相关论文: Online Sketched Newton-Raphson

We consider the problem of Online Convex Optimization (OCO) with two-point bandit feedback. In this setting, a player attempts to minimize a sequence of adversarially generated convex loss functions, while only observing the value of each…

We consider an online two-stage stochastic optimization with long-term constraints over a finite horizon of $T$ periods. At each period, we take the first-stage action, observe a model parameter realization and then take the second-stage…

We study Online Linear Programming (OLP) with batching. The planning horizon is cut into $K$ batches, and the decisions on customers arriving within a batch can be delayed to the end of their associated batch. Compared with OLP without…

We introduce a transformation framework that can be utilized to develop online algorithms with low $\epsilon$-approximate regret in the random-order model from offline approximation algorithms. We first give a general reduction theorem that…

We propose a randomized second-order method for optimization known as the Newton Sketch: it is based on performing an approximate Newton step using a randomly projected or sub-sampled Hessian. For self-concordant functions, we prove that…

We propose the algorithms for online convex optimization which lead to cumulative squared constraint violations of the form $\sum\limits_{t=1}^T\big([g(x_t)]_+\big)^2=O(T^{1-\beta})$, where $\beta\in(0,1)$. Previous literature has focused…

We consider bidding in repeated Bayesian first-price auctions. Bidding algorithms that achieve optimal regret have been extensively studied, but their strategic robustness to the seller's manipulation remains relatively underexplored.…

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…

This paper considers the online nonstochastic control problem of a linear time-invariant system under convex state and input constraints that need to be satisfied at all times. We propose an algorithm called Online Gradient Descent with…

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…

Online linear programming plays an important role in both revenue management and resource allocation, and recent research has focused on developing efficient first-order online learning algorithms. Despite the empirical success of…

Stochastic optimization methods encounter new challenges in the realm of streaming, characterized by a continuous flow of large, high-dimensional data. While first-order methods, like stochastic gradient descent, are the natural choice,…

This article investigates the problem of controlling linear time-invariant systems subject to time-varying and a priori unknown cost functions, state and input constraints, and exogenous disturbances. We combine the online convex…

We propose an online convex optimization algorithm (RescaledExp) that achieves optimal regret in the unconstrained setting without prior knowledge of any bounds on the loss functions. We prove a lower bound showing an exponential separation…

We propose Regularized Overestimated Newton (RON), a Newton-type method with low per-iteration cost and strong global and local convergence guarantees for smooth convex optimization. RON interpolates between gradient descent and globally…

We study non-convex delayed-noise online optimization problems by evaluating dynamic regret in the non-stationary setting when the loss functions are quasar-convex. In particular, we consider scenarios involving quasar-convex functions…

Bandit algorithms have been predominantly analyzed in the convex setting with function-value based stationary regret as the performance measure. In this paper, motivated by online reinforcement learning problems, we propose and analyze…

This paper considers the problem of online trajectory design under time-varying environments. We formulate the general trajectory optimization problem within the framework of time-varying constrained convex optimization and proposed a novel…

Second-order optimization methods are among the most widely used optimization approaches for convex optimization problems, and have recently been used to optimize non-convex optimization problems such as deep learning models. The widely…

Universal online learning aims to achieve optimal regret guarantees without requiring prior knowledge of the curvature of online functions. Existing methods have established minimax-optimal regret bounds for universal online learning, where…