Related papers: Information-theoretic minimax and submodular optim…

Constrained submodular function maximization has been used in subset selection problems such as selection of most informative sensor locations. While these models have been quite popular, the solutions Constrained submodular function…

We study a general class of convex submodular optimization problems with indicator variables. Many applications such as the problem of inferring Markov random fields (MRFs) with a sparsity or robustness prior can be naturally modeled in…

In this paper, we propose an improved numerical algorithm for solving minimax problems based on nonsmooth optimization, quadratic programming and iterative process. We also provide a rigorous proof of convergence for our algorithm under…

Multiplex networks are a common modeling framework for interconnected systems and multimodal data, yet we still lack fundamental insights for how multiplexity affects stochastic processes. We introduce a novel ``Markov chains of Markov…

In this paper we consider a distributed optimization scenario in which a set of processors aims at cooperatively solving a class of min-max optimization problems. This set-up is motivated by peak-demand minimization problems in smart grids.…

We study minimax optimal reinforcement learning in episodic factored Markov decision processes (FMDPs), which are MDPs with conditionally independent transition components. Assuming the factorization is known, we propose two model-based…

Majority-vote ensembles achieve variance reduction by averaging over diverse, approximately independent base learners. When training data exhibits Markov dependence, as in time-series forecasting, reinforcement learning (RL) replay buffers,…

To date, no "information-theoretic" frameworks for reasoning about generalization error have been shown to establish minimax rates for gradient descent in the setting of stochastic convex optimization. In this work, we consider the prospect…

In information theory, some optimization problems result in convex optimization problems on strictly convex functionals of probability densities. In this note, we study these problems and show conditions of minimizers and the uniqueness of…

Batch policy optimization considers leveraging existing data for policy construction before interacting with an environment. Although interest in this problem has grown significantly in recent years, its theoretical foundations remain…

Variational quantum algorithms are poised to have significant impact on high-dimensional optimization, with applications in classical combinatorics, quantum chemistry, and condensed matter. Nevertheless, the optimization landscape of these…

Matrix rank minimization problems are gaining a plenty of recent attention in both mathematical and engineering fields. This class of problems, arising in various and across-discipline applications, is known to be NP-hard in general. In…

We consider a latent space model for dynamic networks, where our objective is to estimate the pairwise inner products plus the intercept of the latent positions. To balance posterior inference and computational scalability, we consider a…

We pose the Kantorovich optimal transport problem as a min-max problem with a Nash equilibrium that can be obtained dynamically via a two-player game, providing a framework for approximating optimal couplings. We prove convergence of the…

Motivated by distributed statistical learning over uncertain communication networks, we study distributed stochastic optimization by networked nodes to cooperatively minimize a sum of convex cost functions. The network is modeled by a…

We study optimal liquidation strategies under partial information for a single asset within a finite time horizon. We propose a model tailored for high-frequency trading, capturing price formation driven solely by order flow through…

The capability of discretization of matrix elements in the problem of quadratic functional minimization with linear member built on matrix in N-dimensional configuration space with discrete coordinates is researched. It is shown, that…

Avoiding overfitting is a central challenge in machine learning, yet many large neural networks readily achieve zero training loss. This puzzling contradiction necessitates new approaches to the study of overfitting. Here we quantify…

We consider Bayesian optimization of an expensive-to-evaluate black-box objective function, where we also have access to cheaper approximations of the objective. In general, such approximations arise in applications such as reinforcement…

We study the problem of designing minimax procedures in linear regression under the quantile risk. We start by considering the realizable setting with independent Gaussian noise, where for any given noise level and distribution of inputs,…