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In this paper we propose a general framework to characterize and solve the stochastic optimization problems with multiple objectives underlying many real world learning applications. We first propose a projection based algorithm which…
Model predictive control (MPC) is a powerful technique for solving dynamic control tasks. In this paper, we show that there exists a close connection between MPC and online learning, an abstract theoretical framework for analyzing online…
Gradient-variation online learning aims to achieve regret guarantees that scale with variations in the gradients of online functions, which has been shown to be crucial for attaining fast convergence in games and robustness in stochastic…
This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…
We study unconstrained Online Linear Optimization with Lipschitz losses. Motivated by the pursuit of instance optimality, we propose a new algorithm that simultaneously achieves ($i$) the AdaGrad-style second order gradient adaptivity; and…
Many advances that have improved the robustness and efficiency of deep reinforcement learning (RL) algorithms can, in one way or another, be understood as introducing additional objectives or constraints in the policy optimization step.…
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…
The paper is devoted to new modifications of recently proposed adaptive methods of Mirror Descent for convex minimization problems in the case of several convex functional constraints. Methods for problems of two classes are considered. The…
Smoothness is known to be crucial for acceleration in offline optimization, and for gradient-variation regret minimization in online learning. Interestingly, these two problems are actually closely connected -- accelerated optimization can…
Models trained with offline data often suffer from continual distribution shifts and expensive labeling in changing environments. This calls for a new online learning paradigm where the learner can continually adapt to changing environments…
Different conflicting optimization criteria arise naturally in various Deep Learning scenarios. These can address different main tasks (i.e., in the setting of Multi-Task Learning), but also main and secondary tasks such as loss…
Learning-to-optimize is an emerging framework that seeks to speed up the solution of certain optimization problems by leveraging training data. Learned optimization solvers have been shown to outperform classical optimization algorithms in…
Online multi-task learning (OMTL) enhances streaming data processing by leveraging the inherent relations among multiple tasks. It can be described as an optimization problem in which a single loss function is defined for multiple tasks.…
A standard way to obtain convergence guarantees in stochastic convex optimization is to run an online learning algorithm and then output the average of its iterates: the actual iterates of the online learning algorithm do not come with…
Stochastically Extended Adversarial (SEA) model is introduced by Sachs et al. [2022] as an interpolation between stochastic and adversarial online convex optimization. Under the smoothness condition, they demonstrate that the expected…
We propose an Adagrad-like algorithm for multi-objective unconstrained optimization that relies on the computation of a common descent direction only. Unlike classical local algorithms for multi-objective optimization, our approach does not…
Multi-objective combinatorial optimization seeks Pareto-optimal solutions over exponentially large discrete spaces, yet existing methods sacrifice generality, scalability, or theoretical guarantees. We reformulate it as an online learning…
We study the problem of online learning (OL) from revealed preferences: a learner wishes to learn a non-strategic agent's private utility function through observing the agent's utility-maximizing actions in a changing environment. We adopt…
To expand the applicability of decentralized online learning, previous studies have proposed several algorithms for decentralized online continuous submodular maximization (D-OCSM) -- a non-convex/non-concave setting with continuous…
We study online learning in adversarial nonstationary environments. Since the future can be very different from the past, a critical challenge is to gracefully forget the history while new data comes in. To formalize this intuition, we…