Improved KL divergence estimators for normalizing flows lead to faster convergence and better approximations.
problem Estimating KL divergences for normalizing flows efficiently and accurately.
method Path-gradient estimators for reverse and forward KL divergences.
result Path-gradient estimators lead to faster convergence and better approximation results.
New AI method generates SDE paths without explicit coefficients.
problem Simulating unknown Markovian SDEs with limited data.
method Uses conditional diffusion models on sample paths.
result Consistently outperforms alternative methods in KL divergence.
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.
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.
The study explores geodesics and KL-divergence on Hölder equilibrium probabilities.
problem Finding the probability that minimizes KL-divergence from a fixed probability in a convex set of probabilities.
method Analyzes geodesics paths on the manifold of Hölder equilibrium probabilities and uses KL-divergence as a metric.
result Explicit equations for the solution of the minimization problem are derived.
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.
New bounds close the score matching gap for diffusion models.
problem The difference between sample quality and score matching loss in diffusion models.
method Theoretical analysis of score matching gap, developing tighter bounds for KL divergence, reverse KL divergence, and Wasserstein distance.
result The quality of score approximation impacts closing the score matching gap for low noise scales.
CR-AIS improves AIS efficiency by constant rate annealing.
problem Efficiently sample from intractable distributions.
method Constant rate annealing schedule for AIS.
result CR-AIS outperforms existing Adaptive AIS methods.
Develops a method for learning proposals in nested importance samplers.
problem Improving sampling quality in complex distributions.
method Nested Variational Inference (NVI) using forward or reverse KL divergence.
result Optimizing nested objectives leads to improved sample quality.
Estimates Schrödinger potentials with minimal sample size.
problem Estimating Schrödinger potentials for generative modeling.
method Empirical Kullback-Leibler risk minimizer over log-potentials.
result Excess KL-risk decreases as fast as O ( log 2 n / n ) O(\log^2 n / n) O ( log 2 n / n ) . Improves inference-time alignment for diffusion models without updating weights.
problem Aligning diffusion models without updating weights for high-reward outputs.
method Trust-Region Iterative Twisted Sequential Monte Carlo (TRI-TSMC) for variance reduction and efficiency.
result Improves primary alignment objectives on text generation tasks.
Generative model prices basket options efficiently.
problem Real-time pricing of basket options with varying market inputs.
method Truncated path signatures and Mixture Density Networks (MDN) for learning the terminal density.
result The model produces small pricing errors and matches Monte Carlo simulations closely.
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.
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 propose to use deep neural networks for generating samples in Monte Carlo integration. Our work is based on non-linear independent components estimation (NICE), which we extend in numerous ways to improve performance and enable its application to integration problems. First, we introduce piecewise-polynomial couplin…
Unified framework for understanding TVO and improving model learning.
problem Improving the tightness and efficiency of variational inference bounds.
method Exponential family interpretation and equal spacing in moment parameters.
result Unified framework and improved gradient estimator for TVO.
A discrete diffusion model learns denoising, scoring, and bridging in different coordinates.
problem Understanding what a discrete diffusion model learns in different coordinate systems.
method Rigorous derivation of continuous-time Markov chain ELBO, Oracle Distance theorem, and exact coordinates for optimizer.
result The negative ELBO is exactly equal to the data entropy plus the path KL from the oracle reverse process to the learned one.
Analyzed a generative model framework through Wasserstein Gradient Flow.
problem Generative modeling challenges.
method Wasserstein Gradient Flow (WGF) interpretation of Drifting Models (GMD).
result Different algorithms correspond to specific limiting points of WGFs on various divergences.
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 i l d e O ( ε − 1 ) ilde{O}(ε^{-1}) i l d e O ( 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.
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.
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 1 2 \frac12 2 1 for a suitable potential function is related to local linear convergence. Nevertheless, KL exponent is in general extremely hard to estimate. I…
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.
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 ( η log ( N R T ) ⋅ d R ) \mathcal{O}\big(η\log (N_{\mathcal R} T)\cdot d_{\mathcal R}\big) O ( η log ( N R T ) ⋅ d R ) logarithmic regret bound. 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.
We consider the problem of function approximation by two-layer neural nets with random weights that are "nearly Gaussian" in the sense of Kullback-Leibler divergence. Our setting is the mean-field limit, where the finite population of neurons in the hidden layer is replaced by a continuous ensemble. We show that the pr…
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.
Pathfinder uses quasi-Newton optimization for variational inference.
problem Approximating complex posterior distributions efficiently.
method Pathfinder combines quasi-Newton optimization with variational methods to approximate log densities.
result Pathfinder produces draws with lower KL divergence than ADVI and comparable to HMC, requiring fewer evaluations.
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.
Improved bounds for estimating discrete distributions in KL divergence.
problem Estimating discrete distributions in KL divergence with accuracy.
method Used Laplace estimator and established concentration bounds.
result Deviation from mean scales as k / n \sqrt{k}/n k / n for n ≥ k n \ge k n ≥ k . Paper analyzes sample complexity of offline MABs with KL regularization.
problem Optimizing sample complexity for offline decision-making with KL-regularized metrics.
method Sharp analysis of KL-PCB, providing upper and lower bounds.
result Characterizes sample complexity for offline MABs with KL regularization.
A new framework predicts hidden Markov model regimes online.
problem Efficiently identify hidden Markov model regimes in streaming data.
method Develops a predictive-first optimisation framework for streaming HMMs, approximating the full posterior predictive distribution.
result The method provides competitive prequential performance compared to Online EM and Sequential Monte Carlo.
Paper proposes a method to stabilize estimation of KL divergence using a discriminator in RKHS.
problem High variance and instability in estimating KL divergence using neural network discriminators.
method Developed a novel construction of the discriminator in RKHS, controlled its complexity, and proved the consistency of the estimator.
result Reduced variance and stabilized training of KL divergence estimates.
Local mass perspective on Bayesian inference
problem Measuring distributional discrepancy in Bayesian inference
method Introducing Mass Index and Regularised Extended KL
result Proving inequalities for comparing local small-ball masses
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.
New method trains neural samplers to sample from multi-modal distributions efficiently.
problem Mode-seeking behavior of reverse KL divergence hinders effective sampling from multi-modal target distributions.
method Minimizing reverse diffusive KL divergence along diffusion trajectories of model and target densities.
result Demonstrated enhanced sampling performance across various multi-modal distributions.
KL-regularized RL from expert demos can lead to slow, unstable learning.
problem Pathological training dynamics in KL-regularized RL from expert demonstrations.
method Empirical analysis and non-parametric behavioral reference policies.
result KL-regularized RL can be significantly improved by using non-parametric behavioral policies.
New KL-divergence for Gaussian distributions based on Wasserstein geometry.
problem Computing KL-divergence for Gaussian distributions efficiently.
method Introducing WKL-divergence based on Wasserstein geometry.
result WKL-divergence evaluates to squared distance between points for Dirac measures.
KL regularization helps RL algorithms by implicitly averaging q-values.
problem Understanding why KL regularization improves RL performance.
method An approximate value iteration scheme, studying KL and entropy regularization.
result Strong performance bound combining linear horizon dependency and averaging effect of estimation errors.
New algorithms achieve logarithmic regret in KL-regularized Markov games.
problem Improving sample efficiency in game-theoretic settings with KL regularization.
method Developed OMG and SOMG algorithms for matrix and Markov games, using best response sampling and superoptimistic bonuses.
result Logarithmic regret in T T T that scales inversely with KL regularization strength β β β . SRFE clarifies KL divergences without unifying learning frameworks.
problem Inductive biases of KL divergences and their limitations.
method Introducing SRFE, a log-moment-based functional of the likelihood ratio.
result SRFE recovers KL divergences as limits and reveals a mean-variance tradeoff.
Unified view of KL-divergence and IPMs via DRE, with new DRM metrics.
problem Unified understanding of KL-divergence and IPMs.
method Unified representation via maximum likelihood density-ratio estimation (DRE).
result Unified form of IPMs and novel DRM metrics.
Entropy regularization improves policy optimization in reinforcement learning.
problem Improving policy optimization in reinforcement learning.
method Entropy regularization is introduced to soften the greedy policy towards a more diverse softmax policy, leading to a continuously parameterized algorithm that interpolates between policy gradient and Q-learning.
result An intermediate algorithm can improve performance in reinforcement learning.
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.