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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 and adversarial data are two widely studied settings in online learning. But many optimization tasks are neither i.i.d. nor fully adversarial, which makes it of fundamental interest to get a better theoretical understanding of…
We study the problem of uncertainty quantification via prediction sets, in an online setting where the data distribution may vary arbitrarily over time. Recent work develops online conformal prediction techniques that leverage regret…
Recently, much work has been done on extending the scope of online learning and incremental stochastic optimization algorithms. In this paper we contribute to this effort in two ways: First, based on a new regret decomposition and a…
In this work, we study nonconvex-strongly convex online bilevel optimization (OBO) using only first-order oracle. Existing OBO algorithms are mainly based on hypergradient descent, which requires access to a Hessian-vector product (HVP)…
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…
Follow-the-Regularized-Leader (FTRL) algorithms are a popular class of learning algorithms for online linear optimization (OLO) that guarantee sub-linear regret, but the choice of regularizer can significantly impact dimension-dependent…
This paper considers the distributed online convex-concave optimization with constraint sets over a multiagent network, in which each agent autonomously generates a series of decision pairs through a designable mechanism to cooperatively…
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…
Robust optimization (RO) is a powerful paradigm for decision making under uncertainty. Existing algorithms for solving RO, including the reformulation approach and the cutting-plane method, do not scale well, hindering the application of RO…
In this paper, the problem of distributed optimization is studied via a network of agents. Each agent only has access to a stochastic gradient of its own objective function in the previous time, and can communicate with its neighbors via a…
This paper proposes distributed algorithms to solve robust convex optimization (RCO) when the constraints are affected by nonlinear uncertainty. We adopt a scenario approach by randomly sampling the uncertainty set. To facilitate the…
Online optimization has emerged as powerful tool in large scale optimization. In this pa- per, we introduce efficient online optimization algorithms based on the alternating direction method (ADM), which can solve online convex optimization…
Despite the modeling power for problems under uncertainty, robust optimization (RO) and adaptive robust optimization (ARO) can exhibit too conservative solutions in terms of objective value degradation compared to the nominal case. One of…
This paper studied a robust concurrent topology optimization (RCTO) approach to design the structure and its composite materials simultaneously. For the first time, the material uncertainty with imprecise probability is integrated into the…
Autonomous microgrid planning is a Mixed-Integer Non Convex decision problem that requires to consider investments in both distribution and generation capacity and represents significant computation challenges. We proposed in a previous…
We study a robust online convex optimization framework, where an adversary can introduce outliers by corrupting loss functions in an arbitrary number of rounds k, unknown to the learner. Our focus is on a novel setting allowing unbounded…
In many sequential decision making applications, the change of decision would bring an additional cost, such as the wear-and-tear cost associated with changing server status. To control the switching cost, we introduce the problem of online…
We study the problem of online learning in predictive control of an unknown linear dynamical system with time varying cost functions which are unknown apriori. Specifically, we study the online learning problem where the control algorithm…
Distributionally Robust Optimization (DRO) is a popular framework for decision-making under uncertainty, but its adversarial nature can lead to overly conservative solutions. To address this, we study ex-ante Distributionally Robust Regret…