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This paper studies online convex optimization with unknown linear budget constraints, where only the gradient information of the objective and the bandit feedback of constraint functions are observed. We propose a safe and efficient…
Motivated by alternating learning dynamics in two-player games, a recent work by Cevher et al.(2024) shows that $o(\sqrt{T})$ alternating regret is possible for any $T$-round adversarial Online Linear Optimization (OLO) problem, and left as…
Decentralized optimization methods often entail information exchange between neighbors. Transmission failures can happen due to network congestion, hardware/software issues, communication outage, and other factors. In this paper, we…
In this paper, the mixed equilibrium problem with coupled inequality constraints in dynamic environments is solved by employing a multi-agent system, where each agent only has access to its own bifunction, its own constraint function, and…
This paper studies bandit convex optimization in non-stationary environments with two-point feedback, using dynamic regret as the performance measure. We propose an algorithm based on bandit mirror descent that extends naturally to…
In this paper, we study dynamic regret in unconstrained online convex optimization (OCO) with movement costs. Specifically, we generalize the standard setting by allowing the movement cost coefficients $\lambda_t$ to vary arbitrarily over…
We address the problem of simultaneously learning and control in an online receding horizon control setting. We consider the control of an unknown linear dynamical system with general cost functions and affine constraints on the control…
Recently, several universal methods have been proposed for online convex optimization which can handle convex, strongly convex and exponentially concave cost functions simultaneously. However, most of these algorithms have been designed…
This paper introduces a new problem-dependent regret measure for online convex optimization with smooth losses. The notion, which we call the $G^\star$ regret, depends on the cumulative squared gradient norm evaluated at the decision in…
We study the problem of $K$-armed dueling bandit for both stochastic and adversarial environments, where the goal of the learner is to aggregate information through relative preferences of pair of decisions points queried in an online…
We consider the problem of online learning in Linear Quadratic Control systems whose state transition and state-action transition matrices $A$ and $B$ may be initially unknown. We devise an online learning algorithm and provide guarantees…
We consider the online convex optimization problem. In the setting of arbitrary sequences and finite set of parameters, we establish a new fast-rate quantile regret bound. Then we investigate the optimization into the L1-ball by…
In this paper, we study a class of online optimization problems with long-term budget constraints where the objective functions are not necessarily concave (nor convex) but they instead satisfy the Diminishing Returns (DR) property.…
In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then,…
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…
Modern control designs in robotics, aerospace, and cyber-physical systems rely heavily on real-world data obtained through system outputs. However, these outputs can be compromised by system faults and malicious attacks, distorting critical…
A Multi-Agent Cooperative Learning (MACL) system is an artificial intelligence (AI) system where multiple learning agents work together to complete a common task. Recent empirical success of MACL systems in various domains (e.g. traffic…
We consider the problem of online regret minimization in linear bandits with access to prior observations (offline data) from the underlying bandit model. There are numerous applications where extensive offline data is often available, such…
This paper examines online distributed Alternating Direction Method of Multipliers (ADMM). The goal is to distributively optimize a global objective function over a network of decision makers under linear constraints. The global objective…
We study online convex optimization with constraints consisting of multiple functional constraints and a relatively simple constraint set, such as a Euclidean ball. As enforcing the constraints at each time step through projections is…