^{-8/3})$…
We study the sequential general online regression, known also as the sequential probability assignments, under logarithmic loss when compared against a broad class of experts. We focus on obtaining tight, often matching, lower and upper…
Omnipredictors are simple prediction functions that encode loss-minimizing predictions with respect to a hypothesis class $H$, simultaneously for every loss function within a class of losses $L$. In this work, we give near-optimal learning…
We consider online optimization with binary decision variables and convex loss functions. We design a new algorithm, binary online gradient descent (bOGD) and bound its expected dynamic regret. We provide a regret bound that holds for any…
We introduce a generic template for developing regret minimization algorithms in the Stochastic Shortest Path (SSP) model, which achieves minimax optimal regret as long as certain properties are ensured. The key of our analysis is a new…
We consider the setting of online logistic regression and consider the regret with respect to the 2-ball of radius B. It is known (see [Hazan et al., 2014]) that any proper algorithm which has logarithmic regret in the number of samples…
Recently a multi-agent variant of the classical multi-armed bandit was proposed to tackle fairness issues in online learning. Inspired by a long line of work in social choice and economics, the goal is to optimize the Nash social welfare…
We consider a family of learning strategies for online optimization problems that evolve in continuous time and we show that they lead to no regret. From a more traditional, discrete-time viewpoint, this continuous-time approach allows us…
Online linear programming (OLP) has gained significant attention from both researchers and practitioners due to its extensive applications, such as online auction, network revenue management, order fulfillment and advertising. Existing OLP…
Consider the classical problem of predicting the next bit in a sequence of bits. A standard performance measure is {\em regret} (loss in payoff) with respect to a set of experts. For example if we measure performance with respect to two…