ERM with f-divergence regularization yields unique solution.
problem Optimizing empirical risk with f-divergence. method Mild conditions on f lead to unique optimal measure. result Equivalence of ERM-fDR to different f-divergence regularization. Regularizes f-divergences with MMD to analyze Wasserstein flows.
problem Limitations of f-divergences in measures' support. method Rewriting MMD regularization as Moreau envelope in RKHS, analyzing gradients.
result Analysis of Wasserstein flows of MMD-regularized f-divergences. This work develops a unified framework for RLHF with general f-divergence regularization.
problem Theoretical understanding of general f-divergence regularization in RLHF. method Holistic approach across f-divergence class, two algorithms based on distinct sampling principles. result Provably efficient algorithms with O(logT) regret and O(1/T) sub-optimality gap. Optimal transport with f-divergence regularization using generalized Sinkhorn algorithm.
problem Optimal transport with f-divergence regularization. method Generalized Sinkhorn algorithm for solving optimal transport problems with various f-divergences. result Strong duality holds, optimums are attained, and convergence to an optimal solution is guaranteed under certain conditions.
Study on geometric Jensen-Shannon divergence for Gaussian measures in Hilbert space.
problem Computing divergence between Gaussian measures in infinite-dimensional Hilbert space.
method Closed form expression and regularization for divergence calculation.
result Closed form expression and regularization for Geometric Jensen-Shannon divergence.
Paper analyzes sample complexity for offline f-divergence-regularized contextual bandits.
problem Lack of tight analyses for sample complexity in offline reinforcement learning.
method Novel pessimism-based analysis for reverse KL divergence, establishing ildeO(ε−1) sample complexity. result Achieves ildeO(ε−1) sample complexity for reverse KL divergence, surpassing existing bounds. New divergences improve estimation and GAN training performance.
problem Improving estimation and training in machine learning models.
method Function-space regularized Rényi divergences.
result New divergences reduce variance and improve training performance.
The paper improves model robustness by regularizing posterior differences.
problem Improving model robustness in noisy input scenarios.
method Posterior differential regularization with f-divergence. result Regularizing with f-divergence improves model robustness. Proposes practical kernel tests for f-divergences with theoretical guarantees.
problem Two-sample testing and machine unlearning evaluation.
method Regularized f-divergence kernel tests, adaptive to hyperparameters. result Different f-divergences highlight localized differences. Proposes a guaranteed regularization method for maximum likelihood estimation using gauge symmetry in Kullback-Leibler divergence.
problem Overfitting in maximum likelihood estimation.
method Introduces a regularization approach based on gauge symmetry in Kullback-Leibler divergence.
result The method provides a theoretically guaranteed optimal model without frequent hyperparameter tuning.
New divergences help audit DP in high dimensions.
problem Challenges in auditing DP in high-dimensional data.
method Propose kernel Rényi divergence and its regularized version for auditing.
result Regularized kernel Rényi divergence can be estimated from samples in high dimensions.
CO2 algorithm creates coresets for generic smooth divergences efficiently.
problem Efficiently creating coresets for generic smooth divergences.
method CO2 algorithm using functional Taylor expansion and maximum mean discrepancy minimization.
result Poly-logarithmically many data points suffice for Sinkhorn divergence approximation.
The paper improves semi-supervised learning using f-divergences and α-Rényi divergences.
problem Improving semi-supervised learning with noisy pseudo-labels.
method Inspired by f-divergences and α-Rényi divergences, the paper develops new empirical risk functions and regularization techniques. result The new methods show better performance than traditional self-training methods, especially in noisy pseudo-label scenarios.
A new model corrects inhomogeneity in Optimal Transport with Boundary.
problem Inhomogeneity in UROT models for Optimal Transport with Boundary.
method Proposed a modified entropic regularization term to make UROT models homogeneous.
result Homogeneous UROT model preserves properties of standard UROT while correcting inhomogeneity.
Paper presents ERM with f-divergence regularization and its properties.
problem Minimizing empirical risk with f-divergence constraints. method Introduces normalization function and solves ERM-fDR via ODE. result Characterizes difference between empirical risks and provides numerical algorithm.
New aggregation strategy handles unbounded losses with regret bounds.
problem Online optimization with unbounded loss functions.
method Follow The Regularized Leader (FTRL) with φ-divergence.
result Worst regret bound for unbounded losses with alternative divergences.
New framework for logarithmically divergent integrals on manifolds with corners.
problem Logarithmically divergent integrals on manifolds with corners.
method Introduces new geometric framework and morphisms in logarithmic geometry.
result Functorial characterization of regularized integration.
This work improves convergence guarantees for unadjusted HMC in KL and Rényi divergences.
problem Understanding convergence properties of unadjusted HMC in divergences like KL and Rényi.
method One-shot couplings to establish regularization and lift convergence bounds.
result Quantitative control of relative density mismatch and warm-start requirements.
Reduced sample complexity for group-invariant distributions.
problem Improving sample complexity for estimating divergences of group-invariant distributions.
method Quantified reduction in sample complexity for Wasserstein-1 metric and Lipschitz-regularized α-divergences under finite and infinite groups.
result Sample complexity reduction proportional to group size for finite groups, and convergence rate depends on intrinsic dimension for infinite groups.
Study on convergence rates for optimal transport with regularization.
problem Convergence analysis of divergence-regularized optimal transport.
method Novel methodology using quantization and martingale couplings.
result Sharp rates for various divergences and transport costs.
Paper shows robust generative learning with minimal assumptions on target distributions.
problem Learning generative models with minimal assumptions on target distributions.
method Lipschitz-regularized α-divergences with minimal assumptions. result Stable learning across various target distributions with minimal assumptions.
Paper studies regularized KKL divergence for distributions with disjoint supports.
problem Inability of original KKL divergence to handle distributions with disjoint supports.
method Proposes a regularized variant of KKL divergence, derives bounds, and provides closed-form expression.
result Regularized KKL divergence is well-defined for all distributions and has finite-sample bounds.
Personalized sleep staging achieved with single-night data using KL-divergence regularization.
problem Improving automatic sleep staging accuracy with limited single-night data.
method KL-divergence regularization for transfer learning from a pretrained model to a personalized model.
result Personalized sleep staging accuracy of 79.6% with KL-divergence regularization.
Sliced-regularized OT improves transport plan accuracy.
problem Optimal transport (OT) approximation accuracy.
method Sliced-regularized optimal transport (SROT) formulation.
result SROT yields more accurate approximations of exact OT than entropic OT.
A new method for faster estimation of Wasserstein distance using Sinkhorn divergence.
problem Estimating the squared Wasserstein distance between probability distributions.
method Proposes a new estimator based on the Sinkhorn divergence with debiasing terms, and analyzes its sample complexity and computational efficiency.
result The proposed estimator allows higher regularization levels, leading to improved computational complexity and speedup in practice.
Paper proposes SinkhornDRL for distributional RL using Sinkhorn divergence and regularized Wasserstein loss.
problem Improving distributional reinforcement learning by minimizing Bellman return distribution differences.
method Introduces SinkhornDRL, a distributional RL algorithm using Sinkhorn divergence and regularized Wasserstein loss.
result SinkhornDRL consistently outperforms or matches existing algorithms on Atari games, especially in multi-dimensional reward settings.
This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to Bregman divergences. Our framework thus naturally generalizes a previously proposed …
KL-constrained API shows optimization issues and improved with regularization.
problem Optimization issues in KL-constrained API algorithms.
method Comparison of KL divergence as a constraint vs. regularizer, empirical evaluation.
result KL-constrained API is not guaranteed to converge and incurs linear regret.
Dual optimization connects ERM-fDR to normalization function.
problem Empirical risk minimization with f-divergence regularization.
method Dual formulation, Legendre-Fenchel transform, implicit function theorem, nonlinear ODE.
result Computational method to calculate normalization function efficiently.
In high-dimensional data, many sparse regression methods have been proposed. However, they may not be robust against outliers. Recently, the use of density power weight has been studied for robust parameter estimation and the corresponding divergences have been discussed. One of such divergences is the γ-divergence a…
The multiplicative update (MU) algorithm has been extensively used to estimate the basis and coefficient matrices in nonnegative matrix factorization (NMF) problems under a wide range of divergences and regularizers. However, theoretical convergence guarantees have only been derived for a few special divergences withou…
By introducing a refinement of the Goldman-Turaev Lie bialgebra, we interpret the divergence cocycle in the Kashiwara-Vergne problem and the Enomoto-Satoh obstructions for the surjectivity of the Johnson homomorphisms as some part of a regular homotopy version of the Turaev cobracket.
Unified framework for high-dimensional online learning with non-divergent error bounds and adaptive gains.
problem Divergence of error bounds in high-dimensional online learning as data batches increase.
method Asynchronous decomposition framework with summary statistics and dynamic regularization.
result Non-divergent error bounds and adaptive gains in sparse online optimization.
New approach to QFT divergences uses curved momentum space.
problem UV divergences in quantum field theory.
method Geodesic metric in curved momentum space.
result Intrinsic suppression of high-energy divergences.
Study statistical guarantees for DRO with OT and OT-regularized divergences.
problem Enhancing adversarial robustness in machine learning models.
method Derive concentration inequalities for supervised learning via DRO-based adversarial training.
result First to cover soft-constraint costs and reweighting mechanisms in adversarial training.
New algorithm stabilizes RL policy learning through divergence regularization.
problem Stabilize policy learning and improve performance in RL.
method Proximity term constraining discounted state-action visitation distributions to be close to each other.
result Proposed algorithm improves stability and final performance in RL tasks.
This work studies Gaussian geometry under entropy-regularized 2-Wasserstein distance.
problem Understanding Gaussian distributions in uncertainty quantification and diffusivity.
method Entropy-regularized 2-Wasserstein distance, closed-form solutions, fixed-point characterization.
result Closed-form expressions for the 2-Sinkhorn divergence and fixed-point barycenter.
Study convergence and approximations of entropic regularized Wasserstein distances for Gaussian and RKHS measures.
problem Convergence and approximations of entropic regularized Wasserstein distances in Gaussian and RKHS settings.
method Analysis of convergence and finite sample approximations of entropic regularized Wasserstein distances in Gaussian and RKHS settings.
result Strictly weaker convergence in 2-Sinkhorn divergence for Gaussian measures compared to exact 2-Wasserstein distance.
We study the Hadamard finite part of divergent integrals of differential forms with singularities on submanifolds. We give formulae for the dependence of the finite part on the choice of regularization and express them in terms of a suitable local residue map. The cases where the submanifold is a complex hypersurface i…
A new method learns robust policies from offline data with latent structures.
problem Conservative policies under unrealistic dynamics shifts.
method d-RRMDP framework with f-divergence regularization and R2PVI algorithm. result R2PVI learns robust policies with superior computational efficiency.
Study compares chi-squared divergence and KL-divergence posteriors for PAC-Bayesian bounds.
problem Investigates optimal posteriors for PAC-Bayesian bounds using chi-squared divergence.
method Analyzes bounds for three distance functions, derives FP equations for computation.
result Chi-squared divergence based posteriors have weaker bounds and worse test errors.
A new gradient flow for MMD with closed-form implementation.
problem Existing gradient flows either lack tractable numerical implementation or require strong assumptions.
method Introduces a (de)-regularized Maximum Mean Discrepancy (DrMMD) and its gradient flow.
result Guarantees near-global convergence for a broad class of targets in both continuous and discrete time.
Bayesian priors and penalties are equivalent in variational inference.
problem Understanding the relationship between Bayesian priors and penalties in variational inference.
method Characterizing the regularizers that can arise in variational inference and providing a systematic way to compute the prior corresponding to a given penalty.
result Equivalence between Bayesian priors and penalties in variational inference.
An optimal feedback controller for a given Markov decision process (MDP) can in principle be synthesized by value or policy iteration. However, if the system dynamics and the reward function are unknown, a learning agent must discover an optimal controller via direct interaction with the environment. Such interactive d…
The aim of this paper is to provide new theoretical and computational understanding on two loss regularizations employed in deep learning, known as local entropy and heat regularization. For both regularized losses we introduce variational characterizations that naturally suggest a two-step scheme for their optimizatio…
Generative adversarial network (GAN) is a minimax game between a generator mimicking the true model and a discriminator distinguishing the samples produced by the generator from the real training samples. Given an unconstrained discriminator able to approximate any function, this game reduces to finding the generative …
Unified ML and adversarial learning via α-divergence.
problem Combining strengths of ML and adversarial learning for better generative models.
method Proposes an α-Bridge to unify ML and adversarial learning using α-divergence.
result Generalizations of the α-Bridge are related to recent adversarial learning regularization approaches.
Proposes NRS to find flat minima in deep neural networks.
problem Finding optimal solutions in deep neural networks with overparameterization.
method NRS leverages the concept of flat minima and uses Kullback-Leibler divergence to regularize the neighborhood region in weight space.
result NRS drives optimizers towards flat minima, improving generalization ability across various model architectures.