arXiv research

New algorithms solve monotone inclusions and convex-concave minimax problems.

Non-affine aggregation rules cannot preserve monotonicity in convex learning.

Improved algorithms for convex-concave min-max optimization and monotone variational inequalities.

The paper addresses how to complete incomplete risk markets by iteratively enhancing welfare.

COMET learns monotonic neural networks by incorporating counterexamples.

A new algorithm finds minimizers in dueling optimization with a monotone adversary.

EPEM efficiently estimates parameters for monotone missing data.

This paper analyzes and improves monotonic accelerated algorithms like M-NAG and M-FISTA.

Survey on extragradient methods for solving nonlinear equations and inclusions.

New iterative schemes solve Yamabe-type equations on closed manifolds.

Fast algorithm recovers principal eigenvector from noisy matrices.

A method for inferring ground-truth signals from degraded sensor data.

A key problem in reinforcement learning for control with general function approximators (such as deep neural networks and other nonlinear functions) is that, for many algorithms employed in practice, updates to the policy or $Q$-function may fail to improve performance---or worse, actually cause the policy performance …

FLOWGEM generates complete datasets from incomplete data with non-monotone MAR missingness.

New ODE models show saddle-point optimization methods converge differently, with last-iterate convergence for OGDA.

New model outperforms Neural ODEs while being more efficient.

New method identifies causal order without sparsity assumptions.

The article classifies curvature functions on compact manifolds with boundaries.

New algorithm solves fair PCA, robust PCA, and sparse PCA problems efficiently.

We consider applications of the theory of balanced weight filtrations and iterated logarithms, initiated in arXiv:1706.01073, to PDEs. The main result is a complete description of the asymptotics of the Yang--Mills flow on the space of metrics on a holomorphic bundle over a Riemann surface. A key ingredient in the argu…

This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their applicability remains limited when the problem dimension is large and the projecti…

As surrogate functions of $L_0$-norm, many nonconvex penalty functions have been proposed to enhance the sparse vector recovery. It is easy to extend these nonconvex penalty functions on singular values of a matrix to enhance low-rank matrix recovery. However, different from convex optimization, solving the nonconvex l…

Support vector machines (SVMs) are an important tool in modern data analysis. Traditionally, support vector machines have been fitted via quadratic programming, either using purpose-built or off-the-shelf algorithms. We present an alternative approach to SVM fitting via the majorization--minimization (MM) paradigm. Alg…

Last-iterate guarantees for learning in co-coercive games under noisy feedback.

Solves capillary curvature problems for specific p values.

DM framework improves robustness and efficiency in latent-mixture models.

GD at EoS edge minimizes logistic loss without monotonic convergence.

DSPI connects natural policy gradient to policy iteration, proving global convergence.

Paper develops an online covariance estimator for nonsmooth stochastic approximation problems.

Single-timescale analysis improves convergence in multi-sequence stochastic approximation.

GD iterates for non-homogeneous deep nets increase margin and converge in direction.

Market makers optimize trading with a new implicit scheme for complex inequalities.

Generalising the idea of the classical EM algorithm that is widely used for computing maximum likelihood estimates, we propose an EM-Control (EM-C) algorithm for solving multi-period finite time horizon stochastic control problems. The new algorithm sequentially updates the control policies in each time period using Mo…

In this paper, we study the problem of monotone (weakly) DR-submodular continuous maximization. While previous methods require the gradient information of the objective function, we propose a derivative-free algorithm LDGM for the first time. We define $β$ and $α$ to characterize how close a function is to continuous D…

New insights into stochastic methods for solving variational inequalities.

A new family of momentum coefficients improves the convergence rate of accelerated algorithms.

This paper considers a cross-layer adaptive modulation system that is modeled as a Markov decision process (MDP). We study how to utilize the monotonicity of the optimal transmission policy to relieve the computational complexity of dynamic programming (DP). In this system, a scheduler controls the bit rate of the m-qu…

In this paper, wireless video transmission to multiple users under total transmission power and minimum required video quality constraints is studied. In order to provide the desired performance levels to the end-users in real-time video transmissions while using the energy resources efficiently, we assume that power c…

A new ML algorithm solves complex economic control problems.

New method for optimistic planning in MDPs using regularization.

Proximal policy optimization and trust region policy optimization (PPO and TRPO) with actor and critic parametrized by neural networks achieve significant empirical success in deep reinforcement learning. However, due to nonconvexity, the global convergence of PPO and TRPO remains less understood, which separates theor…

Generalized Linear Models (GLMs) and Single Index Models (SIMs) provide powerful generalizations of linear regression, where the target variable is assumed to be a (possibly unknown) 1-dimensional function of a linear predictor. In general, these problems entail non-convex estimation procedures, and, in practice, itera…

Paper proposes a new co-clustering method for overlapping clusters and outliers.

Motivated by applications in Game Theory, Optimization, and Generative Adversarial Networks, recent work of Daskalakis et al \cite{DISZ17} and follow-up work of Liang and Stokes \cite{LiangS18} have established that a variant of the widely used Gradient Descent/Ascent procedure, called "Optimistic Gradient Descent/Asce…

RRPI improves offline RL by optimizing policies against worst-case dynamics.

The L1 loss landscape of neural nets near local minima behaves differently, revealing exponential decay and increased vertex density.

The paper addresses monotonicity in machine learning models for fairness and accountability.

In this article, we introduce a mass-decreasing flow for asymptotically flat three-manifolds with nonnegative scalar curvature. This flow is defined by iterating a suitable Ricci flow with surgery and conformal rescalings and has a number of nice properties. In particular, wormholes pinch off and nontrivial spherical s…