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A novel Follow-the-Perturbed-Leader type algorithm is proposed and analyzed for solving general long-term constrained optimization problems in an online manner, where the target and constraint functions are oblivious adversarially generated…

In this paper we study two-player bilinear zero-sum games with constrained strategy spaces. An instance of natural occurrences of such constraints is when mixed strategies are used, which correspond to a probability simplex constraint. We…

In the online non-stochastic control problem, an agent sequentially selects control inputs for a linear dynamical system when facing unknown and adversarially selected convex costs and disturbances. A common metric for evaluating control…

We consider a decentralized online convex optimization problem in a network of agents, where each agent controls only a coordinate (or a part) of the global decision vector. For such a problem, we propose two decentralized variants (ODA-C…

Modern policy optimization methods roughly follow the policy mirror descent (PMD) algorithmic template, for which there are by now numerous theoretical convergence results. However, most of these either target tabular environments, or can…

We introduce an online convex optimization algorithm which utilizes projected subgradient descent with optimal adaptive learning rates. Our method provides second-order minimax-optimal dynamic regret guarantee (i.e. dependent on the sum of…

We study the problems of distributed online and bandit convex optimization against an adaptive adversary. We aim to minimize the average regret on $M$ machines working in parallel over $T$ rounds with $R$ intermittent communications.…

In recent years, attention has been focused on the relationship between black-box optimiza- tion problem and reinforcement learning problem. In this research, we propose the Mirror Descent Search (MDS) algorithm which is applicable both for…

This paper addresses an online convex optimization problem where the cost function at each step depends on a history of past decisions (i.e., memory), and the decision maker has access to limited predictions of future cost values within a…

Many techniques for online optimization problems involve making decisions based solely on presently available information: fewer works take advantage of potential predictions. In this paper, we discuss the problem of online convex…

We address online linear optimization problems when the possible actions of the decision maker are represented by binary vectors. The regret of the decision maker is the difference between her realized loss and the best loss she would have…

Guided policy search algorithms can be used to optimize complex nonlinear policies, such as deep neural networks, without directly computing policy gradients in the high-dimensional parameter space. Instead, these methods use supervised…

We consider the online control problem with an unknown linear dynamical system in the presence of adversarial perturbations and adversarial convex loss functions. Although the problem is widely studied in model-based control, it remains…

This paper is concerned with convergence analysis for the mirror descent (MD) method, a well-known algorithm in convex optimization. An analysis framework via integral quadratic constraints (IQCs) is constructed to analyze the convergence…

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…

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…

This paper presents a comprehensive convergence analysis for the mirror descent (MD) method, a widely used algorithm in convex optimization. The key feature of this algorithm is that it provides a generalization of classical gradient-based…

In this work we consider the online control of a known linear dynamic system with adversarial disturbance and adversarial controller cost. The goal in online control is to minimize the regret, defined as the difference between cumulative…

We consider a stochastic inventory control problem under censored demands, lost sales, and positive lead times. This is a fundamental problem in inventory management, with significant literature establishing near-optimality of a simple…

We study safe reinforcement learning in finite-horizon linear mixture constrained Markov decision processes (CMDPs) with adversarial rewards under full-information feedback and an unknown transition kernel. We propose a primal-dual policy…