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In this paper, we study the non-monotone DR-submodular function maximization over integer lattice. Functions over integer lattice have been defined submodular property that is similar to submodularity of set functions. DR-submodular is a…
Submodular functions are an important class of functions in combinatorial optimization which satisfy the natural properties of decreasing marginal costs. The study of these functions has led to strong structural properties with applications…
We study streaming submodular maximization subject to matching/$b$-matching constraints (MSM/MSbM), and present improved upper and lower bounds for these problems. On the upper bounds front, we give primal-dual algorithms achieving the…
This paper focuses on an online version of the emerging distributed constrained aggregative optimization framework, which is particularly suited for applications arising in cooperative robotics. Agents in a network want to minimize the sum…
This paper is devoted to the study of an inertial accelerated primal-dual algorithm, which is based on a second-order differential system with time scaling, for solving a non-smooth convex optimization problem with linear equality…
We propose a theoretical framework to capture incremental solutions to cardinality constrained maximization problems. The defining characteristic of our framework is that the cardinality/support of the solution is bounded by a value…
We show how to restrict the analysis of a class of online problems that includes the $k$-server problem in finite metrics such that we only have to consider finite sequences of request. When applying the restrictions, both the optimal…
We provide theoretical bounds on the worst case performance of the greedy algorithm in seeking to maximize a normalized, monotone, but not necessarily submodular objective function under a simple partition matroid constraint. We also…
This paper considers the basic problem of scheduling jobs online with preemption to maximize the number of jobs completed by their deadline on $m$ identical machines. The main result is an $O(1)$ competitive deterministic algorithm for any…
Online safe reinforcement learning (RL) plays a key role in dynamic environments, with applications in autonomous driving, robotics, and cybersecurity. The objective is to learn optimal policies that maximize rewards while satisfying safety…
We study offline constrained reinforcement learning from human feedback with multiple preference oracles. Motivated by applications that trade off performance with safety or fairness, we aim to maximize target population utility subject to…
This paper investigates the asymptotic and non-asymptotic behavior of the quantized primal dual algorithm in network utility maximization problems, in which a group of agents maximize the sum of their individual concave objective functions…
This paper studies an online optimal resource reservation problem in communication networks with job transfers where the goal is to minimize the reservation cost while maintaining the blocking cost under a certain budget limit. To tackle…
Makespan minimization on identical machines is a fundamental problem in online scheduling. The goal is to assign a sequence of jobs to $m$ identical parallel machines so as to minimize the maximum completion time of any job. Already in the…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
Recent literature on online learning has focused on developing adaptive algorithms that take advantage of a regularity of the sequence of observations, yet retain worst-case performance guarantees. A complementary direction is to develop…
In this paper, we study the problem of minimizing a sum of convex objective functions, which are locally available to agents in a network. Distributed optimization algorithms make it possible for the agents to cooperatively solve the…
We study the relationship between the competitive ratio and the tail distribution of randomized online minimization problems. To this end, we define a broad class of online problems that includes some of the well-studied problems like…
Maximizing submodular objectives under constraints is a fundamental problem in machine learning and optimization. We study the maximization of a nonnegative, non-monotone $\gamma$-weakly DR-submodular function over a down-closed convex…
We study a family of potential functions for online learning. We show that if the potential function has strictly positive derivatives of order 1-4 then the min-max optimal strategy for the adversary is Brownian motion. Using that fact we…