New method tackles nonconvex-nonconcave problems with local KL condition.
problem Nonconvex-nonconcave minimax problems under varying KL conditions.
method Inexact proximal gradient method for KL-structured subproblems.
result Complexity guarantees for approximate stationary points.
Improved KL bounds and Wasserstein guarantees for diffusion flow matching under minimal conditions.
problem Theoretical convergence properties of Brownian motion based diffusion flow matching.
method Refined analysis under Kullback-Leibler and 2-Wasserstein distances.
result State-of-the-art scaling in KL convergence bounds under minimal conditions.
Conditional diffusion models can approximate target distributions well with Gaussian-mixture reverse kernels.
problem Approximating target distributions in conditional diffusion models.
method Using finite Gaussian mixtures with ReLU-network logits as reverse kernels, reducing the problem to static conditional density approximation.
result The resulting neural reverse-kernel class is dense in conditional KL divergence under exact terminal matching.
New bounds for sequential tests under power-one error levels.
problem Determining stopping times for sequential tests with power-one error levels.
method Proved two lower bounds for stopping times under specific conditions.
result Upper and lower bounds for sequential tests are shown to be tight.
Estimates KL divergence with fairness considerations for sub-populations.
problem Fairly estimate KL divergence between distributions considering sub-populations.
method Proposes multi-group attribution for KL divergence estimation, derived from multi-calibration.
result Shows multi-group attribution provides better KL divergence estimates conditioned on sub-populations.
New method solves complex constrained optimization problems.
problem Constrained nonconvex-nonconcave minimax optimization problems.
method Inexact proximal gradient method using sequential convex programming.
result Established complexity guarantees for approximate stationary points.
Kurdyka-Lojasiewicz (KL) exponent plays an important role in estimating the convergence rate of many contemporary first-order methods. In particular, a KL exponent of 21 for a suitable potential function is related to local linear convergence. Nevertheless, KL exponent is in general extremely hard to estimate. I…
Improved KL convergence bounds for score diffusion models without restrictive assumptions.
problem Lack of comprehensive quantitative results for diffusion models, especially in non-regular scores and estimators.
method Score diffusion models with fixed step size from Ornstein-Uhlenbeck and kinetic semigroups, providing explicit and sharp KL convergence bounds.
result Explicit and sharp convergence bounds in KL applicable to any data distribution with finite Fisher information.
Paper relaxes triangle inequality for KL divergence between Gaussian distributions.
problem KL divergence does not satisfy triangle inequality for Gaussian distributions.
method Investigates relaxed triangle inequality and finds supremum.
result Supremum of KL divergence is found and conditions for attaining it are determined.
New method learns disentangled signals without prior or model constraints.
problem Learning disentangled signals from data without prior or model constraints.
method Minimizes conditional KL divergence using a sequential algorithm to learn de-mixing flow models.
result Method learns self-sufficient signals that can reconstruct missing values.
FORE evaluates occupancy ratios without requiring Bellman completeness.
problem Offline reinforcement learning occupancy ratio estimation.
method Fitted occupancy-ratio evaluation (FORE) using adjoint Bellman recursion.
result FORE achieves convergence in KL without Bellman completeness.
EGMU optimizes portfolios using KL divergence, ensuring positive solutions.
problem Constructing multi-factor target-exposure portfolios efficiently and accurately.
method Convex optimization framework minimizing KL divergence, with explicit solvers.
result Established feasibility and uniqueness of strictly positive solutions under convex-hull conditions.
A1GM method improves efficiency in reconstructing missing data using KL divergence.
problem Efficiently reconstructing missing data in matrices.
method Fast non-gradient-based rank-1 NMF using KL divergence.
result A1GM outperforms gradient methods in efficiency with competitive reconstruction errors.
New algorithm for private non-convex optimization with optimal rates.
problem Private optimization of non-convex functions under KL condition.
method Variance-reduced gradient descent and proximal point method.
result Achieves nearly optimal rates for excess empirical risk.
Cubic-regularized Newton's method (CR) is a popular algorithm that guarantees to produce a second-order stationary solution for solving nonconvex optimization problems. However, existing understandings of the convergence rate of CR are conditioned on special types of geometrical properties of the objective function. In…
We quantify forgetting in post-training models, distinguishing mass and drift.
problem Understanding and preventing forgetting in post-training generative models.
method Developed theoretical results under a two-mode mixture abstraction, formalizing mass and drift forgetting.
result Forgetting can be precisely quantified based on divergence direction, geometric overlap, and training regime.
Decentralized Bayesian learning reduces KL-divergence exponentially.
problem Efficiently learning posterior distributions in a decentralized setting.
method Decentralized Langevin dynamics in a non-convex setting.
result The algorithm converges to the target posterior distribution with exponential decrease in KL-divergence and polynomial decrease in error contributions.
New samplers minimize KL divergence for constrained and non-Euclidean geometries.
problem Efficient sampling from constrained and non-Euclidean distributions.
method Stein Variational Mirror Descent and Mirrored Stein Variational Gradient Descent.
result New samplers converge more rapidly and accurately than prior methods.
New findings show many popular bandit algorithms are unstable, contradicting minimax optimality.
problem Challenges in statistical inference from bandit algorithms due to adaptive, non-i.i.d. nature.
method Analysis of stability properties of optimism-based bandit algorithms.
result Widely used minimax-optimal UCB-style algorithms are unstable.
EM algorithm converges in KL divergence for exponential families via mirror descent.
problem Lack of understanding of EM's non-asymptotic convergence properties.
method Viewing EM as a mirror descent algorithm, showing convergence rates in KL divergence.
result KL divergence rates for EM in exponential families, invariant to parametrization.
Study shows how neural networks generalize with minimal training data.
problem Understanding how neural networks generalize with limited data.
method Mean-field analysis of KL-regularized empirical risk minimization.
result Generalization error rate is O(1/n) for large n. This paper provides guarantees for DFM models using KL divergence.
problem Ensuring generative models match target distributions efficiently.
method Using KL divergence and Brownian motion bridge for generative models.
result Non-asymptotic guarantees for DFM models under specific conditions.
Paper develops a method to compare generative models using KL divergence.
problem Lack of principled uncertainty quantification for generative models.
method Employ Kullback-Leibler divergence to measure generative model distance.
result Effective coverage rates and higher power compared to kernel-based methods.
Paper analyzes inclusive KL inference using Wasserstein gradient flows.
problem Analyzing inclusive KL inference with mathematical tools.
method Gradient flows derived from PDE analysis.
result Unified view of existing sampling algorithms as inclusive-KL inference.
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.
TSC uses HMC and adaptive transport maps to optimize forward KL for variational inference.
problem Variational inference underestimates uncertainty when minimizing reverse KL.
method TSC uses Hamiltonian Monte Carlo and adaptive transport maps to optimize KL(p||q).
result TSC achieves competitive performance in training variational autoencoders on large-scale data.
A classic setting of the stochastic K-armed bandit problem is considered in this note. In this problem it has been known that KL-UCB policy achieves the asymptotically optimal regret bound and KL-UCB+ policy empirically performs better than the KL-UCB policy although the regret bound for the original form of the KL-UCB…
We analyze the Kozachenko--Leonenko (KL) nearest neighbor estimator for the differential entropy. We obtain the first uniform upper bound on its performance over Hölder balls on a torus without assuming any conditions on how close the density could be from zero. Accompanying a new minimax lower bound over the Hölder ba…
Paper bridges VAEs and KDEs for more flexible posterior estimation.
problem Limitations of Gaussian latent space in VAEs and challenges in KL-divergence estimation.
method Approximate posterior with KDEs and derive upper bound of KL-divergence in ELBO.
result Epanechnikov kernel minimizes KL-divergence upper bound asymptotically.
Improved fast rates for decision making with forward-KL regularization in contextual bandits.
problem Improving fast rates for decision making with forward-KL regularization in contextual bandits.
method Streamlined analysis of forward-KL-regularized offline CBs, exploiting the pessimism principle and convex-analytical pipeline.
result First ildeO(ε−1) upper bounds in tabular and general function approximation settings. Causal KL improves on existing metrics for evaluating causal models.
problem Insufficient discrimination between causal models using edit-distance and KL divergence.
method Introducing Causal KL, an augmented KL divergence that considers causal relationships.
result Causal KL variants effectively distinguish between observationally equivalent models.
New algorithm minimizes inclusive KL for VI, improving accuracy.
problem Improving variational inference accuracy with KL(p||q).
method Markovian score climbing (MSC) using stochastic gradients.
result MSC converges to local optimum of inclusive KL without bias.
We consider the problem of training probabilistic conditional random fields (CRFs) in the context of a task where performance is measured using a specific loss function. While maximum likelihood is the most common approach to training CRFs, it ignores the inherent structure of the task's loss function. We describe alte…
Sharp analysis improves RLHF sample complexity with KL-regularization.
problem Improving RLHF sample complexity with KL-regularization.
method Sharp analysis of KL-regularized contextual bandits and RLHF.
result Achieved an O(1/ε) sample complexity when ε is sufficiently small.
New method uses quotient predictor space for better PAC-Bayes bounds, reducing KL divergence and improving model performance.
problem Overparameterized models with continuous symmetries can lead to biased predictions.
method Perform PAC-Bayesian analysis on quotient predictor space, constructing a canonical prior that reflects model's implicit bias.
result The new prior reduces KL divergence and improves model performance in experiments.
The paper finds the optimal wealth growth rate in betting games.
problem Optimizing wealth growth in Kelly betting games against arbitrary hypotheses.
method Analyzes the growth rate using KL divergence and proves it equals a specific limit.
result The optimal wealth growth rate is characterized and proven to be achievable.
The paper develops new algorithms for KL-divergence NMF, proving convergence and performance.
problem Improving NMF for nonnegative data with KL divergence.
method Collect and analyze properties of KL objective function, propose and test new algorithms.
result Guaranteed non-increasing objective function for one proposed algorithm, global convergence.
Logit distance bounds representational similarity of models.
problem Approximating linear similarity when distributions are close.
method Defined a logit distance and proved its relationship to representational dissimilarity.
result Logit distance bounds representational similarity, providing nontrivial control in practice.
This paper tightens the law of the iterated logarithm for empirical KL_inf, applicable to unbounded data.
problem Developing nonasymptotic concentration bounds for empirical KL_inf with optimal constants and rates.
method Presenting a tight law of the iterated logarithm for empirical KL_inf, applicable to unbounded data.
result A tight law of the iterated logarithm for empirical KL_inf, applicable to unbounded data.
Paper analyzes and improves KL-regularized RL for LLMs with logarithmic regret.
problem Improving efficiency of RL fine-tuning for large language models.
method Optimism-based KL-regularized online contextual bandit algorithm with novel regret analysis.
result Achieves an O(ηlog(NRT)⋅dR) logarithmic regret bound. Beta diffusion generates bounded data using multiplicative transitions.
problem Generating data within specific ranges.
method Integrates demasking and denoising with scaled and shifted beta distributions.
result KLUBs are more effective for optimizing beta diffusion compared to negative ELBOs.
Stein variational gradient descent (SVGD) is a deterministic sampling algorithm that iteratively transports a set of particles to approximate given distributions, based on an efficient gradient-based update that guarantees to optimally decrease the KL divergence within a function space. This paper develops the first th…
Paper analyzes risk bounds for in-context learning in multiclass classification.
problem Risk bounds for in-context learning in multiclass classification.
method Formalizes tasks as sequences of labeled examples and queries, estimates conditional class probabilities, establishes oracle inequality for KL divergence.
result ICL achieves minimax optimal rate for conditional probability estimation.
Paper derives convergence rates for NPMLE in Hellinger distance using deep neural networks.
problem Difficulty in proving convergence of excess risk in nonparametric logistic regression.
method Unified approach for analyzing NPMLE, deriving convergence rates in Hellinger distance.
result Derives nearly optimal convergence rates for NPMLE with deep neural networks.
Theory for RLHF generalization under reward shift and clipped KL.
problem Theoretical understanding of RLHF generalization, especially with reward shift and clipped KL.
method Developed generalization theory for RLHF, accounting for reward shift and clipped KL.
result Presented generalization bounds for RLHF, suggesting generalization error from sampling, reward shift, and KL clipping.
KALE flow approximates KL divergence for distributions with disjoint support.
problem Approximating KL divergence for distributions with disjoint support.
method Relaxed KL gradient flow using RKHS, continuously interpolating between KL and MMD.
result Global convergence of KALE flow under sufficient smoothness assumptions.
Rényi Neural Processes replace KL divergence with Rényi divergence to improve NP performance.
problem Parameterization coupling in Neural Processes leads to prior misspecification.
method Propose Rényi Neural Processes (RNP) by replacing KL divergence with Rényi divergence.
result Significant performance improvements in real-world problems, including better log-likelihoods.
The Dirichlet mechanism protects privacy while minimizing KL divergence.
problem Minimizing KL divergence while protecting sensitive data privacy.
method Using the exponential mechanism with the KL divergence loss function, resulting in the Dirichlet mechanism.
result Proved a probability tail bound on KL divergence and derived a lower bound for sample complexity.