arXiv research

The paper studies convergence rates of Tsallis entropic regularization in optimal transport.

Improved optimal regularity for harmonic almost complex structures.

The paper explores optimal regularizers for data sources, linking them to star bodies.

Study on convergence rates for optimal transport with regularization.

Study on regularity of optimal transport maps on convex domains with quadratic cost.

Adaptive reduction scheme approximates optimal policy in regularized MDPs.

Extends optimal regularity and compactness to vector bundles over non-Riemannian manifolds.

Study optimal ridge regularization for out-of-distribution prediction.

We propose and study a general framework for regularized Markov decision processes (MDPs) where the goal is to find an optimal policy that maximizes the expected discounted total reward plus a policy regularization term. The extant entropy-regularized MDPs can be cast into our framework. Moreover, under our framework, …

Tikhonov regularization is robust under specific martingale constraints in distributionally robust optimization.

Optimizes biharmonic map regularity using stratification methods.

New framework for robust regularization under uncertain data distributions.

Study optimal transport on simplex boundary, proving transport map and potential regularity.

New method averages SGD iterates to achieve adjustable regularization.

Study uses property elicitation to understand how fairness regularizers affect optimal decisions.

Proposes reducing random error in stochastic optimization by variance regularization.

Paper develops a method to learn optimal sparsity-promoting regularizers for linear inverse problems.

Entropy regularized algorithms such as Soft Q-learning and Soft Actor-Critic, recently showed state-of-the-art performance on a number of challenging reinforcement learning (RL) tasks. The regularized formulation modifies the standard RL objective and thus generally converges to a policy different from the optimal gree…

Weight decay is one of the standard tricks in the neural network toolbox, but the reasons for its regularization effect are poorly understood, and recent results have cast doubt on the traditional interpretation in terms of $L_2$ regularization. Literal weight decay has been shown to outperform $L_2$ regularization for…

The optimization of the variance supplemented by a budget constraint and an asymmetric $\ell_1$ regularizer is carried out analytically by the replica method borrowed from the theory of disordered systems. The asymmetric regularizer allows us to penalize short and long positions differently, so the present treatment in…

This paper explores how entropic regularization improves Wasserstein estimators' performance.

New approach to portfolio optimization shows entropy regularization is ineffective.

Optimal regularization can prevent the double descent phenomenon in learning models.

Paper introduces robust market making using Wasserstein distance and entropy regularization.

Study MinMax methods for optimization problems, including optimal transport.

Algorithm finds optimal regularizers for online linear optimization.

Unified framework for understanding and optimizing training acceleration.

Regularized policies are robust to adversarial rewards.

Regularization can improve machine learning models' robustness against poisoning attacks.

Optimal ridge regularization computed iteratively from generative parameters.

Proves optimal regularity for sphere minimizers in 3-sphere.

Path regularization reveals convex optimization in deep ReLU networks.

PAR provides a flexible framework for quantization in optimization problems.

In this paper we combine two important extensions of ordinary least squares regression: regularization and optimal scaling. Optimal scaling (sometimes also called optimal scoring) has originally been developed for categorical data, and the process finds quantifications for the categories that are optimal for the regres…

DRAG decreases regularization to accelerate semi-discrete OT convergence.

Many machine learning algorithms minimize a regularized risk, and stochastic optimization is widely used for this task. When working with massive data, it is desirable to perform stochastic optimization in parallel. Unfortunately, many existing stochastic optimization algorithms cannot be parallelized efficiently. In t…

Trajectory optimization using a learned model of the environment is one of the core elements of model-based reinforcement learning. This procedure often suffers from exploiting inaccuracies of the learned model. We propose to regularize trajectory optimization by means of a denoising autoencoder that is trained on the …

We present an adaptive regularization algorithm that can be effectively applied to the optimization problem in deep learning framework. Our regularization algorithm aims to take into account the fitness of data to the current state of model in the determination of regularity to achieve better generalization. The degree…

Develops regularity theory for Beckmann's optimal transport problem.

Introduces self-regularization for analyzing learning algorithms.

Paper analyzes sample complexity of offline MABs with KL regularization.

New method smooths optimization for sparse regularization.

The use of convex regularizers allows for easy optimization, though they often produce biased estimation and inferior prediction performance. Recently, nonconvex regularizers have attracted a lot of attention and outperformed convex ones. However, the resultant optimization problem is much harder. In this paper, for a …

Study optimal transport on globally hyperbolic spacetimes, focusing on weak Kantorovich potentials' regularity.

A new model corrects inhomogeneity in Optimal Transport with Boundary.

New regularizer for machine learning using private data.

We propose a general framework for entropy-regularized average-reward reinforcement learning in Markov decision processes (MDPs). Our approach is based on extending the linear-programming formulation of policy optimization in MDPs to accommodate convex regularization functions. Our key result is showing that using the …

New algorithm stabilizes bi-level hyperparameter optimization.